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Calculus 1 / AB Q&A Archive of June 9, 2025

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June 9 of 2025

(13) $ \int_{0}^{4} \int_{\sqrt{x}}^{2} \sin y^{3} d y d x $

f(x) =sqrtx find a number delta such that if lx-9l<delta, then lsqrtx - 3l<0.1

8 8 3 Düzen Resim Görüntū Pencere Yardim 9 Haz Pzt 21:35 raflar Anorganik 2.pdf Arşiv Favoriler Harita Son Kaydedilenler Son Silinenler Günler Kigiler Anilar Geziler Öne Çikan Fotoğraflar Diger Ortam Turleri Albümler Kibns Foto…

28. Evaluate $ \int x^{x}(\ln x+1) d x $, where $ x>0 $, by making use of the substitution $ u=x^{x} $. (A) $ \frac{1}{2} x^{2}+C $ (B) $ x \ln x+x+C $ (C) $ x \ln x+C $ (D) $ x^{x-1}+C $ (E) $ x^{x}+C $

\[ 2 x=5 \] 16. If $ x^{2}+y^{2}+z^{2}=14 $, find $ \frac{d z}{d t} $, given that $ \frac{d x}{d t}=5, \frac{2 y}{d t}=4 $ when $ (x, y, z)=(2,3,1) $. (A) 18 (B) 8 (C) -2 (D) -12

20. Determine the interval(s) on which the graph of $ g(x)=x^{4}-4 x^{3} $ is concave downwardo (A) $ (-\infty, 0) \cup(2, \infty) $ (B) $ (0,2) $ (C) $ (2, \infty) $ (D) $ (-\infty, 0) $ (E) $ (-2,0) $ 21. The graph of the derivative $ f^{\prime}(x) $ of a function $ y=f(x) $…

1 A student holds a turning fork oscillating at 256 Hz . He walks towards a wall at a constant speed of $ 1.33 \mathrm{~m} / \mathrm{s} $. A. What beat frequency does he observed between the turning fork and it's echo? B. How fast must he walk away from the wall to observe a beat frequency of…

The pressure $ P $ (in kilopascal), volume $ V $ (in litres), and temperature T (in Relvin) of a mole of an ideal gas related by the equation $ P V=8.31 \mathrm{~T} $. Find the rate at which the pressure is changing when the temperature is 300 K and increasing at a rate of \( 0.1…

An automobile having a mass of 1000 kg is driven into a brick wall in a safety test. The bumper behaves like a spring of force constant $ 5.00 \times 10^{6} \mathrm{~N} / \mathrm{m} $ and compresses 3.16 cm as the car is brought to rest. What was the speed of the car before impact, assuming…

4) $ u \times(v \times w)=(u \cdot w) v-(u \cdot v) w $

the parabola $ y=4 x^{2} $. 19. Find the volume of the solid generated by revolving about the $ x $-axis the region bounded by the line $ x-2 y=0 $ and the parabola $ y^{2}-2 x=0 $.

ex: $ L_{p}+B=\{(x, y): 0 \leq x \leq 1,0 \leq y \leq x\} $ Calculate

Differentiate the function $ \mathrm{f}(x)=\frac{2 x^{3}+x^{2}}{x} $ with respect to $ x $.

actice E x $ \infty $ Exam 2 Review- Practice E Desmos | Scientific Calcula Desmos | Graphing Calcula n/assessment_sessions/684713b17713d78834af0266?assessment_item_id=684713b17713d78834af0269 StudyBuddy Help Center Search es - Due Jun 09, 2025 11:59 PM. - The best score out of 5 submissions…

20. Let $ v, v $, and $ w $ be vectors in $ R^{3} $ and $ \theta $ be the angle between $ v $ and $ v, w $. Proof: Definition of crass product For veaters $ v $ and $ w $, the crass product $ v \times w $ is a vect that is perpendlever to both $ v $ and $ w $ with…

01：16 6月9日周一 $ 23 \% $ Rajah 6 menunjukkan sebuah pepejal gabungan yang terdiri daripada sebuan prisma tegak dan sebuah kuboid masing－masing dengan tapak segi empat tepat $ A B C E $ dan tapak segi empat sama EDRQ yang terletak pada satah mengufuk．Segi empat GHLF ialah satah mengufuk dan…

(b) $ \left(125 y^{75}\right)^{\frac{2}{3}} $

10. What is equal to the Young modulus of a material that is extended elastically within the limit of proportionality? A. area under the force-extension graph B. area under the stress-strain graph C. gradient of the force-extension graph D. gradient of the stress-strain graph

25. $ \frac{9 x^{2}-9 x+6}{2 x^{3}-x^{2}-8 x+4} $

EXAMPLE Calculate $ L(x, y) $ and $ Q(x, y) $ for $ f(x, y)=e^{-x^{2}-y^{2}} $ at $ (0,0) $.

Explain each of the solutions in detail.

$ \frac{9 x^{2}-9 x+6}{2 x^{3}-x^{2}-8 x+4} $

B. $ \lim _{x \rightarrow 0} \frac{\frac{1}{(a+x)^{3}}-\frac{1}{a^{3}}}{x} $

The aircraft $ A B $ and $ C $ left an air port $ Q $ af 920 pm A left in the direction of $ 060^{\circ} $ at an avarage speed or 60 km . $ B $ lest in the direction of $ S 40^{\circ} \mathrm{W} $ at an avarage speed of 750 km Cleft directly cuest of $ Q $ at avarage speed of \(…

of equations below. Write your answer(s) as coordinate poi \[ \begin{array}{r} \left\{\frac{5}{6} x=\frac{3}{1}-\frac{3}{4} y\right. \\ \frac{9}{2}=\frac{7}{2} x-9 y \end{array} \]

$ \lim _{x \rightarrow \frac{\pi}{3}}\left(\frac{\sqrt{2 \cos (x)}-1}{2 \cos (2 x)+1}\right) $

Error your answer in the bod before $ \rightarrow \infty \rightarrow \infty $ \begin{tabular}{|l|l|} \hline & \\ \hline \end{tabular}

Evaluate \[ \iint_{S} \mathbf{F} \cdot d \mathbf{S} \] where $ \mathbf{F}=z \mathbf{i}+x \mathbf{j}+y \mathbf{k} $, and $ S $ is the part of the plane $ x+y+z=1 $ in the first octant. \[ 2=1-x-y \]

3. Solve the following systems. (a) $ \left\{\begin{array}{l}x^{\prime}=-x+y+e^{4 t} \sin t \\ y^{\prime}=5 x+3 y+e^{t}\end{array}\right. $.

JUNE 2018 QUESTION 4 a) Determine the specific energy of the flow in a rectangular channel with a width of 7.0 m . The channel conveys water at a rate of $ 15 \mathrm{~m}^{3} / \mathrm{s} $ and a mean velocity of $ 2 \mathrm{~m} / \mathrm{s} $. (CO1-PO1) (C2) Determine; a) $ E $ b) \(…

(a) $ \mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}=\stackrel{\mathrm{CH}_{3}}{\mathrm{CCCH}_{2} \mathrm{CH}_{3}} \xrightarrow[\mathrm{H}_{2} \mathrm{SO}_{4}]{\mathrm{H}_{2} \mathrm{O}} $ ?

(a) Find $ g^{\prime}\left(\frac{\pi}{3}\right) $ if $ g(x)=f(\sec x) $.

QUESTION 2 Solve the following without using a calculator. Show all working out. 2.1 $ 3794 \div 7 $ (Use the long division method) $ 2.2 \sqrt{0,36} $ (Leave you answer as a fractions) $ 2.3\left(1+\frac{1}{5}\right) \times \frac{5}{3} $ \( 2.4 \sqrt{25}-\sqrt[3]{-125}+(-3)^{2}…

3.2. The following data were obtained when a cold-worked metallic material was annealed: (a) Estimate the recovery, recrystallization, and grain growth temperatures; (2) (b) recommend a suitable temperature for obtaining a high-strength, high-electrical conductivity wire; (2) (c) recommend a…

2. Create a set of 3 planes whose intersection would... a. be a plane b. not inters \[ \begin{array}{l} \pi_{1}=3 x+y \\ \pi_{2}=x-5 \end{array} \] [2]

Problem 2.8 Determine the shear and bending rigidity distributions (Fig. P2.8a). Take \[ \begin{aligned} \gamma^{*} & =\frac{1}{400} \\ \chi^{*} & =\frac{1}{20,000} \end{aligned} \] Note: These values correspond to $ s=0.1 $ (see Eq. (2.10)). Figure P2.8a

Linear Eqi incars and $ \pi_{2}: 5 x+y-z-11=0 $. ding 5. Determine the equation for the line of intersection between the planes $ \pi_{1}:-6 x-y-z+20=0 $ \[ y-11 z=-34 \] \[ x=a-2 p \] \( =\left[\begin{array}{ccc|c}-6 & -1 & -1 & -20 \\ 5 & 1 & -1 & 11\end{array}\right] \quad…

9. $ 19 \frac{1}{2}-13 \frac{7}{10}= $ $ 36 \frac{4}{9}-4 \frac{3}{5}= $ $ 17 \frac{2}{7}-8 \frac{5}{6}= $

Problem 2.7 Determine the expressions for the distribution of shear and bending rigidities corresponding to constant deformations $ \gamma^{*} $ and $ \chi^{*} $ (Fig. P2.7a). Figure P2.7a

20. If $ M \triangleleft G, N \triangleleft G $, and $ M \cap N=(e) $, show that for $ m \in M, n \in N, m n=n m $.

Diagonal bracing is added to a rigid frame as indicated in Fig. P2.6a. Figure P2.6a 1. Establish an approximate expression for the equivalent shear beam stiffness for a typical story. Assume the column properties are constant in a story, but vary from story to story. 2. Suppose the diagonal…

3.2. The following data were obtained when a cold-worked metallic material was annealed: (a) Estimate the recovery, recrystallization, and grain growth temperatures; (2) (b) recommend a suitable temperature for obtaining a high-strength, high-electrical conductivity wire; (2) (c) recommend a…

$ \int \frac{d x}{\sqrt{3 x}+1} $

Consider a five-story, five-bay rigid frame modeled as a shear beam (Fig. P2.5a). Assume that all the columns in a story have the same properties, but allow for variation in column size over the stories. Establish an approximate expression for the equivalent shear beam stiffness for a typical…

3.2. The following data were obtained when a cold-worked metallic material was annealed: (a) Estimate the recovery, recrystallization, and grain growth temperatures; (2) (b) recommend a suitable temperature for obtaining a high-strength, high- (2) (c) recommend a such of the alloy. (2) (d)…

csommens

21. $ \sqrt{1+\sqrt{1+\sqrt{1+\ldots \ldots}}} $ (1) equals 1 (2) lies between 0 and 1 (3) lies between 1 and 2 (4) is greater than 2 22. $ \sqrt{2+\sqrt{2+\sqrt{2+\ldots \ldots}}} $ is equal to (1) $ \sqrt{2} $ (2) $ 2 \sqrt{2} $ (3) 2 (4) 3 23. \( \sqrt{12+\sqrt{12+\sqrt{12+\ldots}}}…

$ 3 a^{2} \times\left(2 a^{-1}\right)^{3} $

13.20 The system shown is at rest when a constant $ 30-\mathrm{lb} $ force is applied to collar $ B $. (a) If the force acts through the entire motion, determine the speed of collar $ B $ as it strikes the support at $ C $. (b) After what distance $ d $ should the 30-1b force be…

12. $ \int_{0}^{1} \int_{0}^{1} x y \sqrt{x^{2}+y^{2}} d y d x $

The force-displacement relationship for the structures shown in Fig. 2.4(a), (b), and (c) is written as $ P=k u $. (a) (b) (c) Figure P2.4a Establish the expression for $ k $ for each structure. Comment on the relative efficiency of the structures for resisting lateral loading.

[1-a]Let $ \hat{\mathscr{T}}\left(\Delta x^{\prime}\right)=1-\frac{i}{\hbar} \hat{p} \Delta x^{\prime} $ be the translational operator in one-dimension. Use this operator to show that, for an arbitrary ket vector \( |\alpha\rangle:\left\langle x^{\prime}\right| \hat{p}|\alpha\rangle=-i \hbar…

The force-displacement relationship for the structures shown in Fig. 2.4(a), (b), and (c) is written as $ P=k u $. (a) Establish the expression for $ k $ for each structure. Comment on the relative efficiency of the structures for resisting lateral loading.

3. Solve the following systems. (a) $ \left\{\begin{array}{l}x^{\prime}=-x+y+e^{4 t} \sin t \\ y^{\prime}=5 x+3 y+e^{t}\end{array}\right. $.

The force-displacement relationship for the structures shown in Fig. 2.4(a), (b), and (c) is written as $ P=k u $. (a) (b) (c) Figure P2.4a Establish the expression for $ k $ for each structure. Comment on the relative efficiency of the structures for resisting lateral loading.

39- What are the types of immune cells that secrete interleukins and lymphokines, respectively? $ A-B $ and $ T_{H} $ $ B-T_{H} $ and $ T_{C} $ $ \mathrm{C}-\mathrm{T}_{\mathrm{H}} $ and $ \mathrm{T}_{\mathrm{S}} $ $ D-T_{s} $ and $ T_{H} $

5. $ \sqrt{(5+1)^{2}} $ 6. $ \sqrt{25+144} $ 7. $ \sqrt{25 \times 144} $ e $ \sqrt{10^{2}-4^{2} \times 4} $

Copilot 3 of 7 stion 6 The following function has a single maximum. Evaluate the $ x $ value of the maximum: \[ f(x)=-2 x^{2}+4 x \] (5 marks) estion 7 Given that $ z=-3+4 i $, find the modulus and argument of $ z $ and thus express $ z $ in exponential form (give the argument to two…

maximum: \[ f(x)=-2 x^{2}+4 x \] (5 marks) Question 7 Given that $ z=-3+4 i $, find the modulus and argument of $ z $ and thus express $ z $ in exponential form (give the argument to two decimal places). (5 marks) Question 8 Find the determinant and inverse of the following \( 2 \times…

$ 12 $

12. $ \int_{0}^{1} \int_{0}^{1} x y \sqrt{x^{2}+y^{2}} d y d x $

(b) $ 2 \log _{25} 2 x=\log _{5}(1-x) $ ? (d) $ \log _{x}\left(\frac{2}{3}\right)=-\frac{1}{3} x^{-\frac{1}{3}}=\frac{2}{3} $

der of calculations \begin{tabular}{|l|l|} \hline \multicolumn{2}{|c|}{Examples} \\ \hline $ 2 \sqrt{16} $ & $ \left((10-7)^{2}\right)^{2} $ \\ \hline $ \sqrt{16+9} $ & $ \sqrt{144 \times 16} $ \\ \hline $ 3^{3}-(5-2)^{2} \times 3^{2}+3 $ & $ 3 \sqrt{25}+\sqrt{10^{2}-2^{3} \times} $…

$ 2.4 \sqrt{25}-\sqrt{ }-125+(-3)^{2} $ (4) [12] QUESTION 3 Nali buys furniture worth R18 000 on hire purchase, She pays a R5000 and repays the outstanding amount monthly for the next 3 years. The interest on the outstanding amount is $ 7,5 \% $ per annum. 3.1 Determine the outstanding…

1.8 Determine the rational numbers $ a $ and $ b $ such that: (a) $ \sqrt{7+2 \sqrt{10}}=\sqrt{a}+\sqrt{b} $ (b) $ \sqrt{3+2 \sqrt{2}}=\sqrt{a}+\sqrt{b} $ 1.9 If $ m=\frac{\sqrt{x}+\sqrt{y}}{\sqrt{x}-\sqrt{y}} $, show that $ m=\frac{x+y+\ell}{x-y} $ and find $ \ell $. 1.10 Express…

integrate use improper \[ \int_{t}^{4} \frac{1}{\sqrt{4-x}} d x \]

Q $ \frac{2\left(\cos ^{2} 4 j^{\circ}+\tan ^{2} 60^{\circ}\right)-6\left[\operatorname{sen}^{2} 4 j^{\circ}-\tan ^{2} 60\right]}{\tan ^{2} 30^{\circ}+\cot 60^{\circ}} $

Simplify the following: \[ x=\frac{3180}{990} \] (d) 0.100 \[ \begin{aligned} 1000 x & =168.68 \\ 990 x & =167 \\ x & =\frac{167}{990} \end{aligned} \] (a) $ \left(\frac{3 x^{3}}{y^{2}}\right)^{3} \div\left(\frac{x^{2} y^{-} 3}{4}\right)^{2} \mathbf{4 3 2} \boldsymbol{x}^{\mathbf{5}} $ (b) \(…

7. Simplify the expression below and identify excluded values. \[ \frac{4 a^{2}-36}{24-8 a} \]

11. Solve the equation below. Check for excluded values. \[ \frac{a-8}{a}=\frac{3}{a+5} \]

\[ \frac{\frac{m+14 m+40}{3 m^{3}-6 m^{2}}}{m^{2}+7 m-18} \] 11. Solve the equation below. Check for excluded values. \[ \frac{a-8}{a}=\frac{3}{a+5} \] 13. Given the function $ g(x)=\frac{1}{x-1}+2 $, list the equations for th domain and range, end behavior, and transformations of th

5- Rationalize the denominator of the following: (a) $ \frac{4 \sqrt{3}+5 \sqrt{2}}{\sqrt{48}+\sqrt{18}} $ (b) $ \frac{2}{\sqrt{5}+\sqrt{3}+2} $ 9-2

8. Evaluate $ \int x e^{-2 x} d x $ Solution: Solve inside the box. Hint: Use integration by part

3.3. Assuming Raoult's law to apply to the system $ n $-pentane(1)/n-heptane(2), (a) What are the values of $ x_{1} $ and $ y_{1} $ at $ t=55^{\circ} \mathrm{C} $ and $ P=\frac{1}{2}\left(P_{1}^{\text {sat }}+P_{2}^{\text {sat }}\right) $ ? For these conditions plot the fraction of…

linear or non linear \[ \frac{d^{2} R}{d t^{2}}=\frac{K}{R^{2}} \]

Vb 1) $ \frac{x}{3}-\frac{x}{5}=2 $ Vb 2) $ \frac{x}{6}+1=\frac{2 x}{3} $

7. Evaluate $ \int \frac{2}{x^{2}+3 x+2} d x $

35. Find the power series for $ \sin \left(\frac{\pi}{2}+x\right) $ Solution: Solve inside the box.

* $ 50 \% $ of 195.5

integrate use improper \[ \int_{2}^{5} \frac{1}{x^{5}} d x \]

\begin{tabular}{|l|l|} \hline & $ =-14 x^{2} y^{2} $ \\ \hline i & \\ \hline Vb 3 & $ \left(-x^{2} y\right)\left(-x^{3} y\right)-(x)\left(x^{4}\right)\left(y^{2}\right) $ \\ \hline & $ x^{5} y^{2}= $ \\ \hline & \\ \hline Vb 4 & \( \left(-3 x^{3}\right)\left(2 x^{4}\right)+\left(-2…

3. Find the equation of the line that is tangent to the circle $ x^{2}+y^{2}-2 x+3 y-12=0 $ at the point $ (4,1) $

2. Assume that the export price of a Toyota Corolla from Osaka, Japan is $ ¥ 2,150,000 $. The exchange rate is $ ¥ 87.60 / \$ $. The forecast rate of inflation in the United States is $ 2.2 \% $ per year and is $ 0.0 \% $ per year in Japan. Use this data to answer the following…

2. How much pressure is needed to compress the volume of an iron block by $ 0.10 \% $ ? (Express your answer in $ \mathrm{N} . \mathrm{m}^{-2} $ and compare it to atmospheric pressure.) 3. A cube, edge-length $ =4.5 \mathrm{~cm} $, has a force of 110 N applied parallel, in opposite…

\[ \begin{array}{l} \sqrt{x^{2}+1} d x \\ \text { 1et } x=\tan \theta \\ \frac{d e}{d}=\sec ^{2} b \\ \int_{0}^{\frac{\pi}{4}} \sec \theta \cdot \sec ^{2} \theta \\ \text { when. } 1=1 \\ \operatorname{san} \theta=\frac{\pi}{4} \\ \int_{0}^{\frac{\pi}{4}}+c^{\frac{3}{2}} \\ -\frac{\sec c^{n-1}…

8. What is represented by the gradient of a graph of force (vertical axis) against extension (horizontal axis)? A. Elastic limit C. Stress B. Spring constant D. Young modulus

28. The distance between the points $ (1,2) $ and $ (16, p) $ is 17 . Find the value of $ p $ Solution: Solve inside the box.

In Problems 8.1 through 8.4 , use $ \gamma_{\text {concrete }}=23.58 \mathrm{kN} / \mathrm{m}^{3} $. Also, in Eq. (8.11), use $ k_{1}=k_{2}= $ $ 2 / 3 $ and $ P_{p}=0 $. 8.1 For the cantilever retaining wall shown in Figure P8.1, let the following data be given: Wall dimensions: \(…

In Problems 8.1 through 8.4, use $ \gamma_{\text {concrete }}=23.58 \mathrm{kN} / \mathrm{m}^{3} $. Also, in Eq. (8.11), use $ k_{1}=k_{2}= $ $ 2 / 3 $ and $ P_{p}=0 $. 8.1 For the cantilever retaining wall shown in Figure P8.1, let the following data be given: Wall dimensions: \(…

(c) If one ignores the oscillatory term in the solution to (b)-on the grounds that it averages to zero (see discussion in Example 4.4)-one obtains uncoupled equations of the form \[ -\frac{\hbar^{2}}{2 m} \nabla^{2} \tilde{\Psi}_{ \pm}+V_{ \pm} \tilde{\Psi}_{ \pm}=i \hbar…

\[ N(t)=\frac{40 t-80}{t} \quad t \geqslant 2 . \] calculate the Average velocity of this Function over periods 2 to 5

Find the slope of the normal line to the curve $ y=2 x^{3}-5 x+1 $ at the point where $ x $-coordinate is 1 .

22. If $ y=\cos (3 x-7) $, then nd $ \frac{d^{2} y}{d x^{2}} $

BÀI 4.5 Trong nền kinh tế mở: (ĐVT: tỷ đồng) \[ \begin{array}{llll} \mathrm{C}=60+0.75 \mathrm{Yd} & \mathrm{I}=600 & \mathrm{G}=3,260 & \mathrm{~T}=0.4 \mathrm{Y} \\ \mathrm{X}=2,000 & \mathrm{M}=0.25 \mathrm{Y} & \mathrm{Yp}=7,600 & \mathrm{Un}=5 \% \end{array} \] a. Xác định mức sản lượng…

myFHinfo - Sessio Pulse MySchedule Employee Portal Myschedule Login to Learning Chapter-14-Binor My Course - Intror Untitled 10…

\begin{tabular}{|l|l|l|l|l|l|l|} \hline \multirow[t]{7}{*}{3.} & \multicolumn{6}{|c|}{Find the Optimal Solution of the following transportation problem.} \\ \hline & \multirow{2}{*}{ORIGIN} & \multicolumn{4}{|c|}{DESTINATION} & \\ \hline & & D1 & D2 & D3 & D4 & CAPACI TY \\ \hline & O1 & 1 & 2…

7) A curve has equation $ y=x^{2}-x y $ and passes through re port $ P\left(1 ; \frac{1}{2}\right) $ w Find the equation of the tangent to the wre at $ P $

$ =2 \frac{1}{5} $ c) $ \frac{24}{11}=2 \frac{2}{11} $ c) $ \frac{11}{6}=1 \frac{5}{6} $ \[ \frac{9}{5} \quad \text { f) } \frac{65}{6}=\frac{1}{6} \]

10. (10.0score) The area enclosed by $ y=x $ and $ y=x^{2} $ is A $ 1 / 2 $ B 1 C $ 1 / 6 $ D $ 1 / 3 $ Last question

7. (10.0score) The average value of $ f(x)=\sin x $ on $ [0, \pi] $ is A $ 1 / \pi $ B 0 C $ 2 / \pi $ D 0.5

3:10 .II 5G MEENU MELEPURAKKAL RAJESH (3245203013) $ 11^{\prime} 37^{\prime \prime} $ 9/10 Answer Card Single Choice ( total10question , 100.0score) 9. (10.0score) Compute $ \int e^{2 x} \sin \left(e^{2 x}\right) d x $ A $ 2 \sin \left(e^{2 x}\right)+\mathrm{C} $ B \( \frac{1}{2} \cos…

3:10 .II 5G MEENU MELEPURAKKAL RAJESH (3245203013) 12' 09" 8/10 Answer Card Single Choice ( total10question , 100.0score) 8. (10.0score) Compute $ \int x^{2} \cos x d x $ A $ x^{2} \sin \mathrm{x}+2 \mathrm{x} \cos \mathrm{x}-2 \sin \mathrm{x}+\mathrm{C} $ B \( x^{2} \sin \mathrm{x}+2…

3:08 .II 5G MEENU MELEPURAKKAL RAJESH (3245203013) $ 14^{\prime} 26^{\prime \prime} $ 7/10 Answer Card Single Choice ( total10question , 100.0score) 7. (10.0score) The average value of $ f(x)=\sin x $ on $ [0, \pi] $ is A $ 2 / \pi $ B $ 1 / \pi $ C 0 D 0.5 revious question Next…

$ f(x)=\left\{\begin{aligned} x^{2}, & 0 \leq x \leq 1 \\ 2 x, & 1 \leq x \leq 2\end{aligned}\right. $, find $ \int_{0}^{2} f(x) d x $ A $ \int_{0}^{1} x^{2} d x+\int_{1}^{2} 2 x d x $ B $ \int_{0}^{1} x^{2} d x+\int_{1}^{2} x^{2} d x $ C \( \int_{0}^{1} 2 x d x+\int_{1}^{2} x^{2} d…

3. (10.0score) Compute $ \int x e^{x} d x $ A $ \mathrm{xe}^{\mathrm{x}}+\mathrm{C} $ B $ x e^{x}+x+C $ C $ x e^{x}-e^{x}+C $ D $ x e^{x}+e^{x}+C $

Evaluate, $ 3 \frac{3}{4}+4 \frac{4}{5}+2 \frac{1}{2} $

Use the information below to answer the questions that follow. A linear function passes through the following points: $ A\left(\frac{1}{3},-2\right) $ and $ B\left(1,-\frac{1}{5}\right) $ 13 Fill in the Blank 1 point Write the slope-intercept form of the function. Do not input spaces with…

Use the information below to answer the questions that follow. A linear function has the following characteristics: 8 Fill in the Blank 1 point \[ \begin{array}{l} m=-2 \\ b=8 \end{array} \] Write the function standard form. Do not input spaces with your answer. Use all lower-case…

You have unlimited attempts for this practice. Only the highest score will be kept. Use the information below to answer the questions that follow. A linear function has the following characteristics: 7 Fill in the Blank 1 point \[ \begin{array}{l} m=-2 \\ b=8 \end{array} \] Using only the…

Use the information below to answer the questions that follow. A linear function passes through the following points: $ A\left(\frac{1}{3},-2\right) $ and $ B\left(1,-\frac{1}{5}\right) $ 14 Fill in the Blank 1 point Write the standard form of the linear function. Do not input spaces with…

For each of the following vector laentites, explain true. *Note: there are two main ways that you can go about, showing that the left and the right hand sides are the sa why the two sides are the same. I would suggest trying $ t $ (though longer) to work out. 1) $ u+v=v+u $ 2) \( |u \times…

Use the information below to answer the questions that follow. A linear function passes through the following points: 12 Fill in the Blank 1 point $ A\left(\frac{1}{3},-2\right) $ and $ B\left(1,-\frac{1}{5}\right) $ Using the slope and point A, write the point-slope form of the function.…

3. A cylindrical specimen of stainless steel hav- ing a diameter of $ 12.8 \mathrm{~mm}(0.505 \mathrm{in} $.$ ) and a gauge length of $ $ 50.800 \mathrm{~mm}(2.000 \mathrm{in} $.$ ) is pulled in tension. Use the load-clongation charac- teristics tabulated below to $ complete parts (a)…

2. From experimental observation it is known that, up to a "satisfactory" approximation, that the surface temperature of an object changes at a rate proportional to its relative temperature. That is, the difference between its temperature and the temperature of the surrounding environment. This…

validity. Find the constant term in the expansion of $ \sqrt{x^{2}+32 x+16} $

1. Why are line-voltage thermostats used to control domestic refrigerators? Line-voltage thermostats are used in domestic refrigerators because they can directly switch the compressor or fan motor on and off by handling the full line voltage and current. This eliminates the need for additional…

2. From experimental observation it is known that, up to a "satisfactory" approximation, that the surface temperature of an object changes at a rate proportional to its relative temperature. That is, the difference between its temperature and the temperature of the surrounding environment. This…

Evaluate \[ 1 \frac{7}{8}+2 \frac{5}{6}+3 \cdot \frac{3}{4} \]

2. From experimental observation it is known that, up to a "satisfactory" approximation, that the surface temperature of an object changes at a rate proportional to its relative temperature. That is, the difference between its temperature and the temperature of the surrounding environment. This…

Question 4 A tuning fork vibrating at 512 Hz falls from rest and accelerates at $ 9.80 \mathrm{~m} / \mathrm{s}^{2} $. How far below the point of release is the tuning fork when waves of frequency 485 Hz reach the release point?

8. The distance between the points $ (1,2) $ and $ (16, p) $ is 17 . Find the value of $ p $ Solution: Solve inside the box.

27. Solve the following inequalities $ |3 x-4|<8 $ Solution. Soive ins. de the jox.

dit View History Bookmarks Profiles Tab Window Help ｜Graphing Calculato SLO 3 Written Quiz Homework 3．2 The Derivativ xassouthmostcollege．instructure．com／courses／29892／assignments／1138309？module＿item＿id＝2820830 uiz Student．pdf page 2 All work must be shown to receive credit．（10 points…

35. Verify the identity: $ \cos \left(\frac{3 \pi}{2}+\theta\right)=\sin \theta $.

aluate each integral a. $ \int \frac{x^{2} \mathrm{~d} x}{\sqrt{4-x^{2}}} $ b. $ \int \frac{(x-2) d x}{x^{2}+2 x^{2}} $

Bology Honors B- Imagine Eds onuity.com/player/ St. Mail - Perez, ris-Ou. Gmail Classes Clever I Log in Raz-Kids goguardian MT Bank-mortage Mindful Schools Onl. Population Growth Quiz Active 1 2 3 4 5 6 7 TIME REMAIVING 55:59 The maximum number of wolves that can survive in a particular…

dit View History Bookmarks Profiles Tab Window Help ｜Graphing Calculato SLO 3 Written Quiz Homework 3．2 The Derivativ xassouthmostcollege．instructure．com／courses／29892／assignments／1138309？module＿item＿id＝2820830 uiz Student．pdf page 2 All work must be shown to receive credit．（10 points…

OSNA-Teanis Cerge For Unvernil Homepage Calculus II All Bookmaris Details For this project, type up a report doing the following, to be shared with me over Zoom (as a practice for future recorded presentations). You should include pictures of your work on whiteboard, paper, or drawing app.…

35. Find the slope of the normal line to the curve $ y=2 x^{3}-5 x+1 $ at the point where $ x $-coordinate is 1 . Solution: Solve inside the box.

22. If $ y=\cos (3 x-7) $, then nd $ \frac{d^{2} y}{d x^{2}} $ Soding: Solve inside the box.

20. Using 18 and 19 above $ \int\left(\frac{5}{x^{2}}+6 x\right) d x= $ $ \qquad $ $ +\ldots $ $ \qquad $

APO Quiz: AP Pl Arth Phys Dynn Appli Appl: Newt Newt ssroom.ucscout.org courses/26054/quizes/3014/2/10ke FUT Web App - EA... uc scout phsyics Learn Git DeepSeek Question 4 1 pts A bomber flying at a constant velocity in level flight releases its bomb and hits a target on the ground.…

of difference is 19. What is the RHS of the equation $ \int k f(x) d x= $ $ \square $

18. Complete the following statement. Integral of sum is $ \qquad $ of integral and integral of difference is $ \qquad $ of integral.

$ \begin{array}{l}\sec =1 / \cos \\ y=2 \sin x-4 x^{3}+\tan 3 x \\ y_{y}=2 \cos x-12 x^{2}+3\end{array} $

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Calcular $ P=\int_{-\frac{\pi}{4}}^{\frac{\pi}{4}} \ldots \int_{0}^{2} \ldots e^{-r^{2}} r d r d \theta $ (A) $ \frac{\pi}{2} $ (B) $ \frac{\pi}{4} $ (C) $ \frac{\pi}{3}\left(1-e^{4}\right) $ (D) $ \frac{\pi}{4}\left(1-e^{-4}\right) $

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Home Page - Canyons M Practice Assignment 9.3 Geo coc.instructure.com/courses/58568/assignments/1676027?module_item_id=4299061 MATH-103-... > Assignments > Practice Assignment 9.3 Geometric Sequences 2025SP Home Practice Assignment 9.3 Geometric Sequences Modules Practice Assignment 9.3…

\[ x=3-t, g=6 t, z=7 t+2 \] find the equation for the line of the plane $ 5 x+y+z=4 $ and $ 10 x+y-z=6 $

Home Page - Canyons M Practice Assignment 9.3 Geo: coc.instructure.com/courses/58568/assignments/1676027?module_item_id=4299061 MATH-103-... > Assignments > Practice Assignment 9.3 Geometric Sequences 2025SP Home Practice Assignment 9.3 Geometric Sequences Modules Announcements Grades The…

2. find the equation for the line that is parallel to the line $ x=3-t, g=6 t, z=7 t+2 $

Home Page - Canyons M Practice Assignment 9.3 Geo: coc.instructure.com/courses/58568/assignments/1676027?module_item_id=4299061 MATH-103-... > Assignments > Practice Assignment 9.3 Geometric Sequences 2025SP Home Practice Assignment 9.3 Geometric Sequences Modules Announcements Practice…

Câu 4 Hàm số $ \mathcal{L}\left(t^{2} \cos t\right)(s) $ bằng The function $ \mathcal{L}\left(t^{2} \cos t\right)(s) $ is $ \frac{d}{d s}\left(\frac{1-s^{2}}{\left(s^{2}+1\right)^{2}}\right) $. $ \frac{d}{d s}\left(\frac{s^{2}-1}{\left(s^{2}+1\right)^{2}}\right) $ \( \frac{d^{2}}{d…

Câu 4 Hàm số $ \mathcal{L}\left(t^{2} \cos t\right)(s) $ bằng The function $ \mathcal{L}\left(t^{2} \cos t\right)(s) $ is $ \frac{d}{d s}\left(\frac{1-s^{2}}{\left(s^{2}+1\right)^{2}}\right) $ $ \frac{d}{d s}\left(\frac{s^{2}-1}{\left(s^{2}+1\right)^{2}}\right) $ \( \frac{d^{2}}{d…

Find the degree 3 Taylor polynomial $ T_{3}(x) $ of function \[ \begin{array}{l} f(x)=(3 x+63)^{\frac{5}{4}} \\ \text { at } a=6 . \\ T_{3}(x)= \end{array} \]

16 Mark for Review - Total Security - Dashboard My Assigned Assignme Sign Up - Create a Free Acco Total Adblock x room.collegeboard.org/25/assessments/assignments/68962485 〈AM What is the area of the region between the graphs of $ y=x^{2} $ and $ y=-x $ from $ x=0 $ to $ x=2 $ ? (A) \(…

Find the degree 3 Taylor polynomial $ T_{3}(x) $ of function \[ \begin{array}{l} f(x)=(3 x+63)^{\frac{5}{4}} \\ \text { at } a=6 . \\ T_{3}(x)= \end{array} \]

The factored form of $ 5 x^{2}-18 x-8 $ is $ \qquad $ a.) $ (5 x-4)(x+2) $ b.) $ (5 x+4)(x-2) $ c.) $ (5 x+2)(x-4) $ d.) $ (5 x-2)(x+4) $ SUBMIT MY ANSWER Report an issue with this question

Which of the following graphs shows a parabola with a vertex of $ (-4,4) $ and solutions of $ (-6,0) $ and $ (-2,0) $ ? a.) \begin{tabular}{|l|l|l|l|l|l|l|l|l|l|l|l|l|l|} \hline & & & & & 8 & & & & & & & & \\ \hline & & & & & & & & & & & & & \\ \hline & & & & & 6 & & & & & & & & \\ \hline…

5. When an object is rolling without slipping, the rolling friction force is much less than the friction force when the object is sliding; a silver dollar will roll on its edge much farther than it will slide on its flat side. When an object is rolling without slipping on a horizontal surface,…

$ 72^{\circ} \mathrm{F} $ Clear Home - Dalton State Search Mail - Celena Ross - Outlook Unit 3 Quiz - Linear Functions https://www.knewton.com/learn/course/4bbbc9cb-739e-47b3-90ea-1d12baea30c0/quiz/c5b56b5d-30f6-402b-8633-c61aab6e6aa4 What is the equation of the linear function whose graph is…

31. Verify the identity: \[ \frac{\sin ^{2} \theta}{\cos \theta}=\sec \theta-\cos \theta \]

What is the amplitude, $ |A| $, of the function $ f(x)=5 \cos (x) $ ?

Determine the period, $ P $, of the function $ g(x)=\cos \left(\frac{x}{2}\right) $

3. Calcular: \[ S=\left[\frac{1}{3}+\frac{1}{2}-1\right]-\left[\frac{2}{3}+\frac{1}{2}\right] \] a) $ -\frac{1}{6} $ b) $ \frac{4}{3} $ c) $ -\frac{4}{3} $ d) $ \frac{1}{6} $ c) $ \frac{1}{3} $

Question $ 1(4+4+4+4=16 \mathrm{mrks}) $ Using integration by parts, evaluate each of the following integrals a) $ \int 8 t e^{7 t} d t $ b) $ \int 8 t^{2} e^{7 t^{3}-4} d t $ c) $ \int \frac{2+w}{w^{3}+9 w} d w $ d) $ \int\left(5+2 w^{3}-w^{5}\right)(3 w) d w $ (use integration by…

Use the reference angle of $ 330^{\circ} $ to find $ \cos \left(330^{\circ}\right) $ and $ \sin \left(330^{\circ}\right) $.

Find cosine and sine of the angle $ \pi $. Enter the exact answers.

For the implicitly defined curve: sin(2xy) = cos(y) + 3x a. Use implicit differentiation to find a formula for dy/dx (or y' ). dy/dx = b. Find the slope of the line tangent to the graph of the curve at the point (0, ?/2) . Use exact values. slope = c. Find the equation of the line tangent to…

Questions: When $ t=3.7 \mathrm{~s}, \quad x= $ $ \square $ in. When $ t=7.5 \mathrm{~s}, \quad x= $ $ \square $ in. When $ t=10.5 \mathrm{~s}, \quad x= $ $ \square $ in. For the time interval $ 0 \leq t \leq 12 \mathrm{sec} $, The net dispalcement \[ \Delta x= \] i \(…

Answer all the questions below

(3) $ n(A \times B)=2^{6} $ (4) $ n(A \times(A-B))=9 $ 4. If $ A=\{1,2,3,4,5\} $ and $ B=\{4,5,6\} $, then $ n\{(A \times B) \cap(B \times A)\} $ equals (1) Zero (2) 2 (3) 4 (4) 6 5. If $ A=\{2,4,5\} $ and $ B=\{5,9\} $, then which of the

3. If $ A=\{2,4,5\} $ and $ B=\{1,3\} $, then (1) $ A \times B=B \times A $ (2) $ n(A)=n(B) $ (3) $ n(A \times B)=2^{6} $ (4) $ n(A \times(A-B))=9 $

9. If $ [x] $ and $ \{x\} $ are greatest integer function and fractional part of $ x $ respectively then the value of $ \sum_{r=1}^{2000} \frac{\{x+r\}}{2000} $ is (1) $ x $ (2) $ [x] $ (3) $ \{x\} $ (4) $ x+2001 $

Consider the indefinite integral int x^5 cdot sqrt[5]{x^6 - 7} dx: This can be transformed into a basic integral by letting u = [ ] and du = [ ] dx Performing the substitution yields the integral int [ ] du

Find the limit. ( infty ) and ( -infty ) are possible answers. [ lim _{x ightarrow infty} frac{left(-7 x^{2}-1 ight)^{2}}{(2 x-2)^{2}left(6 x^{2}-9 x ight)}= ] ( square )

Determine the following limits. Enter DNE if a limit fails to exist, except in case of an infinite limit. If an infinite limit exists, enter ( infty ) or ( -infty ), as appropriate. - ( lim _{x ightarrow infty} sqrt{x^{2}+8 x}-sqrt{x^{2}-3 x}= ) ( square ) - ( lim _{x ightarrow-infty}…

This is the link to the graph

*5. Let $ \mathcal{W} $ be the solution set to the matrix equation $ \mathbf{A X}=\mathbf{O} $, where \[ A=\left[\begin{array}{rrrrr} 1 & 2 & 1 & 0 & -1 \\ 2 & -1 & 0 & 1 & 3 \\ 1 & -3 & -1 & 1 & 4 \\ 2 & 9 & 4 & -1 & -7 \end{array}\right] \] (a) Show that $ \mathcal{W} $ is a subspace of…

Question $ 4 \quad(4+5=9 \mathrm{mrks}) $ a) Use partial fractions to solve the definite integral $ \int_{2}^{6} \frac{6 t-5}{(t-4)\left(t^{2}+3\right)} d t $ b) Sketch the curves $ y=2 x^{2}+3 \& 7-y+5 x=0 $ and determine the area enclosed by them.

Use the angle in the unit circle to find the value of the three trigonometric functions below. Enter the exact answers.

i) $ h(x)=3 x+1 $, con Dom $ (h)=\left[-2, \frac{3}{5}\right) $

A child enters a carousel that takes one minute to revolve once around. The child enters at the point $ (0,1) $, that is, on the due north position. Assume the carousel revolves counterclockwise. What are the coordinates of the child after 90 seconds? Enter the exact answer as a point, \(…

Find an equation of the line $ L $, where $ L $ is perpendicular to $ y=\frac{5}{2} x $ and passes through the point $ (2,5) $. \[ \mathrm{y}=\square \] (Type your answer in slope-intercept form. Use integers or fractions for any numbers in the expression.)

ew History Bookmarks Profiles Tab Window Help Ig Calculato SLO 3 Written Quiz Homework 3.2 The Derivative hmostcollege.instructure.com/courses/29892/assignments/1138309?module_item_id=2820830 Ident.pdf Downle Page 2 of 3 Graph. Then using the Continuity Test, determine if the piecewise defined…

Determine the number of bit operations used to compute the boolean product of $ \mathbf{A} $ and $ \mathbf{B} $, where $ \mathbf{A} $ and $ \mathbf{B} $ are $ 2 \times 2 $ zero-one matrices. 4 16 8 2

Determine the following indefinite integrals. (a) $ \int \frac{1}{9 x^{2}+6 x+2} d x $. (b) $ \int \frac{-x+1}{(x+1)(x+2)} d x $. Hint: Decompose into partial fractions first.

Consider the graph of f. The shaded region over [5, 7] has an area of 8 and int_{0}^{7} f(x)dx = 86. Use this information to evaluate the following definite integrals. int_{0}^{5} f(x)dx = int_{5}^{7} f(x)dx = int_{0}^{7} |f(x)|dx = int_{0}^{7} [f(x) + 5]dx = int_{-5}^{2} f(x + 5)dx =

In the above graph, estimate the slope of the tangent line at x = 2.

A 6 foot tall woman walks at a rate of 5 feet per second away from a lamppost that is 24 feet tall. Determine the rate of change of the tip of the woman's shadow when she is 23 feet away from the lamppost. feet per second Determine the rate of change of the length of the woman's shadow when…

Describe the following key features using numbers and interval notation as necessary. If multiple answers exist, use the U symbol to join multiple intervals. If an answer does not exist, enter DNE. Increasing on: Decreasing on: f(x) has an absolute max of [ ] at x = [ ] f(x) has an…

Find the reference angle, the quadrant of the terminal side, and the sine and cosine of 1 : Enter the exact answers. The terminal side of the angle $ 135^{\circ} $ lies in quadrant $ \square $ Click for List . Its reference angle is $ \square $ Number $ { }^{\circ} $.

Problem 6.2 An open layer of clay 4 m thick is subjected to loading that increases the average effective vertical stress from 185 kPa to 310 kPa . Determine: (a) the total settlement, (b) the settlement at the end of 1 year, (c) the time in days for $ 50 \% $ consolidation, (d) the time in…

d) $ f(x)=\frac{6}{7} x-7, \operatorname{con} x>-\frac{4}{5} $.

le Edit View History Bookmarks Profiles Tab Window Help esmos | Graphing Calculato Quiz 3 (3.1-3.2) Homework 3.2 The Derivative texassouthmostcollege.instructure.com/courses/29892/assignments/1138300?module_item_id=2820829 Session I 2025 Syllabus uncements des es 13 e 365 iFuse ett…

Desmos | Graphing Calculato Quiz 3 (3.1-3.2) Homework 3.2 The Derivative texassouthmostcollege.instructure.com/courses/29892/assignments/1138300?module_item_id=2820829 Summer Session I 2025 Quiz 3 (3.1-3.2) 31 mins $ \times $ Progress saved Subr 5 points possible Answered: 5/5 Home Simple…

me File Edit View History Bookmarks Profiles Tab Window Help Desmos | Graphing Calculato Quiz 3 (3.1 - 3.2) Homework 3.2 The Derivativ texassouthmostcollege.instructure.com/courses/29892/assignments/1138300?module_item_id=2820829 Summer Session I 2025 Home Simple…

e File Edit View History Bookmarks Profiles Tab Window Help Desmos | Graphing Calculato: Quiz 3 (3.1 - 3.2) Homework 3.2 The Derivativ texassouthmostcollege.instructure.com/courses/29892/assignments/1138300?module_jtem_id=2820829 Summer Session I 2025 Home Simple…

$ 4^{2 x}+3=1 $

texassouthmostcollege.instructure.com/courses/29892/assignments/1138300?module_item_jd=2820829 Summer Session 12025 Home Simple Syllabus Announcements Modules Grades Office 365 BrainFuse Follett Discover Submit Grades to Colleague Course Evaluations Preliminary COVID-19 Reporting…

texassouthmostcollege．instructure．com／courses／29892／assignments／1138300？module＿item＿jid＝2820829 Summer Session I 2025 Home Simple Syllabus Announcements Modules Grades Office 365 BrainFuse Follett Discover Submit Grades to Colleague Course Evaluations Preliminary COVID－19 Reporting…

Find the are below $ f(x)=-x^{2}+4 x+3 $ above $ g(x) $ $ =x^{2}+7 x^{2}-10 x+5 $ Find the Inliral $ 1 \leq x \frac{x}{2}= $

The graph of the SLOPES of the red function has which color? $ \square $ green blue orange black (0) - green

f(x) =sqrtx find a number delta such that if lx-9l<delta, then lsqrtx - 3l<0.1

Explain each of the solutions in detail.

For the implicitly defined curve: sin(2xy) = cos(y) + 3x a. Use implicit differentiation to find a formula for dy/dx (or y' ). dy/dx = b. Find the slope of the line tangent to the graph of the curve at the point (0, ?/2) . Use exact values. slope = c. Find the equation of the line tangent to…

Answer all the questions below

Consider the indefinite integral int x^5 cdot sqrt[5]{x^6 - 7} dx: This can be transformed into a basic integral by letting u = [ ] and du = [ ] dx Performing the substitution yields the integral int [ ] du

Find the limit. ( infty ) and ( -infty ) are possible answers. [ lim _{x ightarrow infty} frac{left(-7 x^{2}-1 ight)^{2}}{(2 x-2)^{2}left(6 x^{2}-9 x ight)}= ] ( square )

Determine the following limits. Enter DNE if a limit fails to exist, except in case of an infinite limit. If an infinite limit exists, enter ( infty ) or ( -infty ), as appropriate. - ( lim _{x ightarrow infty} sqrt{x^{2}+8 x}-sqrt{x^{2}-3 x}= ) ( square ) - ( lim _{x ightarrow-infty}…

This is the link to the graph

Consider the graph of f. The shaded region over [5, 7] has an area of 8 and int_{0}^{7} f(x)dx = 86. Use this information to evaluate the following definite integrals. int_{0}^{5} f(x)dx = int_{5}^{7} f(x)dx = int_{0}^{7} |f(x)|dx = int_{0}^{7} [f(x) + 5]dx = int_{-5}^{2} f(x + 5)dx =

In the above graph, estimate the slope of the tangent line at x = 2.

A 6 foot tall woman walks at a rate of 5 feet per second away from a lamppost that is 24 feet tall. Determine the rate of change of the tip of the woman's shadow when she is 23 feet away from the lamppost. feet per second Determine the rate of change of the length of the woman's shadow when…

Describe the following key features using numbers and interval notation as necessary. If multiple answers exist, use the U symbol to join multiple intervals. If an answer does not exist, enter DNE. Increasing on: Decreasing on: f(x) has an absolute max of [ ] at x = [ ] f(x) has an…

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