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Basic Calculus

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

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

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

Mathematics - Calculus Sales Problem

Please help with the following problem. Provide a step by step calculation. Sales and Saturation Point : Integration using Separation of Variables - The rate of increase in sales ... (Please see the attached file) Sales: The rate of increase in sales S (in thousands of units) of a product is proportional to the current le

Solving Polynomials by factorizing

Factor 1. x^2 + 12x +36 - y^6 2.9y^2 + 12y + 4 - x^2 solve each equation n^2 + n = 72 (4x + 9)(x - 4)(x + 1) = 0 m^3 = m^2 + 12m (x + 4)(5x - 1 ) = 0 x^ + 6x - 7 = 0 A stereo system installer needs to run speaker wire along the two diagonals of a rectangular room whose dimensions are 40 feet by 75

Riemann sum and volume

See attached file Write a Riemann sum and then a definite integral representing the volume of the region, using the slice shown. Evaluate the integral exactly.

Calculus problem

Please help me in attached problems. A customer ordered a quadratic metal sheet with side length x0=10cm. What is the maximal acceptable error of the side length if the area of the metal sheet should be?... For each of the following functions: state if the function is monotone Decide if it is injective, surjective or bij

Pilot Off Course

A pilot, attempting to fly from Middletown to Westburg, a distance of 200 miles, notices after flying 180 miles that West burg is still 35 miles away because the heading was off by a few degrees. How many degrees was the heading off the desired course (to one decimal place)?

Solving Extraneous Equations

Please solve below exercises using the Equation Editor. Answers are already provided for you from the actual book. You must show however how you have arrived at the answer. Section 6.5 Exercise 55 Sophomore math. A survey of college sophomores showed that of the males were taking mathematics class and of the females

Converging Subsequence

Theorem: Suppose that a sequence S of real numbers has a subsequence that converges to a real number a. Then S converges to a. I know this is true as an if and only if statement, but I need a counter example to show that just one converging subsequence isn't enough. Here are two sequences I'm considering: {1,-1,1,-1,1,-1..

Displacement, Velocity, & Acceleration

1. A test vehicle on a track goes through photo gates spaced 25 m apart at the following times: 2.00 sec, 3.30 sec, 4.30 sec a. Plot the position versus time of the vehicle. b. Plot the average speed of the vehicle in the time intervals versus time. 2. A rally driver has to maintain a constant speed between c

Various calculus problem set

Please see the attached file for complete description 1. Write the first five terms of the arithmetic sequence: a1 = 3; d = 3 2. A spinner is used for which it is equally probable that the pointer will land on any one of six regions. Three of the regions are colored red, two are colored green, and one is colored yellow. If t

Third Prime

Please help, figured out first two primes but am having allot of problems figuring out the third prime. Also need help with additional problem. Thanks Find lim x ->∞ ( (3x-2) / (3x+2) )^x (3x - 2)^x / (3x+2)^x = lim x ->∞ f'(x)/g'(x) x(3x - 2)^(x-1)*(3)/ x(3x-2)^(x-1)*(3) =(3x - 2)^(x-1)/ (3x

Calculus Problems - secant line joining

Q#11. The graph of y=f(x)=x^2 + 2x is shown in the graph. i) Find the slope of the secant line joining (2, f(2)) and (4, f(4)). ii) Find the slope of the secant line joining (2, f(2) and (2+h, f(2+h)) _____ + _____ h Q#12. Suppose an object moves along the y axis so that its locations is y=f(x)=x^2+3x at time x(y

Integral Calculus and Position of an Object

1. R is the region bounded by the curve y = x^2 -2x and the x axis. Sketch the given region R and then find its area. 2. Using the following integral and the facts that v(t) = x'(t) at time t of an object moving along the x axis is given, along with the initial position x(0) of the object. Answer the questions a - c. x'

Related Rates

3.A pulley is suspended 13.5 m above a small bucket of cement on the ground. A rope is put over the pulley. One end of the rope is tied to the bucket and the other end dangles loosely to the ground. A construction worker holds the end of the rope at a constant height (1.5 m) and walks away from beneath the pulley at 1.6 m/s. How

Differential Equations and Vectors - Circle Equation

See the attached file. Question (1) First find a general solution of the differential equation dy/dx=3y. Then find a particular solution that satisfies the initial condition that y(1) = 4 Question (2) Solve the initial value problem dy/dx=y^3 , y(0) = 1 Question (3) Find the centre and radius of the circle describe

Finding the Optimum

The purpose of this project is to find the values of x and y that will yield the optimum (maximum or minimum) value of a system and the optimum value of a system using algebraic and graphical methods. Follow these ten steps (see mp1.jpg) to determine the optimum value of z and the values of x and y that yield the optimum valu

Transportation Cost

For speeds between 40 and 65 mph, a truck gets 480/x miles per gallon when driven at a constant speed of x miles per hour. Diesel gasoline costs 2.23 per gallon, and the driver is paid 15.10 per hour. What is the most economical constant speed between 40 and 65 miles per hour at which to drive the truck.

Velocity, Time and Displacement

A stone is dropped from a high cliff and falls with velocity v = 32t feet per second. How many feet does the stone travel during the first 3 seconds?

Why the Condition is Placed at the End of the Formula

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

finding area of region, total cost function, midpoint rule

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

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

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