Find the average value of f over the given rectangle. f(x,y) = 4x²y, R has vertices (-5,0), (-5,4), (5,4), (5,0). fave = X

Q: her manufacturer plans to make rectangular boxes whose bottom and top measure x by 3x. The container…

A: solution: Given data, Measure of top and bottom =x by 3x Top and bottom cost = $2.20 per square…

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Q: (6) Solve y-9y" + 8y = 0.

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Q: 0 1) Here is the graph of f(x). N 2 4 6 8 x a) list the x-values of the critical points, and…

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Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. y = cos 0SX541

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Q: Find the absolute maximum and minimum values of the function, if they exist, over the indicated…

A: If x=c is a critical point of the function f(x) if f(c) exists and if either f'(c) =0 or f'(c) does…

Q: [6 sin [6 sin(8x) dx = [ Find 6 sin(8x) dx +C

A: To find the integral of 6sin(8x).

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Q: Find the formula for a cubic polynomial, ax³ + bx² + cx + d, with a critical point at x = 2, an…

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Q: a.b= ▸ Find a ⋅ b if |a| = 8, |b| = 10, and the angle between a and b isradians.

A: We can find the dot product using the given data in the below steps.

Q: A Norman window has the shape of a semicircle atop a rectangle so that the diameter of the…

A: Given, A norman window has the shape of a semicircle atop a rectangle so that the diameter of the…

Q: Determine whether the following series converges or diverges. M8 n=1 20 (5n-1)(5n+4) Select the…

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Q: f(x) = x² - 72x² Enter the critical points in increasing order. (a) Use the derivative to find all…

A: The given function fx=x4-72x2. We have to find the critical points of fx and find classify their…

Q: Consider the following function: Step 4 of 4: Enter the x-values of any relative minima, maxima, and…

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Q: Consider the following function. h(t) = + = 6 Find the derivative of the function. h'(t) = X Find…

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Q: For a population growing according to the logistic model, a per capita reproductive rate can be…

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Q: On what intervals is the function f(x)=x2-9x8 both decreasing and concave up? interval(s) = Cine…

A: Given :fx=x9-9x8

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Q: An employee's monthly productivity M, in number of units produced, found to be a function of the…

A: Given query is to find the year when maximum productivity achieved.

Q: Consider the graph of 3x³ + 5y = 18. (a) Find the exact coordinates of the x-intercept. ( ) (b) Find…

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Q: Find the center and radius of the circle with the given equation. x² + (y - 3)2 = 16 (x, y) = (0,3…

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Q: The altitude of a triangle is increasing at a rate of 1.5 centimeters/minute while the area of the…

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Q: A water tank in the shape of a hemispherical bowl of radius 5 m is filled with water to a depth of 2…

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Q: Find the distance from the point (-1,1,5) to the line ä(t) = (- Question Help: Video

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Q: Change the order of integration by integrating first with respect to z, then x, then y. LET* -2 JO 6…

A: Here we have to change the order of the triple integral.

Q: The graph of y = f(x) has the following features: f(1) = -2 lim f(x) = 1 #→1 ● ● lim f(x) = 1 x+1+…

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Q: Find an equation of the tangent line to the curve 2(x² + y²)² = 25(x² - y²) (a lemniscate) at the…

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Q: From the properties of exponential functions, the graph of f(x)=ax always passes through the point…

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Q: Let P(x)= 2x3-5x2-4x+3.  a) List all possible rational zeros of P.  b) Find the complete…

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Q: Find the inflection points, if any, of the function. g(x)= 2x^4 - 4x^3 +9

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Q: 10. Find the antiderivatives (show work) [cos(2x)e* dx A. B. √√x In(x)dx C. f dx √4x²-9

A: As per our guidelines we are allowed to answer only three subparts of the given problem. Kindly…

Q: An inverted pyramid is being filled with water at a constant rate of 35 cubic centimeters per…

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Q: 3. An auditorium with a flat floor has a large screen on one wall. The lower edge of the screen is 3…

A: This question is related to height and distance , We will solve it using given information.

Q: AB2: Let G(x) = ef(x). Find G'(6). AB3: Evaluate xf'(4-x²) dx S²x₁

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Q: 10) Analyze all ordinary and singular points for the following DE's. Must show all work! a) 2x(x -…

A: Please see the below picture for detailed solution.

Q: f(x,y)=√y-5x-8 Find the domain of the function. Express the domain so that coefficients have no…

A: The given function fx, y=y-5x-8. We have to find the domain of the function and sketch its graph.

Q: 45 3) Find the absolute maximum and minimum of f(x)=x+x on [−1,1]. f'(x) = 15x¹ + x =

A: Find the absolute maximum and minimum of f(x)= 452x23+ x53  on [-1, 1].

Q: Find the limit by rewriting the fraction first. xy-3y-8x + 24 x-3 lim (x,y) →(3,7) x #3

A: At first, we will factorise the  numerator .

Q: The Sumeru Akademiya wants to manufacture Canned Knowledge in literal cylindrical cans that could…

A: a. The cost of production C can be modeled as: C(r, h) = 2πr^2(0.02) + 2πrh(0.01) Where the first…

Q: Find and sketch the level curves f(x,y) = c on the same set of coordinate axes for the given values…

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Q: dx = 8x³ 8x3 + 3x, y(2) = 0

A: Given query is to solve the differential equation.

Q: Given is the graph for the second derivative of some function f(x) which has the domain of (-∞, ∞)…

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Q: Find the antiderivtive: 3x5+2x²+3 x8 - dx = + C

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Q: 2. The demand function for a product is modeled by: 500 p a) Determine the elasticity function, E…

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Q: known that a certain kind of algae in the Dead Sea can double in population every 4 days. Suppose…

A: Given query is to find the time for population to quadruple and triple.

Q: Find the particular antiderivative F(x) of f(x) = 6x - 9 that satisfies F(1) = 11. Answer F(x)= =

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Q: From the properties of exponential functions, the graph of f(x)=ax always passes through the point…

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Q: 1. Draw and set up the integrals for the area in the 1st quadrant enclosed by x = 4y² and x = y¹/2.…

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

Q: Solve the following initial value problem, d²y dt² +y= uπ/2(t) +38(t − 3π/2) – U2π(t) (t≥0), - y(0)…

A: NOTE: Refresh your page if you can't see any equations. . the given DE is  take Laplace on both…