The velocity on [4,6] can be modeled by the function v,(t) = 5t³ – 75t² + 360t – 550. %3D 49) Write a piecewise equation for v7(t) on the interval [2,9].

Q: Find the point (x0, y0) on the line 4x + 9y = 12 that is closest tothe origin.

A:

Q: Determine the speed as a function of time t for a particle having position function r(t) (t, 10t2,…

A: We have  r(t) = <t,10t2, t4>  Speed = ||r'(t)||

Q: The position of a particle is given by s(t) = t³ – 20.5t² – 2t, t > 0. When does the particle reach…

A: Given,           The position of a particle is given by st=t3-20.5t2-2t , t≥0.             The…

Q: The position of a particle moving horizontally is given by s(t) = 2t³ – 15t2 + 24t – 11, where s is…

A: Let's find.

Q: An insect is moving on the surface of a hot plate, the temperature of which at the point x units to…

A:

Q: Q2: Find the length of curve: x = cost, y = t+ sint, 0st<.

A: The given curve is: x=cos t ,       y=t+sin t ,        0≤t≤π

Q: i) Pre that at the Point x- of the Crerve Y: 4m-S, the radices of cervatune f' 5is

A:

Q: A particle follows the trajectory x(t) = 3 + 2t, y(t) = 10t – t2 with t measured in seconds and…

A: Given: xt=13t3+2tyt=10t-t2

Q: The r.m.s. value of f(t) = t² across [1,4] is %3D

A:

Q: Find the orthogonal trajectories of the family of curves r² + y² = 2my where m is a constant.

A: As given equation of curve is: x2+y2=2my Differentiate it with respect to x:…

Q: Find the set on which the curve 7 dt t2 + 6t + 15 y = is concave downward. Answer (in interval…

A:

Q: A particle moves on the x-axis with velocity given by v(t) = 3t4 − 11t2 + 9t − 2 for −3 ≤ t ≤ 3 .…

A:

Q: Find f(x) if y = f(x) satisfies %3D dy 42ya3 %3D dæ and the y-intercept of the curve y = f(x) is 4.…

A: Given that, y = f(x) and   dydx=42yx13 and y-intercept of the curve y = f(x) is 4. we have to find…

Q: Where does the line x = 1 + t, y = 3−t, z = 2t intersect the cylinder x² + y² = 16?

A:

Q: If s = 3t2 – 16t-2, when will acceleration be zero? An object moves along a horizontal line…

A:

Q: at what interval is  y=3x^5-5x^3 concave upward?

A: Given y=3x5-5x3

Q: Show that the function (x2+y2 t224이) is a Solution of Loplace's equation d2u dy?

A: It will be solution of given Laplace equation only when, it will satisfy it.

Q: Q3: Find the length of y=√x+2,1 ≤ x ≤ 7, Using ds = Y 04 1+²dy rotating

A:

Q: Find the tangent/sto the parabola (x + 2y)2 + 2x – y – 3 = 0, parallel to the line x – 4y = 2.

A: The equation of the parabola is given as  x+2y2+2x-y-3=0. On simplifying,…

Q: Show that the function f(x, y) = (y + ax)?e+ax satisfies the equation given by ах dy?

A: It is partial derivative problem

Q: The fictional city of Torontino radially has a population density of 1000e-0.017² people per km²,…

A:

Q: Use the contour map to estimate dg/8x at the point (V8,0) for the function g(z, y) = V9-7-. || g(x.…

A:

Q: (A)A particle is moving in a straight line according to the formula s(t) = 2t³ – 9t² + 12t – 15 .…

A: To determine: A particle is moving in a straight line according to the formula:…

Q: Fínd a differentiable curve y(x) that minimizes J = +

A: The objective is to find the differentiable curve yx that minimizes J=∫01y'x2+c2yx2dx if y0=0 and…

Q: Let z be a constant. Find the y" if y = v1 + 2zt + 5z't

A: Let z be a constant  To find y''if y=1+2zt+5z2t3

Q: Show that for motion in a straight line with constant acceleration a, initial velocity v0, and…

A: Let the acceleration a(t) = a, constant.Take integral on both sides to get velocity equation,

Q: If s = 3t – 16t-², when will acceleration be zero? An object moves along a horizontal line according…

A:

Q: The position function of a particle is given below. s(t) = 3 + 6t2 - 61t, t > 0 When does the…

A: Velocity function is the derivative of the position function. So differentiating s(t) with respect…

Q: Find the Maximum value of the function f(x, y) = x² – y² – 2y on the curve x? + y? = 25. %3D -

A: By langrange multiplier method n

Q: Find C so that the line y = 4x + 3 is tangent to the curve y x2 + C.

A: The given equations are y=4x+3 y=x2+c.

Q: find the value of c that the line y=3/2x+6 is tangent to y=c(sqr-root x)  c=

A:

Q: The area which is enclosed by the curve x2 – 10x +4y + y² = 196 is А. 12п В. 15п C. 144 D. 225n

A:

Q: Find c so that the line y = 4x + 3 is tangent to the curve y= x^2 + c?

A:

Q: Find the length of the curve x = 3t2 + 10, y=2t3+ 11, O<t<1.

A: Given,         The length of the curve x=3t2+10 , y=2t3+11 , 0≤t≤1We know that,         The length…

Q: The velocity on [4,6] can be modeled by the function v,(t) = 5t3 – 75t? + 360t –- 550. %3D 49) Write…

A: The piecewise function for velocity function is given as follows :

Q: The position function of a particle moving along the x−axis is given by x(t)=t3−4t2+5t−2, t≥0. Find…

A: We find the velocity by finding the first derivative of x(t)

Q: Suppose the position of an object moving in a straight line is given by s(t) = 7t³ -² +6. Find the…

A:

Q: Find the orthogonal trajectories of the family of curves x² + Y? = R? %3D

A:

Q: An insect is moving on the surface of a hot plate, the temperature of which at the point x units to…

A: As a first step we need to find the gradient of the surface and evaluate the same for the point (1,…

Q: Find f(x) if y = f(x) satisfies dy 50yz da %3D and the y-intercept of the curve y = f(x) is 2.

A:

Q: The position function of a particle is given by = t3 – 10.5t2 – 2t, t > 0 When does the particle…

A:

Q: Find the velocity and acceleration when t = 3. %3D X =t° -3t –5

A: Solution is given as below:

Q: Find the linear approximation of y = V1+ x at x = 0 and use it to approximate V1.05 7.

A:

Q: In the xy-plane, the line x + y = k, where k is a constant, is tangent to the graph of y = x^2 + 3x…

A: Given line is x + y = k, where k is a constant it is tangent to the graph of y = x^2 + 3x + 1…

Q: The position function of a particle is given below. s(t) = t3 + 3t2 - 6t, t 2 0 When does the…

A: The velocity function of a particle is given byv(t)=ddts(t)

Q: Find the isogonal trajectories to a family of straight lines y= cx that cut the lines of the given…

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Q: What is the length of the -3< x S3 segment of the y = v36 – x2 www vwwb w e curve?

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Q: WZ is the midsegment of the trapezoid UVXY. If XY = 6t, WZ = 10t – 2, and UV = 6t + 4, what is the…

A: