### Velocity and Displacement

A toy rocket shot straight up from the ground and travels so that its distance from the ground after t seconds is s(t) = 150t - 16t2 What is the velocity of the rocket after 2 seconds have passed?

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A toy rocket shot straight up from the ground and travels so that its distance from the ground after t seconds is s(t) = 150t - 16t2 What is the velocity of the rocket after 2 seconds have passed?

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Determine which elements of Z_7 (Z sub 7) are primitive roots.

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(See attached file for full problem description)

Verify each equation is an identity (double angle used in this chapter). See attached file for full problem description.

Calculus: Integrate functions and use calculus to solve problems. 1. A company which produces earthenware wants to make a water container which will hold at least 400 ml of water. The water container is modelled by rotating the area enclosed by the graph of y = e^0.5x and the lines x = 0 and x = 5, about the x axis. Will thi

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From a raft 50m offshore, a lifeguard wants to swim to shore and run to a snack bar 100m down the beach. a. if the lifeguard swims at 1m/s and runs at 3m/s, express the total swimming and running time t as a function of the distance b. find the minimum time

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Set up an appropriate iterated integral to find the area of the region bounded by the graphs of y = x^3 - x and y = a(x^2) for x≥0. (take a to be a constant)

Numerical approximations to integrals typically get better -- i.e., their error goes down -- proportional to a power of N, the number of subintervals in the interval of integration. For the upper and lower sums, the error typically goes down like 1/N as N increases. For the midpoint and trapezoidal rules, the error typically goe

Find (with proof) an element a Є Q such that Q(√3, √10)= Q(a) . Find the minimum polynomial of √3 + √10 . Hence, or otherwise, show that x^4 -26x^2 + 49 is irreducible over Q. Find the minimum polynomial of √3 + √10 over Q(√3) . Hence or otherwise factorize x^4 -26x^2 + 49 as a

Please can you explain me with more detail about Lebesgue measure of Q. Why m(Q)=0 and m(In)=2/n? (See attached file for full problem description)

Characters are: Q. Z(2)[x] (mod 2), Z[x], Q, Z(2), Z(3), Z(5), Z(9). all mods ? Decide, giving your reasons, which of the following polynomials is irreducible over . Factorize those polynomials that are reducible into a product of irreducible factors. a) b) c) ? Find, with justification, all monic irreduci

Question: The wheels of a car have a 24-in. diameter. When the car is being driven so that the wheels make 10 revolutions per second, how far will the car travel in one minute?

Keep correct units in problems Water is flowing out of a conical tank(vertex down) of a height 10 feet and radius 6 feet in such a way that the water level is falling at 1/2 foot per minute. How fast is the volume of the water in the tank decreasing when the water in the tank is five feet deep? A 6 foot person walks away

Let Q(t) =< (less than or equal) C + integral from t_0 to t ( K(s) Q(s) ) ds, Where Q(t) is a nonegative function , C > 0 and K(s) >= 0. a).Show that: Q(t) =< Ce^( integral from t_0 to t ( K(s)ds) ), t >= t_0 b). What conclusion can be made if C = 0? ( Note that proof in a may fail is C = 0 ). I want a det

A rectangular theater seats 1620 people. If each row had six more seats in it, the number of rows would be reduced by nine. How many seats would then be in each row?

This an example from my text book and it gives the answer as 17,19,27,29,39 and 49 but it doesn't give steps to solve. On other questions I have been able to determine the equation but I can't seem to solve with 2 variables. Problem: Find all positive two digit odd numbers with this property: When the digits are intercha

1. (Finite Differences) Let f(x) = cos(x+2). Compute f'(0) using the difference quotients given below and step-size h = 2^-n, n = 1,... .5. D + f = (f(x + h) - f(x))/h D o f= (f(x+h)_f(xh))/2h For each difference formula, make a table with the following information. column 1: h column 2: Df column 3: f'(0) ? Df column

(See attached file for full problem description) --- Given a point P with spherical coordinates (4, pi/6, pi/4). Find the xyz coordinates and cylindrical coordinates for P. ---

A car dealer, at a year-end clearance sale, reduces the list price of last year's models by 15%. If a certain model has a discounted price of $8000, what was the list price? How much can be saved by purchasing last year's model?

Here is the problem as it is printed in the book (kreyszig: Advanced Engineering Mathematics. sec. 8.6. Problem 10): ----- (Elliptical Orbit) Consider the motion r(t) = cos t i + 2sin t j. Find the points of maximum speed and acceleration. Find the tangential and normal acceleration. ------ Here is where I am in the p

The displacement (in feet) of a certain particle moving in a straight line is given by: s=t^3/6, where t is measured in seconds. Find the instantaneous velocity when t = 1 Please show me all the steps, explain to me what instantaneous velocity is and how it is calculated (formula).

I would like for you to complete an optimization project. Examples include: the optimum number of hours to study for an exam, the best time to leave for work to avoid traffic, the optimum speed to drive a dirt bike up a hill to achieve the longest jump. I would like you to follow "The Process of Problem Solving" found below

Assume that the distance from New York to Miami is d and that half the distance is traveled at 45mph and half the distance is traveled at 55mph. If the average velocity is given by d/T=d/[0.5d/45+0.5d/55] I'm drawing a complete disconnect between the line above and this: =99/2=49.5(mph) I'm canc

I'm trying to find the average velocity from New York to Miami if half the distance is covered at 45mph and half the distance is covered at 55 mph.