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Basic Calculus

Calculus: Related rates problem using a shoebox-shaped hall.

A multipurpose shoebox-shaped hall is planned. Its length is supposed to be x = 50 meters, the width is supposed to be y = 30 meters, and the height is 10 meters. Furthermore, an expensive diagonal beam is planned, hosting a movable camera car, starting in one (left, back, down) corner and going through the whole hall until

Differentiation and Graphing

Consider the curve xy^2 + y = 3 - x^2. Use implicit differentiation to find the derivative dy/dx Hence determine the tangent to the curve at the point (-2,1) A stone dropped into a still pond sends out a circular ripple whose radius increases at a constant rate of 0.5ms-1. How rapidly is the area enclosed by the ripple inc

Calculus problems

Assignment Problem 1 Given f(x)=x^2+2x+3 Find the difference quotient (f(x+h)-f(x))/h Use the definitional formula given below to find the derivative of the function. f^' (x)=lim?(h?0)??(f(x+h)-f(x))/h? Find the value of the derivative at x = 3. Word-process your solution below. ? Assignment Problem 2 Given,

Internet Resources

The Internet offers many resources to support mathematics instruction. Conduct a search for websites that offer free mathematics resources (e.g., math activities, games, and/or lessons for students). Choose at least one site, provide a summary of its offerings, and evaluate the effectiveness of these offerings in reinforcing mat


A tank is full of water. Find the work W required to pump the water out of the spout. (Use 9.8 m/s2 for g. Use 1000 kg/m3 as the weight density of water.) Part 2: A layer of water Δx m thick which lies x m above the bottom of the tank will be rectangular with length 8 m. Using similar triangles, what will the width be?

Real Valued function on its largest domain and Vectors

Hello, Ive got slight problems which i need to solve and understand for a entry test for a course which i hope to gain entrance into this week and im stuck on two questions on example test which i need help. see attached file can you please help me.

Solutions to Various Problems in Multivariable Calculus

Write out the chain rule for each of the following functions and justify your answer in each case using this following Theorem. Theorem: Chain Rule Let U ⊂ R^m⟶R^p and f:V⊂ R^m⟶R^p be given functions such that g maps U into V, so that f∘g is defined. Suppose g is differentiable at X_0 and f is differentiable at y_0

Use SPSS to test effect of gender on math skills for calculus students

High School teachers were interested in the effect of gender on Math Skills in their calculus students. Analyze and graph the data below to determine if males are better at these types of skills than females. Gender F F F M F M F M M F F M F M M M Math Skills 34 40 38 30 20 40 38 47 26 24 27 37

Applied Calculus Problems

1. Differentiate 5x-1/x / 3-ln x **in words, 5x minus 1 over x, divided by 3 minus ln x** 2. Differentiate (ln(3x) - e^2x +1)^-2 **at the end, is to the -2 power** 3. Find the price elasticity of demand at a price of $2 if D(x)=6 / 3x-1 **The price elasticity of demand is PE(P)= -p D' (p) / d(P) 4. Maximize the area

Precalculus Problems

1) One hundred stones are placed on the ground 3 feet apart, the first being 3 feet from a basket. If the basket and all of the stones are in a straight line, how far does a person travel who starts from the basket and brings the stones to it one by one? 2) 55 Freshman were interviewed about the classes they were taking this

Solving Precalculus Problems

I'm having trouble writing equations for word problems. I would like help in figuring out how to set up the right equations in order to find solutions to the following problems: 1) Marlene rides her bicycle to her friend Jonâ??s house and returns home by the same route. Marlene rides her bike at constant speeds of 6 mph on

Physical and Social Domains

What are the most signification concepts that you have learned about the physical and social domains on the basis of your reading and experience with children? Explain why you chose these concepts. You can include personal experiences also.

Precalculus for technology

#46 Convert each degree measure to radians. 174degrees 50 minutes #58 Convert each radian measure to degrees, write answers to nearest minute. 9.84763 #84 Find the distance in kilometers between each pair of cities, assuming they lie on the same north south line. Farmersville CA, 36degrees North and Pen

Precalculus- please show me the work

Please show me steps to solve it: 1) The populations of termites and spiders in a certain house are growing exponentially.The house contains 100 termites the day you move in. After 4 days, the house contains 200 termites. Three days after moving in, there are two times as many termites as spiders. Eight days after moving in,

Precalculus: ant population on ships

A ship embarked on a long voyage. At the start of the voyage, there were 500 ants in the cargo hold of the ship. One week into the voyage, there were 800 ants. Suppose the population of ants is an exponential function of time. (a) How long did it take the population to double? (b) How long did it take the population to triple?


Please show me steps to solve this: Your Grandfather purchased a house for $55,000 in 1952 and it has increased in value according to a function y = v(x), where x is the number of years owned. These questions probe the future value of the house under various mathematical models. (a) Suppose the value of the house is $75,00

Precalculus for technology is depicted.

7.4 #20 use an identity to write each expression as a single trigonometric function value or as a single number. 1-2sin^2(22)(1/2degree) #30 express each function as a trigonometric function of x. cos 3x #56 write each expression as a sum or difference of trigonometric functions. 8 sin 7x sin 9x #58 write each expression

Precalculus for technology is reiterated.

7.1 #2. if cos (theta) = -.65, then cos(-theta) = _______ #8. find sin (theta), cot (theta) = -(1/3), (theta) in quadrant IV #26 find the remaining five trigonometric functions of (theta), cos (theta) = (1/5), (theta) in quadrant I #56 write each expression in terms of sine and cosine, and simplify so that no quotients appea

Calculating Time Needed to Empty Tank

Filling a tank. A water tank has an inlet pipe and a drain pipe. A full tank can be emptied in 30 minutes if the drain is opened and an empty tank can be filled in 45 minutes with the inlet pipe opened. If both pipes are accidentally opened when the tank is full, then how long will it take to empty the tank?

Sample size: Penny abolition

A researcher wishes to estimate, with 90% confidence, the percentage of adults who support abolishing the penny. His estimate must be accurate within 2% of the true proportion. a) Find the minimum sample size needed, using a prior study that found that 24% of the respondents said they support abolishing the penny. b) No preli

Simply intro calculus questions

1. Evaluate the following limits. a) lim 2x^2 + 0x - 18/x^3 - 27=______. x->3 b) lim (9x + 6)^-1 - 24^-1/x - 2=_______. x->2 2. Let f(x)= {x^2 + 1, x<-4 {-3x + 2, -4<x<5 { 2/x, 5<x a) lim f(x)=________. x->-4^- b) lim f(x)=________. x->-4^+ c) lim f(x)=

Calculating the Flow Rate in Different Scenarios

1. Upstream, downstream: Junior’s boat will go 15 miles per hour in still water. If he can go 12 miles downstream in the same amount of time as it takes to go 9 miles upstream, then what is the speed of the current? 2. Big plane: A six-passenger plane cruises at 180 mph in calm air. If the plane flies 7 miles with the wind


Calc Questions & Answers 1) Make a List of 10 Mathish words or terms that were covered in this Calculus class and provide a brief definition ( more than 10 words) 2) If Zero * Infinity is considered Non-Sense, What is Zero divided by Infinity? Give a 25 word or so explanation 3) Write the sum 2 + 4 + 6 + ..

Derivatives and Trigonometry Functions

I need the full calculations as well as the answers. If I can see how you got from A to B to C I can figure it out, just the answers wouldn't help.10 basic problems. Find the First Derivative K(x)= 1/ (x^4)-(x^2)+1 G(t)= square root of 6t+5 G(x)= 6/[(3x^2)-1]^4 F(r)=[(r^2)-(r^-2)]^-2 Find the Limit lim

4 Calculus questions

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 = &#8730;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!