Numerade

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Suppose $z = x^2 \sin y$, $x = 0s^2 - 3t^2$, $y = -2st$. A. Use the chain rule to find $\frac{\partial z}{\partial s}$ and $\frac{\partial z}{\partial t}$ as functions of x, y, s and t. B. Find the numerical values of $\frac{\partial z}{\partial s}$ and $\frac{\partial z}{\partial t}$ when $(s,t) = (3,2)$.

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Question 1 1 pts The density of the rectangular plate [1, 2] × [3, 4] in the $x$, $y$-plane is $\rho = \frac{y}{4 + xy}$ in kilograms per meter cubed, where $x$, $y$ are in meters. The value of $\cos(3M)$, where $M$ is the mass of the plate, is

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4. Let $x_1$ and $x_2$ be distinct vectors in a vector space $V$. Show that {$x_1, x_2$} is linearly dependent if and only if $x_1$ and $x_2$ is a multiple of the other.

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Students will review the following assessments: The American College of Cardiology and the American Heart Association recommend that individuals ages 40 to 79 assess their risk of cardiovascular disease (CVD). Clients who a health coach may perceive to be at increased risk for heart disease, but who may not perceive that risk themselves, may benefit from completing the ACC/AHA online questionnaire to assess their current risk of having a heart attack in the next 10 years (ACC CV Risk Calculator). Risk-factor profiling involves an assessment of the traditional risk factors for coronary artery disease and may include: blood pressure; indices of diabetes (blood glucose and hemoglobin A1C); measures of overweight/obesity (e.g., body mass index, waist circumference, and body fatness); cigarette smoking; metabolic syndrome; cholesterol, its subfractions, and other lipids; physical activity/fitness; and personality characteristics. For additional information on these risk factors (also sometimes called health factors), review the AHA My Life Check assessment tool at Life Check American Heart Association. Students will create an account and explore the assessment tool. Please answer the following questions. Please list two health behaviors the tool asked about. Please list two health factors the tool asked about. Please list four social context and well-being questions the tool asked Please describe how a health coach could use these tools when working with a client?

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Write the atomic symbols for isotopes with the following: 13 electrons and 14 neutrons Express your answer as an isotope. ???? A chemical reaction does not occur for this question. Submit Request Answer ? Part D an iodine atom with 74 neutrons Express your answer as an isotope. ???? A chemical reaction does not occur for this question.

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The refractory period Multiple Choice contributes to the rhythmicity of contractions. All of the choices are correct. ensures that muscle contraction and most of relaxation has been completed before another cycle begins. prevents tetanic contractions from occurring.

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Find the derivative of the following function using the definition of the derivative. $f(x) = 2x^2 - 16x + 35$

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In this question, we prove that the area of the triangle T_(1) equals (1)/(2)|det[[1,x_(1),y_(1)],[1,x_(2),y_(2)],[1,x_(3),y_(3)]]|. (a) Let T_(2) be the triangle obtained from T_(1) by translating the plane from (x_(1),y_(1)) to (0,0). Find the coordinates of A and B. (b) Show that T_(2) has area (1)/(2)|det[[x_(2)-x_(1),x_(3)-x_(1)],[y_(2)-y_(1),y_(3)-y_(1)]]|. (Hint: see Page 9 of the slides on Oct. 19.) (c) Show that det[[1,x_(1),y_(1)],[1,x_(2),y_(2)],[1,x_(3),y_(3)]]=det[[1,0,0],[x_(1),x_(2)-x_(1),x_(3)-x_(1)],[y_(1),y_(2)-y_(1),y_(3)-y_(1)]]=det[[x_(2)-x_(1),x_(3)-x_(1)],[y_(2)-y_(1),y_(3)-y_(1)]] You have proved that the area of T_(1) is (1)/(2) det [[1,x_(1),y_(1)],[1,x_(2),y_(2)],[1,x_(3),y_(3)]]. (d) Let x_(1)= 6 y_(1)= 2 x_(2)=27 y_(2)= 0 x_(3)=15 y_(3)=15 Find the area of the triangle with vertices at (x_(1),y_(1)),(x_(2),y_(2)), and (x_(3),y_(3)). [10] 1. In this question,we prove that the area of the triangle Ti equals det x3, x2,32 i,y 0 a Let T be the triangle obtained from Ti by translating the plane from iyto 0.0.Find the coordi nates of A and B. x2-x1x3= bShow that T has area det y-yy-y Hint:see Page 9 of the slides on Oct.19. c Show that 1 T1 det r2 1 13 1 0 [x=xx3-x xn=y1y3=y1 det ri (x-x1x3- ( y T2 12 ra 1/3 You have proved that the area of Tisdet =fourth digit of your York student ID =fifth digit of your York student ID =20+sixth digit of your York student ID dLet y2=seventh digit of your York student ID r=10+eighth digit of your York student ID s=10+ninth digit of your York student ID Include your York IDnumber inavour solution Find the area of the triangle with vertices atand

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Obtain the transfer functions $X(s)/F(s)$ and $Y(s)/F(s)$ for the following model. $\dot{x} = -3x + 7y$ $\dot{y} = f(t) - 8y - 3x$

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Newly purchased tires of a particular type are supposed to be filled to a pressure of 30 psi. Let $\mu$ denote the true average pressure. A test is to be carried out to decide whether $\mu$ differs from the target value. Determine the $P$-value for each of the following $z$ test statistic values. (Round your answers to four decimal places.) (a) 2.15 0.0300 See the rounding prompt for how many decimal places are needed. (b) -1.73 0.0836 (c) -0.59 0.5550 See the rounding prompt for how many decimal places are needed. (d) 1.45 0.1470 (e) -4.1 0

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magdalena a.