Consider the position function below. r(t) = (1-1²,3-5t4) for t≥ 0 a. Find the velocity and the speed of the object. b. Find the acceleration of the object.

Q: 7. f* (x² + 8) & dx CO (³ (x-1)

A: We have to solve integral

Q: If 15,18 log (14¹) A = B = = C: = = A log(x) + Blog(y) + Clog(z) then

A:

Q: Tutorial Exercise Evaluate the definite integral. I [²² sin5(x) dx Step 1 To solve the integral…

A: We have to integrate the given term.

Q: 2. Find the equation of the line tangent to the circle x² + y² + 6x - 2y - 15 = 0 at the point…

A: Here the given circle is , x2+y2+6x-2y-15=0 We need to find the tangent to this circle at the point…

Q: Q2/ A. Find the following limits. Answer four only. x+3 i. lim x-3x²+4x+3 X+) √2+1! x-1 lim x-1…

A: Since you have posted multipart questions i can do first three subparts as per our company…

Q: What is the value of x if log, √x-1=2? O 82 65 O 19 0-8

A:

Q: Find its length over the given interval. (Round your answer to four decimal places.) (No Response)

A:

Q: The number of bacteria in a culture is given by the function n(t) = 955eº. where t is measured in…

A: Use exponential function

Q: Question 3 Given the U= {1,2,3,4,5,6,7,8,9,10) and A = {3,4,5,6,7} B = {1,5,7,9} C = {3,6,9} D =…

A:

Q: Write the comple solutions. Rate will be given. Find the derivative and tangent equation equation…

A:

Q: f(t) = 4e-3t - sin 4t + cos 2t

A:

Q: Find the distance between the pair of points (2.5,8.2) and (-0.5,5.2). If necessary, express the…

A:

Q: 3 5. S (t + ²1) ²³ dt t

A: To evaluate the integral.

Q: nd the limit, if it exists. If the limit does not exist, explain why. limx→2 1−|x|^2/1−x^2 You…

A: Given :limx→21-x21-x2

Q: The equation u = 2uxx is O an ordinary differential equation in two variable: t and x O a partial…

A:

Q: Use the formula for continuous compounding to compute the balance in the account after 1, 5, and 20…

A:

Q: Find the first partial derivatives of the following function. f(x,y)=x²-3xy-6y²

A:

Q: J 4 sin xecos* d.c

A:

Q: What is the distance between two points (3,-1) and (-2,-5). 3

A: Given that the two points (3,-1) and (-2,-5)  To find the distance between the two points.

Q: Find r'(t), r(t0), and r'(t0) for the given value of t0. r(t) = (1 + t)i + t3j,    t0 = 1 r'(t0)  =

A: Given the curve r(t)=1+t i+t3 j, t0=1

Q: 4. What is the length of the latus rectum of the ellipse whose equation is + = 1. 16 25

A: Latus rectum of an ellipse is a straight line passing through the foci of the ellipse and…

Q: Solve the system, or show that it has no solution. (If there is no solution, enter NO SOLUTION. If…

A:

Q: 리 The amount of time in seconds, f, it takes for a bungee jumper to free fall is given by the…

A: The amount of time in seconds, t, it takes for a bungee jumper to freefall is given by the function…

Q: Given the equation 5 sin 6xy = 3, evaluate dy Assume that the equation implicitly defines y as a…

A:

Q: Consider the following situation, which involves two options. Determine which option is less…

A: Given: Consider the following situation, which involves two options. Determine which option is less…

Q: 4. A one-way road has an overpass in the form of a semi-ellipse, 15 feet high at the center, 40 feet…

A:

Q: Integration by Parts; For the following integral, which part would be assigned the u and the dv? S…

A:

Q: Consider the following situation, which involves two options. Determine which option is less…

A:

Q: The base of a solid is the circle x² + y² = 9. Cross sections of the solid perpendicular to the…

A: Given: x2+y2=9

Q: a. For the function and point below, find f'(a). b. Determine an equation of the line tangent to the…

A:

Q: Find the volume of the solid formed by rotating the region bounded by the graph of y=1+√x, the…

A:

Q: The interest on an account increases exponentially. If an initial investment of $5000 earns $900 in…

A: Given: Initial amount =$5000 Increase amount =$900 Time =2 years To find: Rate of increase at the…

Q: Use Figure 1 to evaluate the trigonometric function. Enter the exact answer. tan A = B 10 Figure 1 A…

A:

Q: Find the 2nd derivative of f(x) = √2x-x²

A:

Q: Find the volume of the solid that lies under the plane 3x + 2y + z = 12 and above the rectangle. R=…

A:

Q: find the limit, if it exists. If the limit does not exist, explain why. limx→2 1−|x|^2/1−x^2

A:

Q: 03/ A. For the following function f(x). Find: ji. iii. m=? 1-4X m -UX.=-u P(1,-1) f(x)=x-2x² The…

A: See this solution in below

Q: Find the unit tangent vector to the curve at the specified value of the parameter. r(t) = t³i +…

A:

Q: Let g=yf(xy). Show that: - მყ У ӘУ дд - X- = g дх

A:

Q: H.W: Evaluate the integral 30 [ (x²y - 2xy)dydx 0-2 1. 3. 5. 3 1 [ [(2x - 4y)dydx 2π π [[(sinx +…

A: 5.The given integral,        ∫π2π∫0πsinx+cosydx dy

Q: Sketch the function. v(x) = 0.2(x-3)²(x+2)³ Part 1 of 4

A: In this question, we will plot atleast six points to sketch the given function.

Q: Ỉ Ỉ y=0 x=0 (r’–6xy® +5y*) dxdy =

A: Given, ∫02∫03x2-6xy3+5y4dxdy

Q: Solve differential equation dx -(2ln5y+x-¹) 2xy-1

A: Solution is given below:

Q: There is a mound of g pounds of gravel in a quarry. Throughout the day, 400g pounds of gravel is…

A:

Q: If f(x) = x3 − x, find a formula for f'(x) using the definition of derivative. Do not use…

A:

Q: Use the graph of f to find the largest open interval on which f is increasing, and the largest open…

A:

Q: Question Find the angle, in degrees between 0 and 360°, which intersects the unit circle at the…

A:

Q: Find normal line and parallel plane to the function f(x, y, z)=√xyz-4 At point (1,2,8).

A:

Q: The direction field of the DE y' + ye³x+7 = −2y² will have a line segment with positive slope at the…

A: Given: y'+ye3x+7=-2y2

Q: A circular swimming pool has a diameter of 16 ft, the sides are 6 ft high, and the depth of the…

A: