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Basic Calculus

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?

Interest and Finding the Equation of an Ellipse

1. An ellipse with major axis of length 1048 ft. and minor axis of length 898 ft. Assuming that a coordinate system is superimposed on the area in such a way that the center is at the origin and the major and minor axes are on the x- and y- axes of the coordinate system, respectively, find an equation of the ellipse. 2. One

Primitive roots

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

Calculus problem

An open container is such that each horizontal cross section is an equilateral triangle. its base has side of a length 10cm and its top has sides length 10x cm. each sloping edge has length 20cm. the surface of the container is modelled by part of an inverted triangular pyramid. the capacity V(x) litres is : V(x)=1/12 (x^2

Use calculus to solve problems and integrate functions.

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

Various Calculus problems

Any help would be appreciated on finding area of region, total cost function, midpoint rule. marginal cost. (See attached file for full problem description) --- A. Find the area of the region bounded by y=1/x and 2x + 2y=5 B. Find the area of the region bounded by the graphs of y= -x^2 + 2x and y=0 C. Find y=f

Given velocity and distance, please find the minimum time.

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

Short Calculus Problem

**See attached word document*** The total resistance, R, of a particular group is given by the formula: This formula can be simplified to the form where A and B contain no fractions. Please show how to re-write with no fractions and how you arrived at the new equation...

Sample Question: Double Integral

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)

Demonstrating behaviors of calculus

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

Irreducuble Polynomials : Find the Minimum Polynomial and Factorize

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

Irreducible Polynomials

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

Distance Traveled By Car Wheels

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?

Related rates

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

Finite Differences : Difference Quotients, Formulas and Rate of Convergence

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

Finding cylindrical coordinates

(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. ---

Car dealership

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?

Vector differential calculus: velocity and acceleration

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

Business Calculus : Come up with an original optimization project.

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

Average Velocity : Different Speeds over Two Distances

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