Find the average value of the function f(t) = 4 t sine) on the interval [0, 20]. Round your answer to 3 decimal places. O 4.152 O 0.2 O 0.192 O 0.152 O 8

Q: 22. A particle is moving with the given data. Find the position of the particle. (a) v (t) = 3t – H,…

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Q: 6y² -dA where D is the region in the 1st quadrant bounded by y =x' and y= 4x . Evaluate 9.

A: Here we have to evaluate the  integral of a function over a region.

Q: Evaluate the integral (Trigonometric Substitution) 1 (a²x6 – x8)Zdx

A: To find  the  value of given integral.

Q: Find the sum by adding each term together. Use the summation capabilities of a graphing utility to…

A: We have to find the sum of the given series.

Q: Two cars are initially 1200 miles apart. At the same time Car A starts driving at 35 mph to the east…

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Q: %234 #4 Detelmine whe ther the sories Ć 4"-3 4^_3^ converges or diverges. If it converges find its…

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Q: Rates of Change: Oscillating Spring At Answer the following question, and give a written…

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Q: x + 4 dx x² + 2x + 5

A: ∫x+4x2+2x+5dxx+1 is a scalable factor of x2+2x+5, so divide x+4 by x+1=∫x+1x2+2x+5dx+∫3x2+2x+5dx

Q: 18 of 19 50 where T<0< 4r as shown in the diagram A rubber ball is being spun in a outward spiral in…

A: Let's find.

Q: Given any second-order non-homogeneous differential equation, describe how you would decide between…

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Q: 1. Find the moving trihedral and the curvature at any point of the curve R(t) = cost î + sint j + k.…

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Q: Let f(x, y) = 2x2y + 3xy. Use the (limit) definition of partials derivatives to show that fx(x, y) =…

A: This question is related to Partial derivatives, we will solve it using given information.

Q: リ=ー"-4), find a) The x-intercept and the y-intercept b) The interval where the function is…

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Q: What are the slopes of the asymptotes for the hyperbola whose equation is 4x2-9y? = 36? %3D

A: Here, the given equation of the hyperbola is: 4x2-9y2=36 In standard from it can be written as:…

Q: Determine whether the sequence is increasing, decreasing, or not monotonic. (Assume that n begins…

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Q: Find the particular solution of the differential equation that satisfies the initial condition.…

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Q: f(a)'() マxtる %3D

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Q: Evaluate the integral sin x dx (2 + 3 cos x)2

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Q: For what value(s) does the graph of y=3x5 + 10x4 have an infliction? A. 0 and -2 B. -8/3 only C.…

A: An inflection point is a point on the graph at which the second derivative is equal to zero or…

Q: Sketch the following points in space three, A (4,5,3); B (1,7,4) and C (2,4,6). Prove that point A,…

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Q: Determine whether the series is convergent or divergent by expressing s, as a telescoping sum. 00 n2…

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Q: Differentiate f(x) = sin-(2x). Use exact values. f'(x) =

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Q: Convert the following function given in Cartesian Coordinates into Polar form. 25-y 25 Or = cos? 0-…

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Q: de 1+sin e+ cose CO

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Q: 5. Given y=af(1 Find when =1 if f(2) = tand f(2) = 5.

A: Topic = Derivative

Q: 5. Given R(t)= 2 sin ti+5 cos tj+tk. Find T (t) and N(t) of the mov by the given vector.

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Q: Evaluate the integral (2x + 6)dx x² – 2x + 17

A: Given ∫(2x+6)x2-2x+17dxTo evaluate integral:

Q: da

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Q: A mold grows at a rate that is proportional to the amount present. Initially there is 5 oz of mold,…

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Q: V 2 y = 3 Vx

A: Since you have asked multiple questions in a single request, we would be answering only the first…

Q: I am confused how to find the critical point

A: To find the critical point you need the step 2:

Q: A ball is thrown vertically upward from a point 112 ft above the ground with an initial velocity of…

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Q: A ball is thrown vertically upward from a point 112 ft above the ground with an initial velocity of…

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Q: Describe the graph of the equation. r = 19 sin 2t i + 19 cos 2t j O It is a circle of radius 19 in…

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Q: In Exercises 1–8, find the length and direction (when defined) of u X v and v X u. 1. u = 2i – 2j –…

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Q: 2y²e»* dx + 2xyey° dy = 0

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Q: The sides of an equilateral triangle are increasing at a rate of 10 cm/min. At what rate is the area…

A: let side of triangle = x    Given

Q: a 0 0 0 0b0 0 11. Using cofactor method, prove that det M = abcd %3D 00c0 0 0 0 d

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Q: Siven that y = f(x) passes through (2, 1) and f'(x) = 3x² - 5x, find f(x). %3D

A: Given query is to find the function

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Q: Evaluate the integral | 3t³ (t² + 4)5dt

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Q: 13. A model used for the yield of an agricultural crop as a function of the nitrogen level in the…

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Q: Give the generator, the directrix, and the rulings of the cylinder x = lnz. Draw a sketch of the…

A: We need to give generator, the directrix, and the rulings of the cylinder x = lnz.

Q: Lety = 4x² – 4x+3 (a) Find the equation of the tangent line to the graph of the function atX=2; (b)…

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Q: 10. Consider the function defined by f(x) = Vr. Is ƒ differentiable at r = 1? at r = 0? at %D x =…

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Q: 2. [Growth of a tumor] When the radius of a spherical tumor is 6 mm, it is growing at a rate of 0.1…

A: To determine how fast the volume is changing.

Q: Find: d/dt (1/square root of 2t) A. square root of 2t/4t B. - 1/square root of 2t C. 1/2t square…

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Q: 1 dx x+2

A: Given that a integration and we solve this integration by using general property of integration.…

Q: Suppose z is a function of x and y satisfying the equation rey + ye" + ze = 1. Use implicit dz dz…

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Q: Determine the indefinite integral 6.xV-5]7 dx by substitution. (It is recommended that you check…

A: We have to solve  ∫6·x3·x43-57 dx.