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Basic Calculus

Polynomial -- ball is thrown upwards......

If a ball is thrown upwards at 40 feet per second from a rooftop 24 feet above the ground, then its height above the ground t seconds after it is thrown is given by h = - 16 t2 + 40 t + 24. a. Rewrite the above formula with the polynomial on the right hand side factored completely. b. Use the factored version of the fo

Mathematics - Solving Calculus Equations

I really need help on these 4 problems and if you could please post your steps on how to do them, I'd greatly appreciate it. #1 Find an equation for the line tangent to the curve at the point defined by the given value of t. Also, find the value of d2y/dx2 at this point x=6t, y = √t, t = 1/25 The equation for the

Precalcus problems

I am have difficulty understanding these examples, I was able to do a few but am totally stumped on these. Any help would be appreciated. Thanks!

Crate Supported Cables

I'm having a hard time understand how to solve these problems. The textbook provides the answers. But I need help understanding the step to get to the answer. Also, some of the images maybe be slightly misfigured. I had a hard time cut and pasting the images. If possible please provide diagrams on how you got the solutions. Than

Throwing a wrench. An angry construction worker throws his wrench downward from a height of 128 feet with an initial velocity of 32 feet per second. The height of the wrench above the ground after t seconds is given by S(t)16t2  32t  128. a) What is the height of the wrench after 1 second? b) How long does it take for the wrench to reach the ground?

Throwing a wrench. An angry construction worker throws his wrench downward from a height of 128 feet with an initial velocity of 32 feet per second. The height of the wrench above the ground after t seconds is given by S(t)16t2  32t  128. a) What is the height of the wrench after 1 second? b) How long does it take for

Mathematics - Modelling and Simulation - Model the Data

The U.S. Bureau of Public Roads determined the following characteristic total stopping distances D depending on the velocity of cars. Speed M.P.H. (v) 20 30 40 50 60 70 80 Total Stop Distance D (ft) 42 73.5 116 173 248 343 464 a) Determine the best way to model the data. For example, by: a power function, an exponential fu

The Ferris Wheel Activity

A ferris wheel has a diameter of 50 feet and the center is 28 feet off the ground and the eight seats are evenly spaced around the circumference and the ferris wheel rotates counter clockwise once every 60 seconds. a.If the ride lasts 3 minutes, draw a graph that records the distance from the ground every 5 seconds for the le

The impact of mathematics on technology

Hello: I need help with the following: The impact of mathematics on technology. a. Prepare a 1,750 to 2,100-word paper which includes historical background on the mathematicians, their time period(s), and the contributions that affected their society and modern society. Provide specific examples of how the mathematical dev

Acceleration Due to Gravity

At time t=0, a skier leaves the end of a ski jump with a speed v feet per second at an angle, alpha with the horizontal, as shown in the diagram attached (see the attachment). The skier lands 259 feet down the incline 2.9 seconds later. Find the values of v and alpha correct to the nearest whole (0 decimal places).

Orthogonal trajectories of a family of curves.

I need to find the orthogonal trajectories of the family of curves, y = 1/(x+c) where k is an arbitrary constant. So far, I had figured on c = (1/y) - x m1 = -1/(x^2 + (1/y) - x) m2 = x^2 + (1/y) - x I don't know how to figure beyond that. Probably because those were calculated wrong. Please show me how it's done. Tha

Factorizing the polynomials...!!!

Need help figuring this out There are 10 problems = 0.25 points each for a total of 2.5 points. Partial credit may be earned. Problem 1-Find the pair of factors with a product of 18 & a sum of -9. x2 - 9x + 18 = 0 Factor Problems 2-10. Problem 2 x2 - 14x + 49 = Problem 3 15y4 - 35y3 + 10y2 = Problem 4 x3

Properties of Polynomials

1. What is degree of polynomial and is it a monomial, binomial or trinomial? 7x^4 2. Find the quotient and remainder (x^4-2x^2+3) / (x+1) 3. Write without negative exponents: (3xy^2)^-1 4. Factor out greatest common factor: 3x^4-6x^3-15x^2).

Mathematics - Calculus - Derivatives.

Apply differentiation rules to find the derivatives of the functions. Express the derivative dy/dx in terms of x without first rewriting y as a function of x. 1. y=u^5 and u=1/3x-2 Identify a function u of x and an integer such that f(x)=u^n. Then compute f '(x). 1. f(x)= ½+5x^3 2. f(x)=(x^2 - 4x

Rate of Rising Water Level

7. A water softener tank is basically a cylinder of height five feet and diameter 2.5 feet. Water is being pumped into the tank at a rate of 2 cubic feet per minute. How fast is the water level rising at the moment when the water level is 3 feet deep?

Calculus - Critical Points and Points of Inflection

Please see the attached file for the fully formatted problems. f(x) = x^4 - 4x^3 + 10 a) Find f'(x) and f"(x). b) Find all critical points and identify any local max/min. c) Determine the intervals where f(x) is increasing or decreasing. d) Find all possible points of inflections. e) Determine the intervals whe

Fixed and Variable Costs

Costs can be classified into two categories, fixed and variable costs. These costs behave differently based on the level of sales volumes. Suppose we are running a restaurant and have identified certain costs along with the number of annual units sold of 1000. Item: Raw Materials (cost for hamburgers) Total Annual Cost: 650

Mathematics - Applied Calculus - Logarithms and Exponents

Solve for x finding the exact answer simplified 1b) 2 1n x - 1/3 1n x to the second power = 4 Solve for x (estimate valuses to the thousandths) 2a) 1n x = 5 - 1n 2x 2b) 5 = 7 - 3 e to the -2x power 3) f(x) = 2 + 6 / 1 + e to the kx power 3a) IF f(1)=4 find the value of k 3b) find f(2) Applied Calculus 9th

Mathematics - Detailed Calculus Problems

#1 An equation of the line passing through: (3,3) and (3,4) is (A) x=3 (B) y=3 (C) y = 4x-3 . #2 Let f(x) = root{x}+2x^3 and g(x) = sin^2 x . (Note that sin^n x = ( sin x)^n . Then the composition f(g(x)) is (A) ( root{x}+2x^3) * sin^2 x (B) | sin x|+2 sin^6 x (C) none of the above. #3 Let f(x) = 1/2x^2 . The fracti

Evaluting the Integral

Evaluate the integral: 1. ∫cos^3 x sin^4 x dx 2. ∫sin^3 x dx 3. ∫cos^3 x/3 dx 4. ∫x/sqrt 9-x^2 dx 5. ∫1/sqrt 25-x^2 dx 6. ∫x sqrt16-4x^2 dx 7. ∫t/(1-t^2) ^3/2 dt 8. ∫sqrt 4x^2+9/x^4 dx 9. ∫1/x sqrt4x^2 +16 dx

Mathematics - Trigonometry Problems

A surveyor needs to determine the distance across a lake. The surveyor selects two points A and B, on one side of the lake, and one point, C, on the other side of the lake forming a triangle. the distance between points A and B is 50 ft. Angle A measures 70 degrees, and angle B measures 65 degrees. A bridge will be built between

Maximizing Revenue

You can operate a train if at least 200 people buy tickets. The fare will be $8 per person if 200 people buy tickets, but will decrease 1 cent for each additional person over 200. what number of passangers will bring the railroad the maximum revenue?

Mathematics - Calculus in Commerce- Marginal Revenue

The marginal revenue derived from producing q units of a certain commodity is R'(q) = 4q - 1.2q^2 dollars per unit. If the revenue derived from producing 20 units is $30,000 how much revenue should be expected from producing 40 units?

Mathematics - Calculus - Maximizing Profit

Profit - A manufacturer has been selling lamps at $6 apiece, and at this price, consumers have been buying 3,000 lamps per month. The manufacturer wishes to raise the price and estimates that for each $1 increase in price, 1,000 fewer lamps will be sold each month. The manufacturer can produce the lamps at a cost of $4 per l

Mathematics - Calculus in Commerce

Production The output Q at a certain factory is related to inputs x and y by the equation: Q = x^3 + 2xy^2 + 2y^3 If the current levels of input are x = 10 and y = 20, use calculus to estimate the change in input y that should be made to offset an increase of 0.5 in input x so that output will be maintained at its cu

Mathematics - Calculus in Commerce - Marginal Analysis

Marginal Analysis A manufacturer estimates that if x units of a particular commodity are produced, the total cost will be C(x) dollars, where C(x) = x^3 - 24x^2 + 350x + 338 a) At what level of production will the marginal cost C'(x) be minimized? b) At what level of production will the average cost A(x) = C(x)

Mathematics - Calculus - Minimizing Cost.

An electronic firm uses 600 cases of transistors each year. Each case costs $1000. The cost of storing one case for a year is 90 cents and the ordering fee is $30 per shipment. How many cases should the firm order each time to keep total cost at minimum. (Assume that transistors are use at a constant rate throughout the year and