Let s(t) = 4t³ + 12t² – 180t be the equation of motion for a particle. Find a function for the velocity. v(t) Where does the velocity equal zero? [Hint: factor out the GCF.] and t t - - = Find a function for the acceleration of the particle. a(t) -

Q: 3. Differentiate the functions below. 5) y = (2x5 + 3)cos x²

A: Since you have posted multiple questions i can do first question as per our company guidelines…

Q: After his graduation, a Wilfrid Laurier University student departed Earth to find work on Mars. A…

A:

Q: Evaluate ff(3xy)dA, where R is the region bounded by y = 2x and y = x². R

A:

Q: Set up an integral for finding the Laplace transform of the following function: f(t) = { 1 ²+5₂ t 5,…

A:

Q: Calculate the integral, if it converges. If it diverges, enter e5x S²∞ 1+e5x dx = diverges for your…

A:

Q: The radius of a sphere was measured and found to be 8.0 cm with a possible error in measurement of…

A:

Q: Which of the following integral gives an equivalent area solved by the integral: S™/6 O So -1 cos…

A:

Q: Compute the gradient of the following function and evaluate it at the given point P. g(x,y)=x²-3x²y…

A:

Q: Find the component forms of v+w and v- w in 2-space, given that ㅠ ||v|| = 7, ||w|| = 3, v makes an…

A:

Q: Let an = an lim = n→∞ bn O Calculate the limit. (Give an exact answer. Use symbolic notation and…

A:

Q: Consider the following function. g(x) = x3 + 3x2 − 6 on [−3, 1] Find the derivative of the function.…

A:

Q: Strength of a Beam A wooden beam has a rectangular cross section of height h in. and width w in.…

A: We use optimisation techniques using differentiation to find the required dimensions. The answer is…

Q: Find [5 50e0.03x dx

A: I=∫50e0.03xdx∫eaxdx=eaxa+c

Q: Indicate whether each statement below is true or false. (a) If the graph of an equation passes…

A:

Q: The arclength of y = 2x³/2 for 1 ≤ x ≤ 3 is:

A: The function is given as , y=2x32 Find the arc length of y=2x32 for 1≤x≤3.

Q: Consider the function f(x) = 4x² - 4x4. (a) Find all critical numbers c of f. C = (b) f is concave…

A:

Q: A lighthouse stands 500 m off a straight shore and the focused beam of its light revolves four times…

A:

Q: Given the series Σ find the ratio (Express numbers in exact form. Use symbolic notation and…

A:

Q: Which of the following graphs represent the region whose area is denoted by the integral: 3 (2 sec…

A:

Q: 1. Draw and set up the integrals for the area in the 1st quadrant enclosed by x = 4y² and x = y¹/2.…

A: I have solved step by step in detail...go through the solution

Q: Find (s−1)′(−13) using the Inverse Function Theorem, given that s(x)=(−3x−1)/(−2x+9). Note that…

A:

Q: your answers. 5 -3 -6 1. [ 1 7 _3]

A: As per the rules we are supposed to answer the first question and rest other can be reposted.

Q: Find a function f(x) such that f'(x) = 7e² + 4x and f(0) = −2 f(x) =

A: We need to find out the function.

Q: Using the Inverse Function Theorem, what is (h−1)′(−8) given that h(x)=−3x+7/2x+4? Note that…

A:

Q: Consider the following position function. Find (a) the velocity and the speed of the object and (b)…

A:

Q: In R³ you are given the vectors a = (21,-9, -21,-4) b = (x, -35, -16, -23) Choose a such that b…

A:

Q: In(x) x² -dx

A:

Q: 19. ſ² z² In z dz 0

A:

Q: Consider the following series. n = 1 Find the following limit. (If the limit is infinite, enter 'co'…

A: Please see the below picture for detailed solution.

Q: Find the solution to the IVP y" + y = f(x), with y(0) = 1, y'(0) = −1, where 0 x 3π f(x) = 0 using…

A:

Q: Suppose f(x) = x³ − 6x² − 63x + 10. Find the absolute extrema of f on each of the following…

A:

Q: QUESTION 1 If f(x) = 3x +5π, -T<x<T, Then the sum of the Fourier coefficients ao+b₁+ b₂ + b3 is…

A: Please see the below pictures for detailed solution.

Q: r = ep 1 - ecose

A: Given    r=ep1-ecosθ

Q: Find the tangent plane to the equation z = z = > Next Question 5e² -2y at the point (4,8, 5)

A:

Q: Consider the following series. n = 1 Find the following limit. (If the limit is infinite, enter 'co'…

A:

Q: Consider the function in the graph to the right. The function has a maximum of at x = The function…

A: The function has a maximum of -1 at x = -3, meaning that the function reaches its highest value at x…

Q: Find the solution of the following initial value problem. = 9x (x² - 1); g'(x) = 9x xo The solution…

A:

Q: Replace the polar equation r = The equivalent Cartestian equation is y = Choose the correct graph…

A:

Q: Consider the following. u = (5,5), v = (4, 6) (a) Find the projection of u onto v. (b) Find the…

A:

Q: Evaluate the expressions. (Simplify your answers completely. Use only positive exponents in your…

A: Algebra

Q: Match the graphs below with the following descriptions by indicating the graph corresponding to each…

A: Solution: 1. The temperature of a metal ingot placed in the furnace and then removed.

Q: Suppose that the position of a particle is given by s = f(t) = 7t³ + 2t +9. (a) Find the velocity at…

A:

Q: An object is dropped from a tower, 144 ft above the ground. The object's height above the ground t…

A:

Q: 6л Graph the set of points whose polar coordinates satisfy the equation 0= 7 бл Choose the graph…

A:

Q: At what points is the following function continuous? f(x) = x²-2x-8 X-4 6, 1 x #4 x = 4 The function…

A: f(x)=x2-2x-8x-4,x≠46,                   x=4at x=4, f(x)=6

Q: Calculate the Wronskian, W(y₁, ₂'' 1 if the set is linearly independent or not. 1. y₁ = sin2x, y₂ =…

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: 8. Draw a right triangle (with labeled sides) representing the angle (cot-¹(x/2)) and find sin(cot…

A: Since you have posted multiple questions i can do first question as per our company guidelines…

Q: How do I get the explicit solution of the exact ODE (5y−2x)y′ −2y=0?

A:

Q: tion about the origin. hat is the 13. Let T: R2 R2 be the linear transformation such that T(e₁) and…

A: Please see the below picture for detailed solution.

Q: Find the smallest positive root of the equation ex cos(x) 201 Correct to 4-decimal Places, take Xozl…

A: