Activity 1.3.3. A water balloon is tossed vertically in the air from a window. The balloon's height in feet at time f in seconds after being launched is given by s(t) = -161? + 16t + 32. Use this function to respond to each of the following questions. b. Compute the average rate of change of s on the time interval [1,2]. Include units on your answer and write one sentence to explain the meaning of the value you found.

Q: Given the triangle below, find the exact value for sec(@). 13 12

A:

Q: The antiderivative of the function f(x) = 4 + 10x is + 5.0x? + c 4 5.0r? +c 4 + 20.0z? + c + 5.0z?…

A:

Q: Write the partial fraction decomposition of the improper rational expression. x4 + 2x3 + 8x² + 13x +…

A:

Q: Qz: IF U=h cx,g )= Lnce+ ě).show that %3D Sy

A:

Q: The antiderivative of the function f(z): + 9z is +3.0z² +c + 4.5z² + e 6 + 4.5z? + c -6 4.5z2 +c +…

A: Antiderivative of function f(x)=6x2+9x is…

Q: Draw the graph of f(x) = – 5" + 3 10+

A: Graph of 5x (a growth function)passes through (0, 1)whereas -5x is a reflection about x-axis.and…

Q: . The function y = -4 sin (3x + 6) - 1 shifts the graph 2 units to the right. True False

A: To tell whether the given function y = -4 sin (3x + 6) - 1 shifts the graph 2 units to the right or…

Q: You are watering the lawn and aiming the hose upward at an angle of inclination 8. Let rbe the range…

A:

Q: a. To maximize the area of the pen, the sides perpendicular to the barn should be 625 m long and the…

A: Given query is to find the dimensions of each barn.

Q: Evaluate the integral using the following values. x3 dx = 960, x dx = 24, 8. dx = 4 -5x dx

A:

Q: b) [E 1: Consider the series 22-2n 5 n+1 i) Show that the given series is geometric series. ii)…

A:

Q: The value C for the solution of the initial value problem f'(x) = x³ – 7x + 3, given that f(0) = 0.…

A: Given problem:- The value C for the solution of the initial value problem f'(x) = x3 - 7x + 3, given…

Q: Find the centroid of the region bounded by the given curves. 20) The region enclosed by the…

A:

Q: If the formula y = a° is changed by adding one as shown in red below. Which of the following best…

A: Solve the following

Q: A farmer finds that if she plants 40 trees per acre, each tree will yield 35 bushels of fruit. She…

A:

Q: Quly Please paots of antegation Solve the tollowing the 17 3. 3

A:

Q: . A-line perpendicular to the plane 3x-4y+z=1 passes through the point A(-1,3,2). Find the…

A:

Q: ) I would eed help to dentify the surface whose equation is given below, please?  2r^2 + z^2 = 1

A:

Q: 2 2. Evaluate the iterated integral 6x'y dady

A:

Q: A sky diver jumps from a reasonable height above the ground. The air resistance she experiences is…

A: We will find the velocities.

Q: In A ABC, we are told that c = 8, C = 59°, and B = 46°. Find b. Round to the nearest hundredth. A…

A:

Q: Find the absolute maximum value of f(x) = x2 – 2x + 18 over the interval [0, 5]

A:

Q: Find equations of the tangent line and normal line to the given curve at the specified point. y =…

A: On solving this we will get

Q: A person standing close to the edge on top of a 48-foot building throws a ball vertically upward.…

A:

Q: Find the angles of given that a = 30, b = 14, and c = 19. Round to the nearest tenth of a degree. B…

A:

Q: 9. Find the volume of the solid of revolution formed by rotating about the x-axis the region bounded…

A:

Q: Press Es 5. What is the amplitude of the graph below? 4+ -5+ -7- -8+ 4

A: Given problem:-

Q: 29. Find the volume of the parallelepiped PQRS if the vectors V(PQ). V(PR), and V(PS) are,…

A:

Q: You construct an open box with locking tabs from a square piece of material, 24 inches on a side, by…

A: Solution is here

Q: Consider the following parametric equation. x=7(cos(t) + tsin(t)) y=7(sin(t) - tcos(t)) what is…

A:

Q: Let f(x)=√2x2+2x+7f(x)=2x2+2x+7 f'(x)=f′(x)=    f'(5)=f′(5)=

A:

Q: 1)" Given: In(1+ x) = > if x < 1. n + 1 n=0 1. Find the Mlaclaurin series for f(x) = x ln (1+ 3)

A:

Q: 8. Which of the following is the solution to the equation sin? x + 3sin x - 4 = 0 0° 90° + 360k 90°…

A: Topic = Trigonometry

Q: Use summation properties and formulas to rewrite and evaluate the sum. 34 60(3² – 6j + 1) j-1

A:

Q: Suppose that f is a twice differentiable function and that its second partial derivatives are…

A: answer is in next step

Q: 3. What is the amplitude of the graph y = -4sin (x - 2)? The amplitude is. units. 2т 4

A: As we know that; The standard form of the sinusoidal function is: y=asinbx-c Where;…

Q: 00 12x Find a power series for f(x) , ]x| < 1 in the form an. (x? + n=1 Hint: First, find the power…

A:

Q: The cost, in dollars, to produce x designer dog leashes is C(x) = 3x + 7, and the price-demand…

A:

Q: ) f(x) = In(Vxe2x)

A: Given query is to find the derivative if the function.

Q: 8. Which of the following is the solution to the equation sin? x+ 3sin x - 4 = 0 0° 90° + 360k 90°…

A: Given query is to find the solution of the function.

Q: Use Part I of the Fundamental Theorem of Calculus to find the derivative of the function. 8(x) = f…

A:

Q: If f(x) dx = (2x – 14)12 + C, find f(x). %3D f(x) %3D

A:

Q: The value C for the solution of the initial value problem f'(x) = x – 7x + 3, given that f(0) = 0. C…

A: A detailed solution is given below

Q: Let f(x, y) = xe*Y. Find the maximum rate of change of f at the point (2, 1). хе

A: We will find the maximum rate of change.

Q: Determine the way in which the line [x, y, z] = [2,−3, 0] + k[−1,3,−1] intersects the plane[x, y, z]…

A:

Q: x sec (3x) tan (3x)dx

A: ∫ xsec3xtan3xdx

Q: 4 Se + 5x* + 10 cos x + 2)dx 5e" + x° + 10 sin x + 2x + c 5et + x 10 sin x + 2+c - et x° + cos x + 2…

A:

Q: Evaluate the following definite integral. 1 5. (2x + 7)2

A:

Q: Evaluate: (12t3-9t2 + 7)dt

A:

Q: 2/5 (0) M234n 16. 4. 7. 6. 4. 4. 3. 13 14 II 3. 12. 9. 7. 3. 14 3. 91 27 12 2. 91 2. a) - 91 7. 2.…

A: