Share
Explore BrainMass

Basic Calculus

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?

Velocity

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

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?

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

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

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 ≤

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)

Exchange Rate

A) Suppose your company has an international operation. Last month, when the exchange rate between the US Dollar and the Japanese Yen was 130.00, your company contracted to purchase inventory from a Japanese company for Y13,000,000, payable in 30 days in Japanese currency. This month the exchange rate is onyl 125.00. Calculate,

Exchange Rate Gain or Loss

A) Suppose your company has an international operation. Last month, when the exchange rate between the US Dollar and Japanese Yen was 130.00, your compnay contracted to purchase inventory from a Japanese company for Y 13,000,000 payable in 30 days in Japanese currency. This month the exchange rate is only 125.00. Calcualte, if a

Business Calculus : Rate of Change, Slope of Tangent

1. Consider the following table: X 0 1 2 3 4 5 Y 1.5 2.4 3.6 4.5 5.6 6.7 For each of the following intervals, find the average rate of change: (a) [0,1] (b) [0,3] (c) [2,5] (d) [0,5] 2. Consider the following table: X 1 2 3 4 5 6 Y 24 26 28 27 25 23 For each of the following intervals, find the average rat

Usub and parts

Please give step by step detailed solutions and answers to all. Please oh please do not skip steps. I need to see all these problems done so I can understand them and the way to think of solving them. I cannot find a one on one tutor and since I am auditing this course just for knowledge the teacher does not want to waste the

Usubstitution and integretion by parts

Please give step by step detailed solutions and answers to all. Please oh please do not skip steps. I need to see all these problems done so I can understand them and the way to think of solving them. I cannot find a one on one tutor and since I am auditing this course just for knowledge the teacher does not want to waste the

Minimum possible width

A long rectangular sheet of metal strip is to be made into a rain gutter by turning up two sisdes at right angles to the remaining center strip. The rectangular cross-section of the gutter is to have an area of 18 in^2. Find the minimum possible width of the strip. Could you please show all work so I can better grasp the co

Related Rates Example Problem

A particle is moving along the curve y=sqrt x. As the particle passes through the point (4,2), its x-coordinate increases at a rate of 3 cm/s. How fast is the distance from the particle to the origin changing at this instant?

Related rates

A baseball diamond is a square with side 90 ft. A batter hits the ball and runs toward first base with a speed of 24 ft/s. (a) At what rate is his distance from second base decreasing when he is halfway to first base? (b) At what rate is his distance from third base increasing at the same moment?

Related Rates Example

A man starts walking north at 4 ft/s from a point P. Five minutes later a woman starts walking south at 5 ft/s from a point 500 ft due east of P. At what rate are the people moving apart 15 min after the woman starts walking?

Related rates

A spotlight on the ground shines on a wall 12 m away. If a man 2 m tall walks from the spotlight toward the building at a speed of 1.6 m/s, how fast is the length of his shadow on the building decreasing when he is 4 m from the building?

Related Rates and Differential Equations

(a) If A is the area of a circle with radius r and the circle expands as time passes, find dA/dt in terms of dr/dt. (b) Suppose oil spills from a ruptured tanker and spreads in a circular pattern. If the radius of the oil spill increases at a constant rate of 1 m/s, how fast is the area of the spill increasing when the radius

Finding Average Velocity & Instantaneous Velocity

If a ball is thrown into the air with a velocity of 40ft/s, its height in feet after "t" seconds is given by y = 40t-16t^2. a) Find the average velocity for the time period beginning when t=2 and lasting (i) 0.5 seconds (ii) 0.1 second (iii) 0.05 seconds (iv) 0.01 second b) Find the instantaneous velocity when t=2.

Tunnel Problem

In the summer of 1999, construction will begin on a 3000 ft. tunnel that will pass under the Mississippi River, connecting the cities of East St. Louis, Illinois and St. Louis, Missouri. A Missouri-based company has been contracted to begin excavating the tunnel from the Missouri side, while an Illinois-based company will begin

Integer Linear Regression

ASW Publishing Inc., a small publisher of textbooks, must make a decision regarding which books to publish next year. The books under consideration are listed in the following table, along with the projected three year sales expected from each book: Book Subject Type of Book Projected Sales (1000's) Business Calculus Ne

Calculus

30) If f(x) = ln(sin(x^2)), then f''(x)=? Explain. 31) The college is making parking lot, rectangular and enclose 6000 sq meters. A fence will surround the lot and on parallel to one of the sides will divide the lot into two sections. What are the dimensions in meters of the rectangle lot using the least amount of fen

Calculus problems - Limits and area

12) What is limit as h approaches 0 of [cos(pi/2 + h) - cos(pi/2)] / [h] Ans is -1. Explain. 14) The area of the region in the first quadrant between the graph of y=x times the sqrt of (4-x^2) and the x axis is? Ans is 8/3. Explain. 15) If x^2 + y^3 = x^3y^2, then dy/dx = ? Explain. Ans is [3x^2y^2 - 2x]