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Precalculus Q&A Archive of January 31, 2024

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January 31 of 2024

IAREA Factoriza los siguientes trinomios cuadrados perfectos: a) \( x^{2}+18 x+81= \) e) \( x^{2}+30 x+225= \) b) \( x^{2}+24 x+144= \) f) \( 4 x^{2}+12 x+9= \) c) \( x^{2}+20 x+100= \) g) \( 9 x^{2}+30 x+25= \) d) \( x^{2}+16 x+64= \) h) \( 25 x^{2}+10 x+1= \)
\( \triangle \mathrm{ABC} \sim \triangle \mathrm{XYZ} \)
05.- Sabiendo que: \[ \overline{a b c d} \times 99=\overline{e f 1228} \] Calcule el valor de: \( a+b+c+d+e+f \)
- Domina las operaciones básicas de números naturales. (3) Resuelve el crucinúmero. Horizontales 1. Suma de 3562 y 3413. 2. Diferencia entre 13843 y 9687 . 3. Doble de 342. 4. Quinta parte de 7815 . 5. Triple de 133. Verticales a. Resultado de \( 59902 \div 982 \). b. Doble de 455 más quíntuple…
Work out the area of the dotted, purple triangle. Not to scale Zoom
Mojo's Coffee Cart has a consistent contribution margin ratio of \( 55 \% \). The company is purchasing new coffee roasters which will increase its fixed costs from \( \$ 1,500 \) per month to \( \$ 2,000 \) per month. Net income in August, before the purchase of the new roasters, was \( \$…
Directions: Find eoch of the following for \( \mathrm{a}=5 \mathrm{i}-2 \mathrm{j}-4 \mathrm{k}, \mathrm{b}=-\mathrm{i}+7 \mathrm{k} \), and \( \mathrm{e}=\mathrm{i}-6 \mathrm{j}+1 \mathrm{k} \) - 13. \( 7 \mathrm{a}-4 \mathrm{c} \) 14. \( -\mathrm{a}+6 \mathrm{~b}-\mathrm{c} \) 15. \( 3 a+b+5…
Topic: Inventory 8. Mayhew AG has the following inventory, purchases, and sales data for the month of March. The physical inventory count on March 31 shows 500 units on hand. \begin{tabular}{llll} \hline Inventory: & March 1 & 200 units @ \( € 4.00 \) & \( £ 800 \) \\ \hline Purchases: & March…
For questions 11 and 12 , find each of the following for ( p=(-7,-6), q=(-1,-11) ), and ( r=(0,9) ). 11. ( -2 mathrm{p}-mathrm{r} ) 12. ( 8 mathrm{r}+3 mathrm{q} )
19. If the population increases by \( 10 \% \) each year. How long it will take to be doubled! ????? ??? ??\% ???? ???????? ?????? ???? ????? ??? ?? ??????? ????
(A) \( 25 \% \) (B) \( 90 \% \) (C) \( 15 \% \) (D) \( 11 \% \) Ans(A) If the population increases by \( 10 \% \) each year. How long it will take to be doubled! ????? ??? ??\% ???? ???????? ?????? ???? ????? ??? ?? ??????? ???? (A) 4 Years (B) 8 Years (C) 16 Years (D) 9 Years Ans(B) What is…
For questions 7-10, find the magnitude and direction angle of each vector. Give answers in simplest radical form for magnitude and round to the nearest hundredth of a degree for the angle. 7. p = <12, -34> ?12² + -34² 8. z = 12i + 16j Magnitude Direction Angle Magnitude Direction An 9. CD with…
4. Write the vector shown on the graph below as a linear combination of standard unit vectors i and j.
2. Write the component form of the vector shown on the graph below.
16. The magnitude of vector ( v ) along with its direction angle are given below. Write the vector in component form. [ |v|=8 ; heta=330^{circ} ] A. ( langle 4 sqrt{3},-4 angle ) B. ( langle 8,-8 sqrt{3} angle ) C. ( langle 4,-4 sqrt{3} angle ) D. ( langle 8 sqrt{3},-8 angle )
14. Write the vector below in trigonometric form. f = ?-?6, -3?2? A. f = 2?6?cos 240°, sin 240°? B. f = 2?6?cos 60°, sin 60°? C. f = 6?2?cos 210°, sin 210°? D. f = 6?2?cos 240°, sin 240°?
Use synthetic division to determine if \( x-2 \) is a factor of \( x^{3}-2 x^{2}-7 x+4 \). Is \( x-2 \) is a factor of \( x^{3}-2 x^{2}-7 x+4 \) ? Type YES or NO What is the quotient and the remainder? Quotient: \( \mathrm{R} \)
The graph of exponential function \( g \) is shown.
XERCISE 1.5 Find the HCF for these sets of numbers. a) 21 and 84 b) 108 and 270 c) 30,210 and 700 d) 195 and 330
ir (I iA CY \( 18(4 \) f (F
Find each other the following for x=<6,-2,-1>, y=<-4,7,-3>, and z=<11,6,8>
Directions: Find each of the following for x = <6, -2, -1>, y = <-4, 7, -3>, and z = <11, 6, 8> 10. -3x + y - 4z 11. -x + 7y + z 12. 6x + 5y - 2z Directions: Find each of the following for a = 5i - 2j - 4k, b = -i + 7k, and c = i - 6j + 11k. 13. 7a - 4c 14. -a + 6b - c 15. 3a + b + 5c
Directions: Write each vector in component form with the given initial and terminal points, then state the vector as a linear combination. 7. A(-5, 5, -9) and B(1, 3, -7) 8. R(4, 2, -8) and S(1, 9, -8) 9. E(-7, -8, -9) and F(2, -1, 9)
Find the length and the midpoint of the segment with the given endpoints
(7) \( (2 x+y)^{2}-(3 x-2 y)^{2}+(x-4 y)(x+4 y) \) (4) \( x^{6}+\left(x^{3}-3 y\right)\left(x^{3}+3 y\right) \) (10) \( 3 a+b)(3 a \) Answers:
A function f is given, and the indicated transformation is applied to its graph. Write the equation for the final transformed graph. f(x) = x^3 shift upward 5 units y =
Select the correct answer. If \( f(x)=x^{3} \), what is the equation of the graphed function?
1. When \( 2 x^{4}+3 x^{3}+5 x-1 \) is divided by \( x^{2}-2 x+2 \), the remainder is A. \( 11 x-21 \) B. \( 11 x+21 \) C. \( 7 x+10 \) D. \( 7 x-10 \) 1 2. When \( f(x) \) is divided by \( x-3 \), the quotient is \( 4 x^{2}+12 x+38 \) and the remainder is 111 , then \( f(x)= \) A. \( x^{3}+5…
The graph of a function \( f \) is stowi berion: Find \( f(-2) \). \[ f(-2)= \]
Which is the best estimate for the bear population's average growth rate? 1.2 bears per year 2.4 bears per year 12 bears per year 24 bears per year
Jack works as a ranger at Broad Valley State Park. He is studying how conservation efforts are affecting the bears in the park. He made this graph to show the bear population in the park each year from 2010 to 2020.
NTH II \[ \begin{array}{c} f(x)=\frac{x-1}{x^{2}-x-6} \\ x-1=0 \\ x=1 \\ x^{2}-x-6=0 \\ (x+2)(x-3)=0 \end{array} \]
Rewrite each sentence using said to have and It is said, and the given verbs. 1. The performance of the musicians was not as expected. (report) Itwas roported that the performance of the musicians was not as expected. Theperformance of the musicians was reported to be not as expected. 2. The…
Suppose the equation \( \mathrm{Q}_{\mathrm{d}}=(10-0.4 \mathrm{D})-0.6 \mathrm{P} \) describes an individual's demand for iTunes content, with \( \mathrm{D} \) being the price of the device needed to access iTunes content, in \( \$ 100 \) s. a) Draw the individual demand curve and show a…
A sculpture has a hyperbolic cross section. Find the width of the sculpture at a height of 5 feet.
5. The population of a town was 6,50,000. Due to an epidemic, the population of the town went down by \( 12 \% \). Find the current population of the town.
Question 2. Let \( R \) be the bounded region enclosed by the curves \( y=12-x^{2}, y=|x| \) (in the half space \( y \geq 0 \) ). (a) Find the area of the region \( R \), (b) Find the volume of the solid generated by revolving the region \( R \) about the \( x \)-axis.
\( -----\infty----1 \)
\( \sin ^{2} A \cdot \cos ^{2} B+\cos ^{2} A \cdot \sin ^{2} B+\cos ^{2} A \cdot \cos ^{2} B+ \) \( \sin ^{2} A \cdot \sin ^{2} B=1 \)
Dote: Doge Niar Computer Assignment create a webpage and set its tittle as 667 wonders of the world 2024 , set a backiground colowr of webpage to blue create a heading using font colowr Red, size \( =6 \) \& font face = Times New Roman inderline the heading insert image of taj mahal in centse…
Q31. a) If \( (x-a) \) and \( (x-b) \) are factors of \( x^{2}+a x-b \), then find the value of \( a \) and \( b \).
The expected cashflows of a project are: Cash flows year 1 2 3 4 5 \[ \begin{array}{l} 20,000 \\ 30,000 \\ 40,000 \\ 50,060 \\ 30,000 \end{array} \] The Cashpelemes outflows is \( R_{s} \quad 100,000 \) The cost of Capital is \( 10^{\circ} \% \) calculate the FF. a.) \( N P V \) b.…
Cackipgr the end of 3 hours \[ \begin{array}{l} =350000\left(1+\frac{11}{100}\right)^{3} \\ =350000\left(\frac{111}{100}\right)^{3} \\ =350000 \times \frac{111 \times 111 \times 111}{1000000} \\ =478670.85=478671 \end{array} \] The court of bacteria at the end of 3 hours will be 478671…
Consider the circuit below: This circuit is called a Half adder Latch Bit counter PIPO device
\[ =478670.85 \approx 478671 \] The rount of bacteria at the end of 3 hours will be 478671 . Extrise 9.2 7. The population of a town increases at the rate of \( 7 \% \) every year. If the present population is 410000 , calculate the population of the town after 2 years.
3.2 (2) Show that the following equation is hyperbolic: \[ u_{x x}+6 u_{x y}-16 u_{y y}=0 \] (4) Find the canonical form of the equation. Find the general solution \( u(x, y) \).
\begin{tabular}{|c|c|c|} \hline Angila & the insev & \\ \hline & \( 2 y \) & \( 2 x^{3} \) \\ \hline & \( 40^{\circ} \) & \( 3 r^{-1} \) \\ \hline & \( e x \) & 32 \\ \hline \end{tabular} s Whint Atquit of raflscica did she muds iscomatly: disgram to illus raike zour answer.
12.Verify the Stokes' theorem for \( A=(y-z+2) \hat{\imath}+(y z+4) \hat{\jmath}-x z \hat{k} \), where \( \mathrm{S} \) is the surface of th cube \( x=0, y=0, z=0, x=2, y=2 \) and \( z=2 \) above the \( x y \)-plne. 14
1. Sebuah kotak ditarik dengan arah tarikan seperti gambar berikut. Hitunglah besar usaha yang dilakukan untuk menarik kotak tersebut!
2. Escribe la equivalencia en años. a) 1 década y 12 lustros b) 5 siglos, 9 déca
\[ \frac{\log _{3} 27-\log _{1 / 4} 64}{\log _{3} 1 / 81} \] Solve without using logarithm table
find the vertices and locate the foci for the following hyperbola equation: x2/144 - y2/25=1
1 The speed of a pebble thrown from the top of a cliff is shown alongside. a Find the gradient and \( y \)-intercept of the line, and explain what these values mean. b Find the equation of the line. c Find the speed of the pebble after 8 seconds.
tw below. \( \frac{12}{2}(1) \operatorname{G(1)}=\frac{40(5+2)}{(3+10)\left(5^{2}-1.4\right)} \) a) find the traw fer tue - \( G(z) \) fr \( t=1 \). assimilt the system is preceded by a ZOH. b) we 70 lab to draw the rot locus 7 the systen with nespect to \( K \). C) What is the rawes \( k \)…
The incomes of a group of 10,000 persons were found to be normally distributed with mean Rs. 525 and standard deviation Rs.60. Find (i) the number of persons having incomes between Rs. 500 and 550, (ii) the lowest income of the richest 500 .
2. Six equal trapezoidal sections form a conference table in the shape of hexagon, with hexagonal opening in the middle. From the dimensions shown, find the area of the table (gray area shown in the figure below). [7 marks]
A rectangular piece of card is cut in a straight line along its diagonal, as shown below. Work out the size of angle \( y \). Give your answer in degrees to 1 d.p. Not drawn accurately
Let A= [-4,9,9 -3,1,8] and B = [-6,8,-5 -8,-7-3] find +B
\( \frac{\left(x^{4} y z^{-3}\right) \times \sqrt{x^{-5} y^{2} z}}{x z^{7 / 2}} \)
\( \operatorname{Hx}_{0}^{\sqrt{2}} \int_{0}^{3 y} \int_{0}^{8-x^{2}-y^{2}} d z d x d y \)
\( \int_{0}^{\sqrt{2}} \int_{0}^{3 y} \int_{x^{2}+3 y^{2}}^{8-x^{2}-y^{2}} d z d x d y \)
Prob. 18 Test the convergence of the series: \[ \sum_{n=1}^{\infty} \frac{1^{2} \cdot 5^{2} \cdot 9^{2}---(4 n-3)^{2}}{4^{2} \cdot 8^{2} \cdot 12^{2}--(4 n)^{2}} \] [R.T.U. 2019]
2. Kedva akar Persamaan Kuadrat \[ x^{2}-2 p x+p^{2}-a^{2}+2 a r-r^{2} \text { adalah... } \]
Give the order of matrix, and identify the given element of matrix. [-2/-1 12/9 -8/-12 5/-14]; a12
\( x^{4}-1=0 \)
Find the dimensions of the rectangular box of maximum volume that can be inscribed in a sphere of radius \( a \).
Solve the system by the substituiton method x+y=7 & y=×*2-10×+25
Graph the inequality x+y<-5.
solve the system of equations by the substituiton method: x + y = 6 y = 2 x
Use the coding matrix A= [2/5 1/3 and its inverse A-*1 [3/-5 -1/2 to d3code the cryptogram [9/25 6/17]
6.21. Gi?i các ph??ng trình sau: ?) \( \log (x+1)=2 \); c) \( \ln x+\ln (x-1)=\ln 4 x \);
\( 6 x^{2}-x y-15 y^{2} \)
If g(x)= √(3x^2 + 9x) Domain of f(x)= [-4, √6] Determines Fog's domain
DOSSIER3: SEUIL DE RENTABILITE (5pts)L'entreprise SAWADOGO & FILS commercialise cinq produits A, B, C, D, E aux prix respectifs de 550FCFA; 350 FCFA; 680 FCFA; 720 FCFA; 480 FCFA.Son circuit de distribution est composé de deux canaux :Canal grossistes: 3 grands distributeurs ALPHA, BETA ET…
Que. On June \( 1^{\text {st }} \) a company received a contract to supply 6000 units of a product. The terms of contract requires that 1000 units be shipped till the end of June, 3000 units in July and 2000 units in August. The company can manufacture 1500 units per month on regular time and…
f) \( 4 x^{2}-36=0 \)
On Earth, a plastic ball was dropped from two different heights. The speed of the ball when it hit the ground was recorded each time. What will the ball's speed be when it hits the ground if it is dropped from a height of 40 meters? \begin{tabular}{|c|c|} \hline Platform height & Speed when it…
A person invested $8300 for one year at 4% at 9% and the remainder at 14% the total annual income from these investments was $892 amount of money invested at 14% was 500 more than amount invested at 4% and 9% combined the amount invested at each rate each rate
Suppose we know the point (3, 5) is a point on the graph of a one-to-one function 𝑓. Explain how to find 𝑓(3) and 𝑓-1 (5).
Given that \( \frac{z-7}{4}-\frac{z-3}{2}=1 \), calculate the value of \( z \).
II. Solve the following problems. what is the acceleration \( \underline{\underline{\text { in } m}} / \mathrm{s}^{2}= \) ?
In Exercises 55–66, refer to the right triangle dia for angle measures in decimal degrees. 55. ? = 32° and c = 12 ft 56. ? 57. ? = 72° and c = 9.7 mm 58. ? 59. ? = 54.2° and a = 111 mi 60. ?
\( f(x)=\left\{\begin{array}{ll}3 x^{6} \sin \frac{1}{x} & \text { if } x \neq 0 \\ 0 & \text { if } x=0\end{array}\right. \)
\( \int \frac{z^{2}+z+1}{\sqrt{z}} d z \)
1. \( \left\{\begin{array}{l}y^{2}+x-y-61=0 \\ y^{2}+x-16 y+59=0\end{array}\right. \) 2. \( \left\{\begin{array}{l}y^{2}+x-6 y=8 \\ 13 y^{2}+x+18 y=-4\end{array}\right. \)
What Have I Learned fo Prar? Use the elimination method bo selwe wath system ne (1). \( \left\{\begin{array}{l}y^{3}+x-y=51=0 \\ y^{3}+z-16 y \text { i } 59=0\end{array}\right. \) (2) \( \left\{\begin{array}{l}v^{3}+z-n v-8 \\ 13 y^{3}+z+18 y=-4\end{array}\right. \) 3. \(…
1. \( \left\{\begin{array}{l}y^{2}+x-y-61=0 \\ y^{2}+x-16 y+59=0\end{array}\right. \) 2. \( \left\{\begin{array}{l}y^{2}+x-6 y=8 \\ 13 y^{2}+x+18 y=-4\end{array}\right. \) 3. \( \left\{\begin{array}{l}2 \hat{x}^{2}+\hat{y}^{2}=y x+16 y=-1 y \\ 2 x^{2}+y^{2}-21 x+16 y=17\end{array}\right. \) 4.…
\( y=x^{3}-1 \) Prove that \( x^{2} y_{3}-2 x y_{2}+2 y_{2}=0 \).
When surveyors measure land that slopes significantly?
CHALLENGE Q 14 Solve \( 5 x^{2}-x^{2} e^{2 x}+2 e^{2 x}=10 \) giving your answers in exact form.
\( y=\frac{2}{x^{4}+1}= \)
Find an angle between 0 degrees and 360 degrees that is coterminal with a 1050 degrees angle.
For questions 11 and 12 , find each of the following for ( p=(-7,-6), q=(-1,-11) ), and ( r=(0,9) ). 11. ( -2 mathrm{p}-mathrm{r} ) 12. ( 8 mathrm{r}+3 mathrm{q} )
For questions 7-10, find the magnitude and direction angle of each vector. Give answers in simplest radical form for magnitude and round to the nearest hundredth of a degree for the angle. 7. p = <12, -34> ?12² + -34² 8. z = 12i + 16j Magnitude Direction Angle Magnitude Direction An 9. CD with…
4. Write the vector shown on the graph below as a linear combination of standard unit vectors i and j.
2. Write the component form of the vector shown on the graph below.
16. The magnitude of vector ( v ) along with its direction angle are given below. Write the vector in component form. [ |v|=8 ; heta=330^{circ} ] A. ( langle 4 sqrt{3},-4 angle ) B. ( langle 8,-8 sqrt{3} angle ) C. ( langle 4,-4 sqrt{3} angle ) D. ( langle 8 sqrt{3},-8 angle )
14. Write the vector below in trigonometric form. f = ?-?6, -3?2? A. f = 2?6?cos 240°, sin 240°? B. f = 2?6?cos 60°, sin 60°? C. f = 6?2?cos 210°, sin 210°? D. f = 6?2?cos 240°, sin 240°?
Find each other the following for x=<6,-2,-1>, y=<-4,7,-3>, and z=<11,6,8>
Directions: Find each of the following for x = <6, -2, -1>, y = <-4, 7, -3>, and z = <11, 6, 8> 10. -3x + y - 4z 11. -x + 7y + z 12. 6x + 5y - 2z Directions: Find each of the following for a = 5i - 2j - 4k, b = -i + 7k, and c = i - 6j + 11k. 13. 7a - 4c 14. -a + 6b - c 15. 3a + b + 5c
Directions: Write each vector in component form with the given initial and terminal points, then state the vector as a linear combination. 7. A(-5, 5, -9) and B(1, 3, -7) 8. R(4, 2, -8) and S(1, 9, -8) 9. E(-7, -8, -9) and F(2, -1, 9)
Find the length and the midpoint of the segment with the given endpoints
A function f is given, and the indicated transformation is applied to its graph. Write the equation for the final transformed graph. f(x) = x^3 shift upward 5 units y =
find the vertices and locate the foci for the following hyperbola equation: x2/144 - y2/25=1
2. Six equal trapezoidal sections form a conference table in the shape of hexagon, with hexagonal opening in the middle. From the dimensions shown, find the area of the table (gray area shown in the figure below). [7 marks]
Let A= [-4,9,9 -3,1,8] and B = [-6,8,-5 -8,-7-3] find +B
Give the order of matrix, and identify the given element of matrix. [-2/-1 12/9 -8/-12 5/-14]; a12
Solve the system by the substituiton method x+y=7 & y=×*2-10×+25
Graph the inequality x+y<-5.
solve the system of equations by the substituiton method: x + y = 6 y = 2 x
If g(x)= √(3x^2 + 9x) Domain of f(x)= [-4, √6] Determines Fog's domain
A person invested $8300 for one year at 4% at 9% and the remainder at 14% the total annual income from these investments was $892 amount of money invested at 14% was 500 more than amount invested at 4% and 9% combined the amount invested at each rate each rate
Suppose we know the point (3, 5) is a point on the graph of a one-to-one function 𝑓. Explain how to find 𝑓(3) and 𝑓-1 (5).
In Exercises 55–66, refer to the right triangle dia for angle measures in decimal degrees. 55. ? = 32° and c = 12 ft 56. ? 57. ? = 72° and c = 9.7 mm 58. ? 59. ? = 54.2° and a = 111 mi 60. ?
Find an angle between 0 degrees and 360 degrees that is coterminal with a 1050 degrees angle.