Graph the given function using a chart of values. (Use -3 ≤ x ≤ 3.) h(x) = -3(2-x) y 30 y 30

Q: Solve the given initial-value problem. dx dt dy = 25x - y dt x(1) = 0, y(1) = 1 x(t) = 0 = -11x - y…

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Q: Question 5 (a) Find an equation of the curve that passes through the point (0, -2) and whose slope…

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Q: In a display, there are 20 toys in the first row, 23 toys in the second row, and so on in an…

A: topic- arithmetic sequence

Q: Find the average cost function if cost and revenue are given by C(x) = 164 +8.9x and R(x) = 3x…

A: Given;  C(x)=164+8.9x R(x)=3x-0.07x2.

Q: Choose the gradient of the function : f(x, y) = ex² Select one: O None of these ○ (6ye+²+³y², 2xer²…

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Q: For the cubic polynomial function f(x) = ax³ + bx² + cx + d, find a, b, c, and d so that 0 is a…

A: Solution of given question is written in below steps.

Q: Convert the point (x,y,z)=(-1,-4,0) to cylindrical coordinates. Give answers as positive values,…

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Q: 2. A differential equation that is a function of x only O will produce a slope field with parallel…

A: Here, given that the differential equation is a function of x only. So, dydx=f(x)⇒y=F(x)+C, where…

Q: Solve the initial value problem. dy do y=0 +y=10 cos 0,0>0, y(x) = 1 THEE

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Q: f(x)=1/x-7 find an equation of the tangent line at the point (-2,-1/9)

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Q: 10. (a) Describe the transformations of y = x³ into the function f(x) = 8(x-1)³ -5. = (b) Describe…

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Q: 6 5 4 3 2 I | y = f(x) 1 1 01 2 ? | 3 4 | 1 + 5 6 7 1 X 89

A: Topic- limits

Q: 2 ƒ² ƒ² (x − 3y²) dydx = −12. - Select one: O True

A: ∫02∫12x-3y2dydx=∫02x-7dx=-12

Q: Use the substitution method to solve the system -x+y=-2 4x - 3y = 9 Your answer is x= y =

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Q: Given the graph of f'(x) below, where the Domf (x) = (-∞, ∞). Find the interval(s) for which f (x)…

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Q: 3. The particular solution of the differential equation dy for which y(0) = 20 is dt 4 O y =…

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Q: Chelsea received a loan of $1,300 at 5.75% compounded quarterly. She had to make payments at the end…

A: We need to find payments.

Q: Use the Product Rule or Quotient Rule to find the derivative of f(x) = O None of these. f'(x) =…

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Q: Calculate M6 for f(x) = √√2x over [3, 6]. (Use decimal notation. Give your answer to two decimal…

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Q: [²² y dydx = 2. Select one: O True O False

A: Select one

Q: 7. The cost function for a particular product is given by C(x)=0.001x^3 −0.18x^2 +12x +200 dollars,…

A: Solution: C(x)=0.001x3 −0.18x2 +12x +200

Q: Q1. If g = xy — yz — zx and F = x²y ī − 2 y²zī – z²x k, find F. grad g and cross product of F and…

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Q: Find f'(x) and find the value(s) of x where f'(x) = 0. f(x) = f'(x) = X x² +49

A: We need to find x values where f'(x)=0

Q: |-2 Evaluate the triple integral ²³ cos (y²) dz dx dy.

A: Here we have to perform triple integration

Q: 3) Find the Taylor series for the function g(x) = x²e³x+¹ centered at a = 1.

A: To find the Taylor series for the function gx=x2e3x+1 centered at a=1.

Q: Determine the x-intercept(s) of the functiony = 4(x + 7)³ − 32

A: To calculate x-intercept, we should plug y=0 in the given equation. Given equation is y=4x+73-32…

Q: II) Let ƒ be the piecewise function f(x) = 2³+ 6x² + 8x x+2 2¹-2, 1-x-2, " x≤-1, x -2 -1 1 1) Sketch…

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Q: The graph of y = f(x) is shown below (dashed curve). Manipulate the green draggable points to obtain…

A: Given data ÷ Graph of y=fx is shown with dashed line curve. We need to graph  y=2fx+1-4

Q: Evaluate • F. dr. F(x, y) = xi + yj C: r(t) = (7t + 5)i + tj, 0 st≤ 1

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Q: Find the local maxima and minima for the function. Find the intervals on which it is increasing and…

A: Given that functiony=x+1  ,4≤x≤10Solution :y=x+1y'=12x+1y4=4+1=5y10=10+1=11local maxima at x=10local…

Q: 7. Given f(x)=√x² + 3, determine p(x), q(x), and r(x) such that f(x) = p(q(r(x))). ✓✓

A: We need to find p(x),q(x),r(x)

Q: Use the Product Rule or Quotient Rule to find the derivative. f(z) = (3x-²+5) (-4x−³+4). ○ f'(z) =…

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Q: 3. The differential equation dy = =X dx 1. will produce a family of quadratic functions. II. will…

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Q: y(x) = 4x²y" + y = 0, y(-1) = 6, y'(-1) = 3 , x < 0

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Q: Given the graph of ƒ' (x) below, where the Dom f (x) = (-∞, ∞). Find the interval(s) for which f"…

A: We have the graph of f'(x) and  we need to tell where f''(x) is &gt;0So, f''(x)&gt;0 when f'(x) is…

Q: consider the hyperbola represented by the equation - (x+5)^2/9^2+ (y-7)^2/13^2= 1

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Q: (a) Find the area of the region bounded by the given curves x+y=0, x = y² + 3y.

A: x+y=0  -----(1)x=-y x=y2+3y ------(2) for points of intersection y2+3y=-yy2+4y=0y(y+4)=0y=0,-4

Q: 4. Which of the following differential equations has the slope field below 22 ܟ O dy dx dx dx ܔܔܔ…

A: The given slope field is for dydx = -xy . Because slope y'(x) of the solution y(x) is determined…

Q: Consider the function f(x) = x³ + 9x² + 15x. Step 1: Find all values of x that correspond to…

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Q: Which of the following are true statements? Mark all that are true. Olim f(x) = 6 and lim f(x) = 6…

A: Limits

Q: The side of a square is growing at the rate of 5 centimeters per second . Find the growth rate of…

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Q: Let F = (7yz)i + (2xz)j + (1xy)k. Compute the following: A. div(F) = B. curl(F) =i+j+k C.…

A: We know the expression for the divergence of vector point function F→=F1i+F2j+F3k is:…

Q: Calculate the volume under the elliptic paraboloid z = 4x2 + 6y2 and over the rectangle R = [-2, 2]…

A: The solution for the above question is shown below.

Q: Question (x,y) = (0,0) Let f(x,y)=√+² (x,y)=(0,0) The function is continuous at the point (0, 0) if…

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Q: Calculate f((5x + 2y)i + (4x + 7y) 3) · dr where C' is the circular path with center (a, b) and…

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Q: An oil tanker aground on a reef is forming a circular oil slick about 0.2 foot thick. To estimate…

A: Given,  Figure :

Q: Convert the point (x,y,z)=(5,-3,-5) to spherical coordinates. Give answers as positive values,…

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Q: The cost function for a particular product is given by C(x)=0.001x^3 −0.24x^2 +27.9x +110 dollars,…

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Q: (d) Find the volume of the solids generated by revolving the region bounded by the curves y = 2x -…

A: Solved below

Q: Find the total mass of the wire with density p. r(t) = cos(t)i + sin(t)j, p(x, y) = x+y, Ostsn

A: Please see the below picture for detailed solution.