Assuming that the equation below defines y as a differentiable function of x, find the value of dy/dx at the given point. dy 2 3x² + xy + y² - 37 = 0, (3,2) (3,2) ….. (Type an integer or a simplified fraction.)

Q: 1 Let C = 0 1 a) Find C-1 b) Use C¹ to solve the following system. 1 x + 3y 30 14 - 1 2 = 7 y + 4z =…

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Q: Find Duf at P. f(x, y, z) = 6x²y³z¹; P(1, −2, 2); u = 1+ 2 3 k

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Q: The population of a town is now 15,000 and t years from now will be growing at the rate 100√t people…

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Q: Find the directional derivative of f(x, y, z) = in the direction from P to Q(3, 8, -2). NOTE: Enter…

A: The directional derivative of the function f in the direction of u is: Duf=∇f·uu

Q: 2. Rewrite the integral f(x, y, z)dzdxdy using the order dxdydz.

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Q: 9. Find the volume of the solid of revolution obtained by rotating the region in the xy-plane…

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Q: Find the future value of the following annuity due. Then determine how much of this value is from…

A: As per the concept of annuity:FVA=P1+rkn×k-1×1+rkrk          Equation 1   Here:FVA=Future value of…

Q: Let (P) be the quadric surface given by the following equation y=5+x² +=² Then:

A: Given : Let (P) be the quadratic surface given by the following equation  y = 5 + x2 + z2…

Q: Find the most general antiderivative. (Use C for the constant of integration. Remember to use…

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Q: A company produces a special new type of TV. The company has fixed costs of $480,000, and it costs…

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Q: Graph the system of inequalities. x≤2 y≥3-3x Use the graphing tool to graph the system of…

A: x≤2 line x=2     y≥3-3x draw line y=3-3x x y 0 3 1 0 check for orgin y≥3-3x0≥3-3(0)0≥3…

Q: The parametric equations of the line through the points A(0,0,1) and B(1,2,2) are:

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Q: A box with a square base and open top must have a volume of 97556 cm³. We wish to find the…

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Q: Maximize the value of the function A=4xy subject to x + 2y = 24. DO NOT answer any of the following…

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Q: a. Write the equation of the line that represents the linear approximation to the following function…

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Q: Estimate I = = [₁² (1420² I≈ (a) Left endpoints. (4x² + 4x + 1) dx using n = 3 subintervals, and I≈…

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Q: A rectangle is inscribed in a semicircle of radius r= 11, as shown in the figure. Find a function…

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Q: tt (seconds) 0 2 4 6 8 Velocity (ft/sec) 0 2 8 14 30   Shown in the table is the velocity of a car…

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Q: Solve the separable differential equation dx 1 = x² + dt 49 and find the particular solution…

A: dxdt=x2+149 ; x0=1

Q: At 0° Celsius, the heat loss H (in kilocalories per square meter per hour) from a person's body can…

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Q: - 2 sin(1-1) inches per hour, where t represents hours since 12 a.m. The water level of a certain…

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Q: Find the area of the shaded region. y=0 3 9 N6 y=x√9-x² y = 0 3 X

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Q: Write a formula for the distance between a point (x, y) on the graph of y = x and the point (3, 11).…

A: given y=x4point is (3,11)distance between two points (x1,y1) and (x2,y2) is D=(x2-x1)2+(y2-y1)2

Q: Problem 1. Find the local maximum and minimum values (and their locations) and any saddle point (s)…

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Q: What is the equation of the verti asymptote of the following grap

A: here , we have graph of a function , then we have to find equation of vertical asymptotes :-

Q: You are given the graph of a function f. 0 concave downward 1 Determine the intervals where the…

A: You are given a graph of a function f. To determine the intervals where the graph of f is concave…

Q: Which curve does it need to be label and what area are we shading in?

A: Labeled graph is given below,

Q: Evaluate the integral. (Use C for the constant of integration. Remember to use absolute values where…

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Q: Find f'(a). f(x)= 16+x-8x²

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Q: Find the derivative of the function at Po in the direction of A. f(x,y)= - 4xy + 4y², Po(0,-6),…

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Q: Find sin(), cos), and tan from the given information. tan(x) = √2, 0° < x < 90° 1 sin()-6-2√3 COS 11…

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Q: Evaluate the integral. (Use C for the constant of integration. Remember to use absolute values where…

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Q: The general form of an antiderivative of the function f(x)=2 cos(x+π)�(�)=2 cos(�+�)  is   F(x)=

A: To determine the general form of an antiderivative of the following function. fx=2 cosx+π

Q: A hot-air balloon is 120 ft above the ground when a motorcycle (traveling in a straight line on a…

A: Given that , dxdt=66 ft/secdydt=12 ft/secdzdt=?

Q: ist

A: Given Graph:-

Q: Find the area of the shaded region. y 15 10 5 2 y=7x-x² y = 2x 4 (5, 10) 6 Co 8 X

A: Area between the two curves f(x) and g(x) can be calculated using theformula:Area=∫abf(x)-g(x)dx

Q: The figure shows graphs off. f", and f". Identify each curve.

A: let's say N is the number of turning points of the function f turning points function N f(x)…

Q: tank is full of water. Find the work W required to pump the water out o T 1 m Ť 4 m 12 m 4 m

A: The volume of the water of thickness '∆x' at height of x from the bottom.  In △CGB &amp; △CFEFE∥GB.…

Q: Glorious Gadgets is a retailer of astronomy equipment. They purchase equipment from a supplier and…

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Q: Sketch the graphs of the functions. O O f(x) = x³ + x² - 2x and g(x) = 0 L -8 -6 -4 -2 y 8 6 4 2 -2…

A: To draw the graph f(x)=x3+x2-2x

Q: d Find the position of a body moving on a coordinate line at time t for an acceleration a = (0) =…

A: a=d2sdt2=8e2t v(0)=20,  s(0)=6

Q: Use the graph of the function f(x) above to complete the following. f(2) is_ OA. Positive OB. Zero…

A: value of the function at x=2

Q: Question 5 What is the exact value of A B C 위~ SI 2 2 ㅠ 200(1) - 40%(1 COS D √6 2

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Q: Consida a function that has all of the following properties: Ind w Janga дко for r <2 20 for ملو 9"…

A: Please see the below picture for detailed solution.

Q: Given x + y + z = 2 and Po(0,2,0), find the following. (a) Find the equation for the tangent plane…

A: x+y+z=2

Q: Find the directional derivative off at the given point in the direction indicated by the angle 0.…

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Q: k=2 2k (-5)k+1

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Q: Find the value or values of c that satisfy the equation the following function and interval. f(x) =…

A: find values at function

Q: Use the limit of a Riemann sum to find the area under the following function over the given interval…

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Q: Determine possible values of x and z such that a is perpendicular to b and a is perpendicular to c…

A: We have to determine possible values of x.