7 The velocity of a moving vehicle is given by the equation v=(2t+3¹ The task is to: a) Use the Chain Rule to determine an equation for the acceleration when adv dt

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Q: You are stationary on the ground and are watching a bird fly by horizontally at a rate of 10 m/sec.…

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Q: A country's postal service will accept a package if its length plus its girth (the distance all the…

A: Let x be  a side of the package square base and y be the length of the package.

Q: 5 Given sine. and 13 5 0 ₁ + (-1/3) ² - O 5 13 12 13 12 5 ◎[-] 1+ 13 13 12 13 cose= 5 °(9)²+(3)³²-…

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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: A particle moves along the x-axis so that at time t > 0 its position is given by x(t) = 3t³ - 27t² +…

A: Given that , xt=3t3-27t2+45t-33 find the total distance traveled by the particle from 0≤t≤6.

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A: giveny=4x2-x3

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Q: A particle moves along the x-axis so that at time t 0 its velocity is given by v(t) = −20t³ + 60t.…

A: A particle moves along the x-axis so that at time t &gt; 0 its velocity is given by v(t) = −20ť³ +…

Q: becasue

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Q: Let F(t) = (4t¹ +4, t² − 4t³, 2tª). Find the line (L) tangent to r(t) at the point (68, 36, 32) L:…

A: Given vector:- r→t=4t4+4,t2-4t3,2t4

Q: Consider the function f(x)=x² e-6x. (a) Find the intervals on which f is increasing or decreasing.…

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Q: Find the values of x, y and z that correspond to the critical point of the function: f(x, y) 5x² −…

A: need to find out the critical point.

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A: We can find solution sets.

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A: Concept: Formulas used (f·g)'=f'g+fg'eln(a)=addxex=ex

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Q: Consider the region bounded by the curve y = 27x − x 4 and the x-axis. Use the trapezoidal rule with…

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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: A particle moves along the x-axis so that at time t 0 its position is given by x(t) = −t² − 2t + 35.…

A: solution:-particle's positionx(t)=-t2-2t+35where t≥0particle velocityv=ddtx(t)=ddt-t2-2t+35v=-2t-2

Q: Given the vector-valued functions u(t)= esti+e-¹ + 2tk v(t) = 2ti - 3t² + 3k d find (u(t) v(t)) when…

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Q: A particle moves along the x-axis so that at time t> 0 its position is given by x(t) = t4 - 18t² –…

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Q: J 1 (4-x²)3/2 dx

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Q: g(x) = 7 cos(x), 0 14 0 1 T O 1 T

A: Given query is to find average value of the function.

Q: 1. Consider the curve given by xy² - x³y = 6. dy_3x²y-y² dx 2xy - x³ a. Show that = b. Find all…

A: Topic = Derivative

Q: The graph of a function is given. Draw the graph of its derivative. 13) + -15 -10 + -5 15- 10+ 5+…

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Q: Please show your answer to 4 decimal places. - 4x² - y²-x+y Suppose that f(x, y) = e then the…

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Q: 112 15 A rocket is being launched. After a while, it rises at a constant velocity of 10 miles per…

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Q: Prove that the following differential equation: (1 + x2)y'' + 2xy' - 2y = 0 has the following…

A: To prove that y is solution of a differential equation then we just substitute the value of y' and…

Q: 12. D(x): = 1800 Vx+1 S(x) = 2√x + 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: each value 19. cos 8T (377)

A: The objective of the question is determine the value of cos (8π).

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Q: Find a function that satisfies the given conditions and sketch its graph. lim f(x)=0, lim f(x) = ∞o,…

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Q: If g(x, y) = x2 + y2 − 6x, find the gradient vector ∇g(1, 4) and use it to find the tangent line to…

A: Concept: Gradient of function g(x, y) ∇g(x,y)=∂g∂x,∂g∂y Equation of the tangent line at g at point…

Q: Determine whether the sequence with the given nth term is monotonic and whether it is bounded. Use a…

A: A sequence an is said to be monotone if it is either increasing (i.e., an≤an+1) or decreasing (i.e.,…

Q: 1. The income from Ming's robotics business for the next 10 years is given by the income stream f(t)…

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Q: 7 Newton's laws of cooling proposes that the rate of change of temperature is proportional to the…

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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: Solve the DE. (x³ + xy²-y)dx + (y³ + x²y + x) dy = 0 O arctan(‡)=C − x y O arctan (=) = C - x² - y²…

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Q: Determine whether the improper integral diverges or converges. 1 e2x + e-2x 1. converges O diverges…

A: Here we have to determine whether the improper integral diverges or converges. I=∫0∞1e2x+e-2xdx

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Q: Below are the polar coordinates. Find the Cartesian Coordinates. (0,5) (-5,0) (0.-5)

A: The polar coordinate is 5, 3π2 We have to convert the Polar coordinate to cartesian Coordinates.

Q: Solve the DE. (1 + y²) dx + (1+x²) dy = 0 O tan x + tan y = C e + ey = C O lnx + lny = In C arctan x…

A: Topic = Differential equation

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Q: dz 4-1² Siv Ans. T

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Q: ************** The length of a rectangle is increasing at a rate of 9 cm/s and its width is…

A: Given the following values of a rectangle, length, l=7cm and width, w=4cm rate of change of length,…