The volume of a balloon is inflated from 0 to 8 m³ in 5 minutes. What is the average rate of change for the radius of the balloon in these 5 minutes? Round your answer to 3 decimal places. You may assume that the balloon is perfectly spherical in the process. Answer:

Q: Differentiate the function. f'(v) = f(v) = 3 √√√v - 3vev V V

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Q: Find the average rate of change of the function over the given interval. P(0)=03-202+60; [1,2] ΔΡ ΔΘ…

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Q: Write the sum without sigma notation. Then evaluate. 6 Σ sin kn k=2 Write out the sum. 6 Σ sin kn =…

A: Given series ∑k=26sinkπ

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Q: Let f(x)=2 ta(a), Find f'(z). f'(z) -

A: Given query is to find derivative.

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Q: Find the limit of f(x) = lim f(x)= -7+- X as x approaches co and as x approaches -8. lim f(x) = X→∞0…

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Q: 1. Suppose that y is defined implicitly as a function of r by the following equation: 3y² + 2xy + x²…

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Q: Differentiate the function. g'(x) = g(x) = In(xe−8x)

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Q: If sec(a) O 4/6 6/4 = 250 88 88 13 find the value of cot(a) where a terminates in the first…

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Q: 24. Below is the graph of f(x) lim f(x) = x-1 f(-1)=

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Q: Consider the following curve. 1 + x 4 + ex Find y'(x). y'(x) = y = 1 Find an equation of the tangent…

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Q: Given the non-homogeneous differential equation y "- 4y + 4y=e²x What is its auxiliary equation? 0…

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Q: Identify the open intervals on which the graph below is increasing and decreasing. -5 -4 -3 -2 -1…

A: Solve the following

Q: ind the equation of the plane that contains (1, -2, 1), (1, 0, 2) and (0, -2, 2)

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Q: Determine all values of x. (if any), at which the graph of the function has a horizontal tangent.…

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Q: -X xy' + (1 + x)y = e¯* sin(2x)

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Q: Use graphs to evaluate 2π S 0 sin x dx and 2π So 0 cos x dx.

A: The given integrals ∫02πsinx dx and ∫02πcosx dx. We have to find the value of the integrals using…

Q: Use geometry to evaluate the following integral. 5 frixe 1 f(x)dx, where f(x) = 2x if 1≤x≤2 6-2x if…

A: NOTE: Refresh your page if you can't see any equations. . the given function is  first we need to…

Q: Find the volume of the solid whose base is the region enclosed by y = x² and y = 1, and the cross…

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Q: Use the method of undetermined coefficients to solve the given nonhomogeneous system. X(t) = dx dt…

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Q: If g(x) = f* √u² + 2 du, what is d²g / dx²? 0

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Q: (a) nsider the change of variable from cartesian coordinates (x, y, z) to coordi- nates (r, y, 0) in…

A: Please see the below pictures for detailed solution.

Q: Graph the integrand, and use area to evaluate the definite integral The value of the definite…

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Q: Differentiate. g'(0) = g(0) = eº (tan(0) — 0)

A: dexdx=ex  d(tanx)dx=sec2xd dx(a.b)=adbdx+bdadxgiven  g(θ)=eθ(tanθ-θ)

Q: 2) Find div( xi + 4yj + 2zk)

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Q: Find the absolute maximum and minimum values of the following function on the given interval. Then…

A: use derivative and critical points for absolute maxima/absolute minima

Q: Evaluate the integral by making the given substitution. sec(52)tan (5x)dz, u = 5x + C

A: we know that   dxndx=nxn-1d(secx)dx=secxtanx

Q: 5) Find the divergence of (√x² + y² + z² 5) kî + yî yj + zk)

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Q: 8). If y is a differentiable function of X, then the slope of the curve of; 3 = 6 at point where y=1…

A: Note: Since the student has mentioned to solve question no. (8), so we are solving according to…

Q: Graph the circle given below by moving the key points: To graph the circle, drag the center point to…

A: Solve the following

Q: can you please explain in words how the equation 3y^2 + 2xy + x^2 = 6 turned into 6y+2y+2x+2x=0??

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Q: (n^ + n)(n^ − n) = (n)H = H'(u) = Differentiate.

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Q: EC: Find the derivative of g(x) (x) = = 0 cos(t²) dt cos(1¹) di

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Q: Convert the following equation to Cartesian coordinates. Describe the resulting curve. rsin 0=6 The…

A: in cartesian  coordinates  x=rcosθ  and  y=rsinθgiven  rsinθ=6

Q: Find a "cartesian" equation for the circle which is given by the polar equation r = 2 sin 0, and…

A: Given query is to find the Cartesian equation and the centre of the circle.

Q: (-26)³ 6 If so, write it in the form f(x) = kx². Is the function g(x) The function is g(x) = kx² ||…

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Q: Given the homogeneous differential equation, (4D³-3D+1)y=0. The roots of the auxiliary are Om = -1,2…

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Q: The total cost of producing x magazines is given by the function C(x)=600+17x−0.1x2+0.5x3. Find the…

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Q: 14. Given g(x) = f(t². + 6t16) dt, find intervals on increasing / decreasing and concave up/ concave…

A: The given integral function is: g(x)=∫-22x t2+6t-16 dt

Q: Consider each function to be in the form y = kx, and identify k or p as requested. Answer with the…

A: Given function:- y=2x

Q: y = x^ex

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Q: A drone flies with velocity v(t) = 3ti-fj+4k. When t = 1, the drone is at (3,2,2).

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Q: 2 sin 0, 3. Find a "cartesian" equation for the circle which is given by the polar equation r = and…

A: The polar equation is  r=2 sin θ

Q: In the figure, the regions A, B, C and D bounded by the x-axis and the graph of f have the following…

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Q: Sketch the curve. r = 9 cos(8) O -4 ac -2 O y 2 -8…

A: Given query is to sketch the curve and find the area.

Q: sin(2x) x y = if x = л, dx = 0.25 find the differential. Round your answer to three decimal places.

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Q: : You need to provide a clear and detailed solution for the following Questions: Question 1 Given…

A: Solution: Given data, y"-7y'+10y = -2e3t

Q: Find dy/dx. x=tsin(t), y = t² + 5t

A: SOLUTION-

Q: Using Laplace transform to solve the IVP: y" - 7y=e5t, y(0) = 0, y'(0) = 0, then, we have Select…

A: We know, L{y"}=s²L{y}-sy(0)-y'(0) L{y'}=sL{y}-y(0) L{eat}=1/(s-a)