iddle man who is 6ft tall is attempting to escape from prison. He runs at a speed of 14ft/sec in a straight line towards the prison wal which he thinks he can climb over. the gurad shines a spotlight which is located on the ground 100ft from the wall onto riddleman form a shadow on the wall. at what rate is his shadown on the prison wall decreasing when he is 60ft from the wall?

Q: 30. Physical Science A plane flying into a headwind travels 2200 miles in 5 hours. The return flight…

A: A plane flying into a headwind travels 2200 miles in 5 hours. The return flight along the same route…

Q: Solve for 0≤x≤ 10 3xln(sinx) + (sinx)x=4

A:

Q: For the following problem, find the quadratic function y = f(x) that has the given vertex and whose…

A:

Q: Determine and sketch the set of pairs (x, y) IN RxIR that satisfy | x/ +) y) = 1

A: if we use this principle to find the set of points (x,y) such that |x|+|y|=1.

Q: How would you solve the integral S x² This is equal to S da - S da + S da, 4x which are all easy…

A: The denominator of the integrand is .Write is as,

Q: Find the area of the region under the graph of f on [a, b]. f(x) = e-x/2; [-1, 6]

A:

Q: Let r(t) = (−5t5 + 1, −4e¯5t, sin(−2t)). 1 f F (1) Find [F(t r(t)dt (don't include the +C) r(t)dt =…

A:

Q: 2 derivative y=x²-a3

A:

Q: When we want to solve the integral using the method of partial fractions, we first factor the…

A:

Q: SOLVE: Y" - Sy=0 -

A: given differential equation

Q: A differentiable function f has one critical number at x = 8. Identify the relative extrema of f at…

A:

Q: Analyze the function below. Which of the following is/are true? 8f()81818 x+2 as x→-1+, f (x) →∞ as…

A: Function is not defined where denominator is equal to 0.

Q: Write the equation of the vertical line at which the graph is discontinuous. Then, write what y…

A: Given

Q: 45-60. Areas of regions Find the area of the following regions. 45. The region outside the circle r…

A:

Q: Find the area of the shaded region. y = 0 2 square units y 2 -2 y=x√√4-x² y=0 2 X

A:

Q: if f'(x) = 5 - (8/x^2) , x≠0, find the value of f(4) given that 2f(1) = 4 + f(2)

A:

Q: Let ŕ(t) = (3t¹ — 1, −et, 5 sin(−t)) Find the unit tangent vector T(t) at the point t = 0. Round to…

A: we have to find tangent.

Q: Sketch the level curves of f(x, y) = y + 2x r² +3 at k = 0, 1 on a common Cartesian plane.

A:

Q: 1. Show that vi = efx and y = Ιρλα Ε

A:

Q: 3. How long would it take to double a $1500 principal if: a. interest is compounded quarterly at…

A: The principal amount is $1500 and the rate of interest is 2.76%

Q: Niet t 8- 6 4- 2- -8-6-4-20 To A' 6 -8 -2- 2468 X José is able to move triangle A to triangle A…

A:

Q: Find the general solution of the differential equation. 16y(4) y(x) = = y

A:

Q: A radioactive material decays at a rate which is proportional to the amount of radioactivity…

A:

Q: Question 2.31) Show that the equation *¹²= 2x must have at least one solution on the interval (0,2).…

A: Question no. (2.31):To show that the equation  must have at least one solution on the interval .To…

Q: 5. * Let {an)neN be the sequence defined by a₁ = 1, for any n ≥ 1 (a) Write down a₁, a2, a3, a4…

A:

Q: |x = 1+ t 5. Determine the distance between the point (4, 3, 2) and the plane y = 2 + s z = 3+s+t a.…

A:

Q: Each derivative represents the first line of a "first principles" definition for some function f(x).…

A:

Q: 2. In Test 1, we have used the following theorem without a proof. Write up a proof for it. The…

A:

Q: (d) lim x→0 cos(a + x) cos(a — x) * (e) lim x48 * (f) lim xxx 2x - 1 2x + 1 X x In(e³ + 3) In(e5x +…

A: Note: Since you have posted multiple questions we will solve the first question for you. If you want…

Q: It is known that f g (x) dx = e³, f₁² g (x) dx = 4, and 4, and f g (x) dx = 12. Find S₂ g(x) dx. $9…

A: As per our guidelines we are supposed to answer only one question, so I solved first question…

Q: cot5 x csc ³ x dx | si S sin² x cos² x dx cos 7x cos 5x dx

A: To evaluating the following integrals.

Q: K 2 Find the average rate of change of the function f(x)= x + 7x from x₁ = 1 to x₂ = 3. The average…

A:

Q: If f(x) = 5 sec (3x), find f'(x). 15 sec (3x) tan (3x) Find f'(3).

A: We are given that f(x)=5 sec(3x)From the first part, we get f'(x)= 15 sec(3x) tan(3x)Now, we need to…

Q: Use the limit definition of the derivative to find the instantaneous rate of change of f(x) = 5x² +…

A:

Q: Critical Thinking Question: to be agreed upon by the group, and written below by the recorder.…

A:

Q: 2. Let C be the parametric curve

A:

Q: Find the integral. Stan'xsec¹x dx

A:

Q: Given the figure below... 18 what is the value of V. W? -18 6√5 -6√5 12 -12 6 -6 13 A 3√5 -3√5 √5 3…

A:

Q: Given the vector-valued functions е u(t)= e ti+e-4 + 4tk v(t) = −ti + 4t²j + 4k d find (ū(t) · v(t))…

A:

Q: Determine whether existence of at least one solution is guaranteed and whether uniqueness of that…

A:

Q: 1 Find the inverse function (on the given interval, if specified) and graph both f and f on the same…

A: The given function  for .The aim is to find the inverse function and sketch its graph.

Q: 4. Consider the function g(x) = 2-πXx XA if x ≤ a if x > a Use the IVT (Intermediate Value Theorem)…

A:

Q: The following chart shows student population in a certain elementary school over a 5 year period.…

A:

Q: Find the point of inflection of the graph of the function. (If an answer does not exist, enter DNE.)…

A: The given function is

Q: Fill in the blanks using the two graphs below. y = f(x) -10- -2 -3 -4 -10 f(6) y = g(x) *Be sure you…

A: We have to fill the blanks using the given two graphs.

Q: h→0 h 5. Use the limit definition of derivatives to compute f'(x), where f(x) = ax²+bx+c. Assume…

A:

Q: Evaluate the limit of the indeterminate quotient. 1²_1-12 lim 2-4 2-4 Number

A:

Q: 2. Find y' and y" for both of the following functions. a) y = ex sin x b) y = tan x

A:

Q: Evaluate the piecewise function. -10 8 10 f(4)= f(2)= f(-8)= -

A: given graph of function

Q: Calculate and type the final answer in the space. You may use either scientific notation or standard…

A: The given expression