Complete parts a through c. S Consider an object moving along a line with the given velocity v. Assume t is time measured in seconds and velocities have units of a. Determine when the motion is in the positive direction and when it is in the negative direction. b. Find the displacement over the given interval. c. Find the distance traveled over the given interval v(t) 3t2 36t+105; [0,8] a. When is the motion in the positive direction? Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. O A. For t-values that satisfy (Use a comma to separate answers as needed. Type your answers in interval notation.) O B. The motion is never in the positive direction

Q: Help in #1 please.

A: Given information:The parametric equation is  

Q: Please sketch this by hand! And show all your steps as im doing my best to fully understand the proc...

A: (A) The function has an absolute maximum but no local maximum. This means the graph is strictly incr...

Q: Let R be the region bounded by y x, x 1, and y 0. Use the shell method to find the volume of the sol...

A: (A)It is given that, the region bounded by y = x2, x = 1 and y = 0.The region around the line y = -8...

Q: a. find the critical points of f on the given interval b. Determine the absolute extreme values of f...

A: Given information:The given function is .

Q: The region is formed by the graphs of y 4x and y 12-x. Find the volume of the solid obtained by revo...

A: For the shaded part the outer radius = 12-x and inner radius = 4sqrt(x).  

Q: Is y=ex +8x+5 a solution to the initial value problem shown below? y′−y=−8x+3 y(0)=6 Select the ...

A: The given differential equation is y’-y=-8x+3.The solution of the deferential equation is given as, ...

Q: skecth the graph a) f(x)=(x-2)2(x+3)   b)f(x) = x2-1/x   c)f(x) = 2x/x2-1    d)f(x) = -23 + 7x2 - 2x...

A: To sketch the graph of given function :

Q: Determine the following indefinite integral. 324 dx, x> In 18 A dx 324- e2x Type an exact answer. Us...

A: The given integral is,

Q: Marginal Revenue. Suppose the total revenue function for a blender is R(x)= 36x-0.01x2 dollars where...

A: The total revenue function for a blender is R(x)= 36x-0.01x2 dollars where x is the number of units ...

Q: Find the intervals on which f is increasing and the intervals on which it is decreasing   f(x) = -2 ...

A: First, we find f'(x).

Q: The equation of the line tangnet to the graph of 24e^x at x=2?

A: Find the derivative of the given function.

Q: please explain how to do question 7c

A: The given integral is ∫(1-3x)4dx.

Q: Help with #8

A: Let's understand the formula for calculation of curvature.For a function, y(x) the curvature is give...

Q: Hello, How is tan^-1 (tan (6pi/7)=-pi/7 possible? I don't know how it should be a negative or to use...

A: First consider:

Q: How can I get the result? Which is the result?

A: The function is given by,

Q: Determine whether the alternating series converges or diverges

A: Check whether the series is convergent or divergent.

Q: Find the area, in square units, bounded above by f(x)=6x2 −2x−19 and below by g(x)=7x2 +12x+21.

A: f(x)=6x2 −2x−19 and g(x) = 7x2 +12x+21.As a first step, we need to find the point of intersection of...

Q: 3x4 y‴+9x4 =5xy′+5x5 y″+9lnx   Determine the order of the differential equation shown above.

A: The given differential equation is,

Q: If the marginal revenue(in dollars per unit) for a month is given by MR'= -0.006x+36, find the total...

A: The marginal revenue for a month is MR′ = -0.006x + 36.The total revenue from the production and sal...

Q: The following integral is  The integral of g(x)dx from 7 to 2

A: The given integrals are,

Q: The funciton f in the figure satisfies the lim f(x)=5 as x approaches 4.  Determine the maximum valu...

A: (A) From the inequality |f(x)-5|<1 , we\'ll find range of f(x) first.

Q: #28 please

A: The given function of hyperbola can be written in terms of y as: Plugging this value in the objectiv...

Q: SImplify   (h3-4h)/(h3-2h2)

A: Simplify the given expression as follows.

Q: I need help with this please. How do I find the volume generated by revolving the region bounded by ...

A: Given information:The region bounded by y = -sinx and y=0, from x= -2pi to x=0, about the x-axis

Q: Use logarithmic differentiaion to evaluate f`(x) f(x) = (5x)^(ln 5x)

A:

Q: Find the area of the following region, expressing your result in terms of the positive integer n 2 2...

A: Obtain the limits of the integral by equating the functions as follows.

Q: How do I solve the initial value problem using P(x), Q(x) and v(x)?

A: First we find P(t) and Q(t) by comparing with y\'+P(t)y=Q(t).

Q: Assume a person invests $12000 at the end of each year for 30 years at an annual interest rate of r....

A: Part (a)The future value amount should be equal to A = $ 1,000,000.Please see the white board.The mi...

Q: Consider the following velocity function. Complete the sentence: The same distance could have been t...

A: The given velocity function is,

Q: Is y=e6x −3x−2 a solution to the differential equation shown below? y′−6y=7x+3

A: Here given differential equation is:Find the solution of given differential equation and match the g...

Q: Use a reference triangle in an appropriate quadrant to find the given angle.

A: The given equation is,

Q: For the following function f, find the antiderivative F that satisfies the given condition.   F(v) =

A: First, we find the general solution using integration. 

Q: How can I do this? Which is the result?

A: Given:The function is 

Q: I need help on how to contruct the definite integral needed to find the area of the geometric shape ...

A: Formula of area of triangle is = (1/2)*b*h, where b=base, h=height 

Q: Let R be the region bounded by the following curves. Find the volume of the solid generated when R i...

A: The given curves are y=x, y=4x, y=16.The graph of the region formed by these curves is,

Q: How can I get the result? Which is the result?

A: To find the equation of the tangent line approximation T to the graph of f at the given point.The gi...

Q: 2 sec x Ay and the 2 In the figure to the right, the equation of the solid curve is y equation of th...

A: The curves are given by,

Q: Find the area of the region described. 18 The region bounded by y and y1 2 9+x The area of the regio...

A: y = 18 / (9 + x2)As a first step we need to find the points of intersection of the curve and the lin...

Q: Use the Substitution​Formula, Integral from a to b f left parenthesis g left parenthesis x right par...

A: Let us assume y=(sec x)/4

Q: Determine the radius of convergence of the following power series. Then test the endpoints to determ...

A: The power series is given as

Q: Decide which integral of the Divergence Theorem to use and compute the outward flux of the vector fi...

A: From the Divergence theorem, for a positively oriented boundary surface (outward Normal) of region E...

Q: Activity 6 Related Rates of 96 fi/min . How fast is the 11. A spherical hot air balloon is inflated ...

A: Firstly, we find dr/dt by using the formula of volume of sphere .We differentiate V with respect to ...

Q: PK P (K-P)e 8. Scientists use the Logistic Growth function P(t) = to model population growth where P...

A: The logistic growth function is given by,

Q: Suppose that the cost funtion for a commodity is  C(x)= 300+6x+1/20x^2 dollars (a) Find the marginal...

A: The given Cost function for a commodity is C(x) = 300 + 6x + (1/20)x2.(a) To find the marginal cost ...

Q: 1000 Find the marginal cost when q = 10. 9 The average coste for producing q units of a product is g...

A: The average cost c is given by ,

Q: If l0g x=0.35 and fog6N0.5, evaluate the fo llowig expression.

A: Here, we use the above log rules.

Q: Determine the area, in square units, of the region bounded by g(x)=6x+12 and f(x)=x2 +7x−8 over the ...

A: We have to find the area under the curve of g(x), then substract the area under the curve of f(x). T...

Q: y′=−2ex −2x2 +3x+6 y(0)=5 Solve the initial value problem above. Do not include "y=" in your answer.

A: Given that  y′ = -2ex -2x2 +3x +6; y(0) = 5.That is dy/dx = -2ex -2x2 +3x +6.dy =(  -2ex -2x2 +3x +6...

Q: Use any method to determine if the series converges or diverges. Give reasons for your answer.

A: Refer to the question.Here we have to find the convergence of the series,

Q: The problem and graph are imbedded in the image.

A: Given information:An arch is 645cft high and has a 600ft base. It can be modeled by the parabola