A particle moves along the x-axis so that at time t 0 its velocity is given by v(t) = −20t³ + 60t. Determine all intervals when the speed of the particle is increasing.

Q: The figure shows the graph of a function. At x = 0 is the given function differentiable, and/ or…

A: Topic - Continuity and differentiability of a function for a function to be continuous at x=a,it…

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A: Given query is to find the integral.

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A: Let fx,y,z=2x2+3y2+z2-9 Gradient vector ∇fx,y,z=fxx,y,z,fyx,y,z,fzx,y,z

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Q: بنا -3 Amplitude: -2 Period: Midline: y = 7 6 Based on the graph above, determine the amplitude,…

A: We have given graph of the function  Amplitude is the height from the centre line to peak.…

Q: e Fundamental Theorem of Calculus Part II to find the derivatives of foll (2) = √²* √√₁ + 1³ dt

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Q: 5x Calculate all four second-order partial derivatives of f(x, y) = sin | ¹(5). fxx (x, y) = fry (x,…

A: We can evaluate the four partial derivatives by using the partial derivative rules

Q: 1. What is the length of the latus rectum of a parabola x² - 8x - 20y + 56 = 0?

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: Refer to the figure and find the volume V generated by rotating the given region about the specified…

A: Let's find volume when R2 rotated about AB line.

Q: Find the derivative of the function. 14 logg(t) t g' (t) = g(t) =

A: Topic = Derivative

Q: A pool shaped like the bottom half of a sphere is being filled at a rate of 22 cubic feet per…

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Q: If f(4) = 13 and f '(x) ≥ 1 for 4 ≤ x ≤ 7, how small can f(7) possibly be? Need Help? Read It Watch…

A: See this solution in below.

Q: What is the integrating factor of (1 + cos x) y' = sin x (sin x + sin xcosx sin x 0 1 + cos x CSC X…

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Q: A tank contains 70 kg of salt and 2000 L of water. Pure water enters a tank at the rate 6 L/min. The…

A: NOTE: Refresh your page if you can't see any equations. . y=amount of salt at time t…

Q: limx→5 x²+2x-35 x-5

A: We need to find limx→5x2+2x-35x-5.

Q: 1. At all times, the length of the long leg of a right triangle is 3 times the length x of the short…

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Q: Particle Motion from Equation (Level 2) Oct 23, 8:53:22 PM A particle moves along the x-axis so that…

A: we will find the required.

Q: Find a unit normal vector for the following function at the point P(1,−3,1): f(x,y)=x3 (Please show…

A: See the answer below

Q: an more work be shown on how to solve this

A: By using a scalar projection to find the shortest distance from the point 1,-2, 5to the plane given…

Q: A surveyor wants to know the length of a tunnel built through a mountain. According to his…

A: A surveyor wants to know the length of a tunnel built through a mountain. According to his…

Q: Find the indefinite integral. (Use C for the constant of integration 2 cosh(√x) X dx

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Q: Consider the region bounded by the curve y = 27x − x 4 and the x-axis.  Use Simpson’s Rule with six…

A: Here,             We have given a function now we have to find out the area bounded by the given…

Q: If lim x→3 f(x)-4 x-1 = 2, then lim f(x) = x →3

A: To find the limit of the function at x=3.

Q: A population of insects increases at a rate of 270 + 14t + 1.5t2 insects per day. Find the insect…

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Q: Find x. Round your answer to the nearest tenth of a degree. 11 4 x = []。

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Q: 3 (x-2) y'= y + 2(x-2)

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Q: Suppose f ¹ is the inverse function of a differentiable function f and f(2)=9, f'(2) = }, then (f…

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Q: The graph of y = g(x), shown below, consists of straight lines and a semicircle. Using known are…

A: We can evaluate the definite integral .

Q: limx→3 0 4 01 O O 3-x 4-√√²+7 O None of the above

A: We need to find: limx→3 3-x4-x2+7

Q: 5 -5 x dx =

A: Topic = Integration

Q: Suppose sin(0) = -and that 0 terminates in Quadrant IV. Fin a) tan(0) b) cos(0) 2 D 13 Ag 1+ it

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Q: Write the equation of the line in slope-interecept form that passes through (4,6) and (4,-3). Then…

A: To find the equation of the line passing through given points

Q: Find the principal unit normal vector to the curve at the specified value of the parameter. r(t)-+-2…

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Q: Find the unit tangent vector to the curve at the specified value of the parameter ()+8², ti T(1) -

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Q: Express the following as a single logarithm. In(13+x³) + ln x - ln (cosx) = |

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Q: The quantity demanded per month of an item is related to the unit price by the 45 demand equation…

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Q: At noon, ship A is 40 nautical miles due west of ship B. Ship A is sailing west at 20 knots and ship…

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Q: Oct 23, 9:35:15 PM A particle moves along the x-axis so that at time t 0 its position is given by…

A: Given query is to find interval where speed is decreasing.

Q: The sum of four times a number and 1 more than the number is the same as the difference between −27…

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Q: Let r(t) = ( −2+²+2, −3e¹, − 3 sin(2t)). Find fr(t)dt (don't include the +C) fr(t)dt = ([ ])+C

A: Topic = Integration

Q: Find the particular solution of the differential equation x²y" + 11xy' +29y=0 (x > 0) satisfying the…

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Q: Find the Maclaurin series for f(x) using the definition of a Maclaurin series. [Assume that f has a…

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Q: What is the least possible degree of the polynomial graphed above?

A: We know that ,                          Least degree of polynomial is given by n+1 . where n is…

Q: Suppose that f(x, y) = x² − xy + y² – 5x + 5y with D = {(x, y) | 0 ≤ y ≤ x ≤ 5}. - 1. The critical…

A: need to find out the critical point point of absolute maximum, absolute minimum.

Q: Find 7' (t), given r(t) = (- 4√t, - 3 ln(3t), 3e-³). F' (t) =

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