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Basic Calculus

Short Calculus Problem for Resistance

**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)

Square base and no top is to be made from a square piece

19. A box with a square base and no top is to be made from a square piece of cardboard by cutting out a 3 inch square from each corner and folding up the sides. If the box is to hold 75 cubic inches, what size piece of cardboard should be used?

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

Irreducible Polynomials : Minimum Polynomial and Factorization

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 product of quadratic factors over

Lebesgue Measure Explained

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)

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?


A stone is thrown vertically upwards so that its height, measured in feet, after t seconds is given by s(t) = 100t - 16t^2. What is its initial velocity? Determine the maximum height of the stone and the time of flight of the stone. ---

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

Initial-Value Problem for System of Differential Equations

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

Interchanging Digits

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 interchang

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. ---

remainder of the lot is to have an area of 844 square yards

A corner lost has dimensions 25 by 40 yards. The city plans to take a strip of uniform width along the two sides bordering the streets in order to widen these roads. How wide should the strip be if the remainder of the lot is to have an area of 844 square yards?

List price and discount

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

Instantaneous Velocity

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).

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

Math problems:Algebra, Economics and some Calculus

Please see attached. 1. A factory working at 83% of capacity produces 231 widgets per day. How many widgets would it produce if it worked at full capacity? 2. Solve for X: x - 2.4 = 1.5 .3 3. Simplify: (Recall: x-3 = 1/x3) 91/2 a2/3 b-1/5 b4/5 4. PROTRAC, Inc. produces two line


Factorize: 1) (r+6)^3-216 2) 7(3k-1)^2+26(3k-1)-8

Average and Maximum Velocity : Flow of Blood

The velocity v of blood that flows in a blood vessel with radius R and length l at a distance r from the central axis is v(r)=(P/4(eta)l)(R^2-r^2) where P is the pressure difference between the ends of the vessel and (eta) is the viscosity of the blood. Find the average velocity (with respect to r) over the interval 0 &#8804;

Calculus: Four good word problems in calculus

#1 A tumor may be regarded as a population of multiplying cells. It is found empirically that the "Birth Rate" of the cells in the tumor decrease exponentially with time, so that B(t)=B0e^(-at)... find the limiting population of the tumor. (See attachment for full questions)