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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

Closed unit disc

Please see attachment Find the maximum of...over the closed unit disc.

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)?

Average

Mary, Pete and Michael were the only 3 students in a seminar in history. The class consisted of 15 sessions. Mary missed 1 of the classes, Pete missed 2 of the classes and Michael missed 2 of the classes. What is the average number of classes missed per student?

Word problem

A survey of college sophomores showed that 5/6 of the males were taking a mathematics class and 3/4 of the females were taking a mathematics class. One-third of the males were enrolled in calculus, and 1/5 of the females were enrolled in calculus. If just as many males as females were surveyed then what fraction of the surveyed

Find a parametric representation for each of the surfaces.

Find a parametric representation for each of the surfaces. 1.) The part of the sphere x^2 + y^2 + z^2 = 4 that lies above the cone z= square root of x^2 + y^2 2.) The part of the cylinder x^2 + z^2 = 1 that lies between the planes y= -1 and y= 3

Conservative force

Please see attached page for problem. From a plot of F guess whether it is conservative. Then determine whether your guess is correct.

Area under loop

Find the area of the region enclosed by one loop of the curve. r = 6sin(11*theta)

Relationship between weight and blood pressure.

See attached file. The relationship between the weight of a child (w, in pounds) and the child's blood pressure (P, in millimeters of mercury) is given by the function above. a. Find the rate of change of blood pressure with respect to weight when the child's weight is 60lbs. b. Find the weight (to the nearest pound)

Metrics

For x an element of R upper k and y an element of R upper k define d1 (x, y) = max{|x of i - y of i| : 1≤i≤k} and d2 (x, y) = min{|x of i - y of i| : 1≤i≤k}. Determine for each of these whether it is a metric or not. Fully explain your answers. Thank you so much.

Find the polar coordinates.

The Cartesian coordinates of a point are given. Find the polar coordinates (r,theta) of the point, where r > 0 and 0 less than or equal to theta < 2pie points are (-1, square root of 3)

Converting Rectangular and Parametric Equations

Eliminate the parameter. Find a rectangular equation for the plane curve defined by the parametric equations. x = 3t, y = t + 7 y = 3x + 7 y = x/3 + 7 y = x/3 - 7 y = 3x - 7 Find a set of parametric equations for the rectangular equation: y = 2x - 2 x = t/2; y = t - 1 y = 2t; 2x = t + 2 y = 2t2 -

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..

What is the period of the current?

The current I , in amperes, flowing through a particular AC circuit at time t seconds is I = 120sin(70(pi)t-pi/6) What is the period of the current? 1/35 seconds pi/120 seconds 1/420 seconds 70m seconds

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