1. Use an appropriate substitution to solve these four ODES: (a) dy dx = x + 3y 3x + y

Q: Find a value of c> 1 so that the average value of Ax) = (²) cos(4) on the interval [1, c] is -0.9.…

A: Given function:- fx=9πx2cosπx

Q: Oil spilled from a ruptured tanker spreads in a circle whose area increases at a constant rate of 9…

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Q: Find the horizontal asymptote of the function. Give your answer as an equation of a line. If an…

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Q: Find y" by implicit differentiation. 2x³ + 5y³ = 2 y" = 2x² 5y2 X

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Q: Evaluate the iterated integral S S (11x+10y (11x+10y + 14)dx dy. 4-2

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Q: Model the data using an exponential function f(x) = Abx. x 0 1 2 f(x) 600 1,200 2,400 f(x) =

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Q: (a) Find the derivative of g(x) = 5arctan( for x > 0. Simplify your answer. g'(x) = (b) Find the…

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Given h(x) tangent line to h(x) at x = -1? = -2x³ +=; x (A) y - 1= 5(x - 1) (B) y-3-7(x + 1) (C) y -…

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Q: 10. What are the absolute minimum of f(x) = 3x³ — x − 1 over [−1, 1] -3 (at x = −1) 01 (at x = = 1)…

A: We need to find the absolute minimum of f(x)=3x3-x-1 over [-1,1]

Q: Answer the following questions for the function f(x)=x√√x²+4 defined on the interval -5 ≤ x ≤ 4.…

A: “Since you have posted a question with multiple sub-parts, we will solve first three sub parts for…

Q: R/4 4. ST¹ x sin 2x dx

A: To Find : ∫0π4xsin2x dx

Q: If you have 120 meters of fencing and want to enclose a rectangular area up against a long, straight…

A: Given f you have 120 meters of fencing and want to enclose a rectangular area up against a long,…

Q: The graph below is generated from the function h (z) -7 -6 -5 Find a, b, and c. a= [Select] b=…

A: The graph below is generated from the function hx=x-5x-ax+bx-c. To find a, b, and c.

Q: The general solution to the differential equation. expression for f (x) and its domain? A (В C D…

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Q: A box with a square base and no top is to be made from a square piece of carboard by cutting 7 in.…

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Q: Find the values of x for which the series converges. (Enter your answer using interval notation.) 8…

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Q: art 1 or what value(s) of x does the graph of have a horizontal tangent? C = art 2 Differentiate the…

A: For calculating horizontal tangent for  f(x)=10x^3-15x^2-60x-30 Where it's derivative is equal to…

Q: What is the Point of Inflection of the following graph? 15 -0.5- O --0.5- (0,0) 0.5 (0.333, -0.296)…

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Q: Find the moment about the x-axis of a wire of constant density that lies along the curve y = √7x…

A: We have to find the moment about the x-axis of a wire of constant density that lies along the curve…

Q: Use series to approximate the definite integral to within the indicated accuracy: 0.7 sin(x³) dx,…

A: I have solved step by step in detail...go through the solution

Q: Let f(x, y, z) = xy + 2². In this problem, we find the directional derivative of f at (4, -2, 1) in…

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Q: 9. Suppose P = spending s (in a. Is the profi $41,000? R $2000, etc.

A: Given function P = -0.1s3 + 6s2 + 400where P = profit s = spending on advertising

Q: 2. (a) (b) (c) Evaluate the definite integral. S = 1 1 + t² 2 [² (²2-²3) dr dx dt 812 218 [² (2x −…

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Q: Model the data using an exponential function f(x) = Abx. x 1 2 f(x) −54 −72.9 f(x) =

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Q: Two boats leave a dock at the same time. One boat travels south at 10 mi/hr and the other travels…

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Q: -. Let f(x) = 3x²(x − 1)². minimum or neither. Als

A: The given function is ; f(x)=3x2(x-1) 7.

Q: Let f(t) = (t² + 4t+6) (7t² + 3). Find f' (t). f' (t) Find f'(3). f' (3) =

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Q: Find the solution to x'=y y'=4x+3y if x(0)=0 and y(0)=2 x(t)=? y(t)=?

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Q: Use the graph of the derivative f' of a continuous function f is shown. (Assume f' continues to ∞.)…

A: Use the graph of the derivative f'(x) of a continuous function f is shown .

Q: 7. Find d when 5x² +3x³y -3y³ = 44. Write an equation of the tangent line at the point (2,2).

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Q: 42. Use cylindrical coordinates to find the volume of the region bounded below by the plane z = 1…

A: The solution is shown below-

Q: here are 8 toll of carpet. Each roll of carpet is 6 yards long. How long are the 8 rolls of carpet…

A: Given, total no. of carpet  rolls= 8 units Length of each roll = 6yards

Q: Suppose that f(x) and g(x) are given by the power series and CO g(x) = 16+ 40x+37x² + 48x³+. By…

A: The given data is: fx=4+7x+2x2+3x3+.....gx=16+40x+37x2+48x3+....

Q: 37. lim x-0+ 39) lim log₂ x log₂ 3x In(x - 2) 2 x→2+ ln(x² - 4)

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Q: Write an integral that represents the area of the shaded region of the figure. Do not evaluate the…

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Q: Find the absolute extrema of the function on the closed interval. Use a graphing utility to verify…

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Q: Santos wants to build a rectangular enclosure for his animals. One side of the pen will be against…

A: We need to find the dimensions that will maximize the area of the enclosure.

Q: If the cost of selling y yards of fabric is given by C (y) = ○ 10 ㅇ 의해 의 10 3y 3 2 find an…

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Q: The average value of the function f(x) = (2) cos(4) on the interval [2, 20] is: sin(x/20) A) B) C)…

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Q: 4. (4-2x+y) dy dx = Jo J2x-4

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Q: Suppose you turn off the engine of your car when the temperature of the engine reaches 188 °F. If…

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Q: 1 Find the area of the surface generated by revolving the curve x = 3 cos (3t), y = 2 + 1 sin (3t)…

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Q: Consider the linear system y' = Aỹ with (a) Find the general solution. 1 4 = (-5₁3) A -1

A: To find the general solution of the linear system y' = A y, we first need to find the eigenvalues…

Q: Find the point on the line 2x + 7y+3=0 which is closest to the point (3, 4). )

A: Let P(x,y) be the point on 2x+7y=-3 7y=-3-2xy=-3-2x7 Distance…

Q: Consider the power series (−1)¹ (7x − 3)¹ - √n +9 Find the center, a, radius of convergence, R, and…

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Q: The count in a bacteria culture was 300 after 10 minutes and 2000 after 30 minutes. Assuming the…

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Q: A box in the shape of a rectangular prism has a volume of 96 cubic feet. The box has a length of…

A: Box

Q: 4. The chipmunk population in a region was 280 chipmunks in 2010. By 2015, the population increased…

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Q: Find the global maximum and global minimum values of the function f(x)=x^3−6x^2−63x+7 over each of…

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Q: Find the solution to the linear system of differential equations x'= -10x -9y y'= 6x + 5y…

A: Given Data : Here the given system of differential equations is, x'=-10x-9yy'=6x+5y with initial…