Below is the velocity function, in feet per second, for a particle moving along a straight line. Find (a) the displacement and (b) the total distance that the particle travels over the given interval. v(t) = t³ - 15t² +66t-80 2≤t≤7 (a) Displacement: (b) Total distance:

Q: use implicit differentiation if applicable show proof (complete solution) y=e(x+c) is a solution of…

A: The given equation is

Q: », The graph on the left represents the function y = f(x). Graph the transformed functions listed.…

A: Given, the graph of the function y=f(x) (figure), we find the graph of the transformed functionsa.…

Q: Complete the table. (Round your answers to four decimal places. If an answer does not exist, enter…

A:

Q: Find dy dx dy dx for y = √u and u = x2 + 3.

A:

Q: Evaluate limx→−1 11/123 Does Not Exist O 0 O 1 2 x+2-1 x+1

A:

Q: Problem 3.4: Use Rationalization to Evaluate a Limit Algebraically Evaluate the following limit: aja…

A:

Q: A certain drug ingested by a patient is initially 20 mg. After 10 hours, the amount of the drug in…

A: Law of Decay is given as follows Where A is the amount any time t  is the initial amount k is the…

Q: Find y as a function of t if y (0) = 7, y'(0) = 3. y(t) = 25y" +50y + 106y = 0,

A:

Q: Figure 3 shows the amount of nicotine, N = f(t), in mg, in a person's bloodstream as a function of…

A: we are given a graph that shows the amount of nicotine N in mg in the blood stream against the time…

Q: Let g(x) - [₁6'd -3 g'(x) = -0 6t²dt. Find g'(x).

A:

Q: 65. Finding slope locations Let f(x) = 2x³ - 3x² - 12x + 4. - a. Find all points on the graph of f…

A: Given:

Q: Part D. Problem Solving: (1) Predicting the Cost of a Compact Car. In 2010, the cost of a compact…

A: Solution-Given in 2010, the cost of a compact car averaged $8000, In 2013, the cost of a compact car…

Q: If f(x) = 4x²-x², find f(x), f(x), F"(x), and f(4)(x). f'(x) F"(x) = F"(x) = f(4)(x) = 0000 Graph f,…

A:

Q: . a) Compute the point of intersection of the two lines r(t) = (2 + t, 1 + 2t, 5+ 3t) and r₂(t) =…

A: To solve the following problem given two parametric lines

Q: Consider the vector function r(t) = (6e²t)i + (5t sin(t) + 7)3 + (ln(8t + 1) − 4)k. dr -. Compute…

A: Concept:Putting the value of in the vector we will get the value of  Then putting this value in the…

Q: Example 3 Video Example < Find equations of the tangent line and normal line to the curve y=x√x at…

A:

Q: Find a function whose graph is a parabola with vertex (1, −4) and that passes through the point (3,…

A:

Q: Problems 9-18, The graph of a polynomial function y = f(x), is shown at right. Identify the…

A:

Q: Rewrite the following expression in terms of exponentials and simplify the result as much as you…

A: Given3sinh(3ln x)

Q: Find the point at which the line intersects the given plane. x = 3-t, y = 5 + t, z = 5t; x-y + 2z =…

A:

Q: For each of the table of values below, determine if the function represented is even, odd or…

A:

Q: Part D. Problem Solving: (1) Predicting the Cost of a Compact Car. In 2010, the cost of a compact…

A: The equation of the straight line passing through the points  is given by

Q: Poiseuille's Law gives the rate of flow, R, of a gas through a cylindrical pipe in terms of the…

A:

Q: The fox population in a certain region has an annual growth rate of 9 percent per year. It is…

A: A fox population in a certain region has an annual growth rate  percent per year.It is estimated…

Q: where the function f(x) = 2x² - 16x³ - 126x² +9 is increasing and where it is decreasing. tion start…

A: In this question, we will find the interval of increasing and decreasing.

Q: Find the derivative of the function. x x+5

A:

Q: 3x + 12y9z = 1, -24x + 48y + 56z = 0 parallel O perpendicular O neither If neither, find the angle…

A: 3x+12y-9z=1-24x+48y+56z=0

Q: How can I find the area of the region bounded by the given curves for y2 = x, y3 = x. The answer…

A:

Q: The solution to the Initial value problem x" + 2x + 17x = 4 cos(4t), x(0) = 0, r'(0) = 0 is the sum…

A:

Q: Find the gradient of the function at the given point. Function Point f(x, y, z)=√√x² + y² + z² (5,…

A:

Q: A right-circular cylindrical tank of height 8 ft and radius 4 ft is laying horizontally and is full…

A:

Q: Given this integral: [x²sin(x³) dx What is the best analytical method to solve it? Determine this…

A: The given integral is x2)

Q: Let f(x) In(5x - 25) Determine where f(x) is continuous, algebraically. (Enter your f(x) is…

A: For a  function  to be continuous at a point P ,f  must be defined at P

Q: sin 3x cos 2x dx

A:

Q: Find an equation of the tangent line to the graph of y = B(x) at x = 18 if B(18) = 0 and B'(18) = -…

A:

Q: 78-81. Derivatives from a graph Let F = f + g and G = 3f - g, where the graphs of f and g are shown…

A: The derivative of a function at a point is given by the value of the slope of the graph of a…

Q: (4) A soft-drink vendor at a popular beach analyzes his sales records, and finds that if he sells z…

A: A soft-drink vendor at a popular beach analyzes his sales records, and finds that if sells x cans of…

Q: +² (3+x)4 a) Find f'(x) using the Quotient Rule and the Extended Power Rule. b) Note that f(x) =…

A:

Q: Which of the following are true statements? Mark all that are true. ƒ(x) = 0 0 0 0 lim_f(x) = 8…

A: find true statements from given statements

Q: 11. Find the values of A & B that would make the given function continuous everywhere x²-4 f(x)=-…

A:

Q: Find the derivative of the function by the limit process. f(x) = 7x - 5

A:

Q: Find the critical point(s) of the function f(x, y) = 3x¹ + 3y¹ – xy. The critical point that lies in…

A:

Q: Find the derivative of the function. f(0) = cos(8²) F'(8) =

A:

Q: EXAMPLE 7 Video Example) Evaluate lim e³x. x-o SOLUTION 3 If we let t ==, we know that t→-00 as x→0.…

A: Evaluate limx→0−e3/x

Q: Find the solution of with y(0) = 9 and y'(0) = 7. Y y" + 3y = 126 sin(3t) + 162 cos(3t)

A:

Q: Find the four second partial derivatives. Observe that the second mixed partials are equal. z = 5xex…

A: Here we have  .......................... (1)

Q: Give an example of four sets A, B, C and D such that (AUC) x (BUD) ≤ (A x B) U (C x D).

A: The set A is a subset of B if every element of A is in B

Q: This is an example of an Undamped Forced Oscillation where the phenomenon of Pure Resonance Occurs.…

A:

Q: derivative of in, in (-3,0) the direction of P P(-3,0),

A:

Q: Q2: A particle move on the path has parabola shape with equationf(x) = a + bx + cx²; Find the…

A: