The equation of motion of a particle is s = t4 - 3t3 + t2 – t, where s is in meters and t is in seconds. (Assume t > 0.) (a) Find the velocity, v(t), and acceleration, a(t), as functions of t. v(t) a(t) = (b) Find the acceleration (in m/s2) after 1.5 s. a(1.5) = m/s2

Q: 3. A container in the shape of a (right) cylindrical can with an open top of volume 87 cm³ is to be…

A:

Q: In Exercises 33-42, determine if the given vector field has a potential. If so, find one. 34.…

A: Solved below

Q: The average price of a two-bedroom apartment downtown New York City during the real estate boom from…

A: Given: The average price of the property from 1994 to 2004:

Q: 8x³ + 4xy - y³ = 1

A: Given :

Q: After the release of radioactive material into the atmosphere from a nuclear power plant in a…

A:

Q: Evaluate the indefinite integral. (Use symbolic notation and fractions where needed. Use C for the…

A:

Q: A company manufactures and sells x television sets per month. The monthly cost and price-demand…

A:

Q: If f(x) = 6(a-3/+7), find f'(2). Find f'(5).

A:

Q: 9. 5- 8. 7- 4- h(x) 6- 3- 4 g(x) 3. 17 4 3. X-values 1 3. X-values 4 g(x) If f(x) then h(x) f'(1) =…

A: This is a problem related to derivative of the function. Based on the general formula and concept we…

Q: Use local linear approximation to estimate In(1.08)

A: Given problem:- Use local linear approximation to estimate ln(1.08)

Q: Write the logarithmic equation in exponential form. log7343 = 3 7³ = 77 7343 = 2 7³ = 14 3437 = 2 7³…

A: We will write in exponential form.

Q: b) c) dx x²(x²-16)2 S S- dx 1 (4x²+3)2 S. X = X = dx = dx =

A:

Q: J 3 If f(x) = then f'(x) = f'(-5) = = to dt > Next Question

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: 5. Evaluate [62³e¹dA; R= [0, 2] × [0, 2] R

A:

Q: (r2 – 4xy – 2y2) dx + (y2 +4xy – 2x2) dy = 0 - Solve

A: To solve the differential equation.

Q: Evaluate Ic (2x - y) dx + (x + 3y) dy. C: arc on y = x5/2 from (0, 0) to (4, 32) X

A:

Q: 3. A container in the shape of a (right) cylindrical can with an open top of volume 87 cm³ is to be…

A:

Q: sec7(t) tan(t) dt Evaluate the following integral using substitution rule or integration by…

A: We have to find the solutions

Q: Find the slope of the tangent line to the curve - 2x² - 2xy - 1y³: 1y³ = - 11 at the point (-2,-1).

A:

Q: Consider the following. y 2 y=4-x² (2.0), X 0.5 1.0 1.5 2.0 2.5 3.0 (a) Form the integral that…

A:

Q: 2. If the Profit function for producing x units is P(x) = 0.0035x³ + 120x, then the marginal profit…

A:

Q: 8. Find the scalar equation of the line passing through the point (1, 5) that has a normal vector…

A:

Q: or each of the following integrals, indicate the trigonometric substitution that could be used to…

A:

Q: 4. Elizabeth needs 2 1/3 cups of sugar for vanilla cake and 1 3/4 cups of sugar for chocolate cake.…

A:

Q: Use Cramer's Rule to solve this system of linear equations for y only: 2x - 4y - 2z = - 4 4x + 3z =…

A:

Q: The logistic growth function f(t)= 116,000 1+5500 e describes the number of people, f(t), who have…

A: f(t)=116,0001+5500 e-tA)when epidemic begin;t=0f(0)=116,0001+5500=21.087The number of people…

Q: Determine whether the alternating series converges. 31n k Σ(-1) k k=3 The series diverges.

A:

Q: Consider the following. f(x) = 25 25 20 15 10 g(x)=x² 5 X -4 -2 2 4 6 i (a) Form the integral that…

A: We are given a shaded region bounded by functions  f(x) =25 and g(x) =x2 where x≥0 We have to  1.…

Q: For the plane curve x = 4t, y = 3t²1, where 0 ≤ t ≤ 3, the arc length is given by 3 [ f(t) dt. Find…

A:

Q: Evaluate the indefinite integral. (Use symbolic notation and fractions where needed. Use C for the…

A:

Q: 21 · 8* cos (8*) dx =

A: ∫21*8xcos(8x)dxSubstitute u=8x→dudx=ln(8)*8x→dx=1ln(8)*8xdu=21ln(8)∫cos(u)du

Q: Find the length of the part of the curve y = = between x = 1 and x = 2.

A:

Q: * Using the formula sin(bx)] dx = (721 ) eax [a sin(bx) – b cos(bx)] + C a² + b². |[e-8x sin(6x)] dx…

A:

Q: The equations for free fall at the surfaces of Saturn and Jupiter (s in meters, t in seconds) are s…

A:

Q: 1. If z = f(x, y) has continuous second-order partial derivatives and x = r cos 0, y = r sin 0,…

A:

Q: Find the absolute maximum and absolute minimum values off on the given interval. (Round all answers…

A:

Q: 3. A snowball is rolling down a hill, getting bigger as it goes. Assume the snowball remains a…

A:

Q: What is the difference between a function and a parametric curve? Make sure to justify your answer.…

A: This is a problem related to function and parametric equation for the same. Based on the general…

Q: Evaluate the limit 5 + 71 lim 2 - 5x

A:

Q: QUESTION 15 Find the polar equation for the curve represented by the given Cartesian equation. x + y…

A: To find the polar equation of the curve with given cartesian equation.

Q: Let y = 2x². Find the change in y, Ay when I = 4 and Ar 0.1 Sesse Find the differential dy when = 4…

A:

Q: Full Solutions 1. CHOOSE ANY TWO of the following problems and determine i) the Optimization…

A: Note: There are multiple questions. No specific question has been asked.So, We will solve the first…

Q: Find the area of the region enclosed by the graphs of x = y³ - 14y and y + 3x = 0.

A:

Q: 4x - 82 6х — 10

A:

Q: Evaluate the integral of the following using Miscellaneous Substitution 3. x /x*+ 1dx

A:

Q: 1. Find the area of the region enclosed by the given curves. a) y - x² = 2x and x + 4 = y b) x = y¹,…

A:

Q: dr Let A be the area of a circle with radius 7. If dt 3, find dA dt when T I 7

A:

Q: Cours A swimming pool is nearly empty, holding only 5100 gallons of water. A system is set up so…

A:

Q: a) Find a polynomial P(x)= a + a₁x+0₂2² +03x³ +ay 20² +a5 205 of degree 5 such that as = 1, and…

A:

Q: In the simple model of a national economy:

A: answer is in next step