A toy rocket is shot into the air. Its height, in meters, after t seconds is given by h(t) = -4.9t^2 + 8t + 1.2 a)Determine the height of the rocket after 3 s b) Determine the rate of change of the height of the rocket after 2 s and 4s. c) How long does it take the rocket to hit the ground? d) How fast was the rocket traveling when it hit the ground? Explain your reasoning

Q: According to a study, a vehicle's fuel economy, in miles per gallon (mpg), decreases rapidly for spe...

A: The given graph is:

Q: dy 3. 1+ sin 4y

A:

Q: Compute the discriminant D(x, y) of the function. f(x, y) = x' + yt – 6x – 2y² + 1 (Express numbers ...

A:

Q: In a college meal plan you pay a membership fee, then all of your meals are at a fixed price per wee...

A:

Q: p) Find f o g oh with its domain of definition: f(x) = |x – 4|, g(x) = 1 ,h(x) = Vx %3D %3D X - 1 c)...

A: We have to find the domain of the function in first problem.  We also have to find the function g(t)...

Q: 7. The height (in meters) of a projectile shot vertically upward from a point 2 m above ground level...

A: We have to find the velocity, maximum height and time to reach maximum height.   According to our gu...

Q: (a) Find all the zeros of the polynomial function P(x)=x² +6.x+ 20. Use a graph to help get started....

A: Explanation of the answer is as follows

Q: Test the series below for convergence using the Root Test. 2n +1 3n +4 The limit of the root test si...

A: Given ∑    n=1∞2n+13n+4n We have to find f(n) , limit and we have to check that series is converge o...

Q: 5 sin“(3t) dt

A:

Q: A If w= f (x, y), where x = rcos 0 and y = rsin 0 , show that 2 1 + 2 +

A:

Q: Using the Newton method evaluate 2x* + 24x3 + 61x2 – 16x + 1 = 0. Let the initial guess X, %3! 0.9

A:

Q: f(x+h) = x^2+2xh+h^2-3x-3h compute and simplify. f(x+h)-f(x) =

A:

Q: Find the general solution of the given second-order differential equation. у" - у' — 30у %3D 0 y(x)

A:

Q: Obtain Pole, zero, gain values of the transfer functions given below. Also verify your result theore...

A: We have to obtain the values of pole zeros and the gain of the given transfer function.   Note- As p...

Q: cot () 11. 12. sec

A: Find the value of  11) cot(5π/3)  12)sec(11π/6) 

Q: f(x) + x2[f(x)]³ = 10 and f(1) = 2, find f '(1). (1) = %3D

A: Please refer to the image below

Q: The number of visitors P to a website in a given week over a 1-year period is given by P(t) = 122+ (...

A:

Q: d) 14 tan*x dx

A:

Q: The given graph of the derivative f′ of a function ff is shown. Assuming the graphs continue in the ...

A:

Q: Find the directions in which the function increases and decreases most rapidly at Po. Then find the ...

A: See the details solution in below

Q: let

A: F(s) = (s+1)/(s+9),  

Q: Compute the following limit. 1-e3* as x approaches 0 3x O-7/3 O-5/3 O-2/3 O 2/3

A:

Q: x + 3)* = 3y*find the third derivative

A: Given query is to find third derivative.

Q: 3. Use partial fraction decomposition to find each integral. Show all your steps. x3-3x²+1 a) S *²-3...

A: First we divide the numerator by the denominator because the degree of the numerator is greater than...

Q: 102! can be simplified to without use of a calculator: 99!

A:

Q: Find dy / dx by implicit differentiation. xy + 5x + 5x2 = 2 dy / dx =

A: xy+5x+5x2=2

Q: Find each limit. Use - o or oo when appropriate. 4x -8 f(x) = - (x-8)4 (A) lim f(x) (B) lim f(x) (C)...

A: A)

Q: The included angle of the two sides of constant equal length s of an isosceles triangle is 0. (a) Fi...

A:

Q: The cube root of 64a+/27b³ (There is a divide sign also.) 3164a+/27b3 (All is under the radial and i...

A: We need to simplify 64a427b33. Now,                 64a427b33=64a4327b33=4aa327b33=4aa33b

Q: Question #3 a) Find the x-position of all critical points for f(x)= 4x' – 15x² – 18x +1 (Show work, ...

A:

Q: ydy y +4y+11

A:

Q: 8. Find the equation of the tangent line to the graph of y = ; at point P(4, –5). 9. Determine the i...

A:

Q: Counting techniques (Using permuations or Combinations): How many outcomes are possible if you roll...

A: Given query is to find the number of possible outcomes when we roll 4 dice.

Q: Find the maximum and minimum values of g(x) =1+ x + x2 + x³ + x4 + x on the interval [0, 2].

A:

Q: Explain the following intervals on the line numbers-3<x<5

A: We will explain the given interval on the number line in the following step.

Q: Consider the function f(r) (- 00, A, A, B), (B, C, and C, ox) where A, and C are the critical number...

A:

Q: x + + 8)(6y – 1) = 0 find the second derivative %3D

A:

Q: - A= 1 Then adjA IS 4 4 1 O -1 4

A: Topic:-  matrix algebra

Q: Problem 7. (1 point) Let f(x) Then (fo g)(2) =, (fo g)(x) =|| = 2x + 4 and g(x) = 5x2 + 5x.

A:

Q: 5. [(csc h5B- coth 5B) dß

A:

Q: (x) = 2x - 3           x = 5 Compute f -1 (x

A:

Q: Solve using integrable combination technique only: (x^2y^3−(6+1)y)dx+(x^3y^2+(9+1)x)dy=0

A: Solve using integrable combination technique only: (x^2y^3−(6+1)y)dx+(x^3y^2+(9+1)x)dy=0

Q: Evaluate the integral. TO 9t sin(7t) dt

A: Given query is to find the value of the integral.

Q: sinx - cosx + 1 sinx + 1 %3D Hint: the conjugate of the denominator XS200S sinx + cosx - 1 cosx is s...

A:

Q: Use any method to determine whether the series converge. 00 19 (a) > EI Vk + 1 This series * cos () ...

A: (a) The given series is: ∑k=1∞19k+1 Let, ak=19k+1, k≥1  

Q: An object moves along the y-axis (marked in feet) so that its position at time x seconds) is given b...

A:

Q: 13. Determine algebraically whether g(x)= is an even function, an odd function, or neither.

A:

Q: 04cm. If its heig ght . Figure 5.1

A: Note: - Since you have asked multiple questions, we will solve the first question for you. If you wa...

Q: +++ = 1 find the second derivative y

A: topic - second derivative of a function

Q: Determine whether the integral is divergent or convergent. If it is convergent, evaluate it. If not,...

A: