Questions on Algebra: Functions, Domain, NOT graphing answered by real tutors!

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Question 1193178: A rectangle is inscribed in a circle of radius r. If the rectangle has a length of 3x, write the area of the rectangle as a function of both x and r
Click here to see answer by ankor@dixie-net.com(22740)

Question 1193173: Let f(x)=√(3x-5 ) and g(x)=5x^2-3. Find (f∘g)(x) and (g∘f)(x), simplify your answers.
Click here to see answer by greenestamps(13200)

Question 1193243: Is f(x)-g(x)=g(x)-f(x) true for all functions? Justify your answer
Is (f+g)(x)=(g+f)(x) true for all functions? Justify your answer
Click here to see answer by ikleyn(52794)

Question 1193282: You have designed a screen saver for your computer that is an expanding circle, constantly changing colors. The circle starts as a dot in the middle of the screen and expands outward. With a 21" screen, you have a viewing area with a 10" radius. The circle reaches the corners in 5 seconds. Express the area of the circle as a function of time t in seconds.
Click here to see answer by ikleyn(52794)

Question 1193108: Use the logarithmic differentiation to differentiate the function
f(x)=∛((x^4 (x-2))/((x^2-2)(2x+3))) .

Click here to see answer by Edwin McCravy(20056)

Question 1193439: what two numbers get -135 and -6?

Click here to see answer by ikleyn(52794)

Question 1193439: what two numbers get -135 and -6?

Click here to see answer by josgarithmetic(39618)

Question 1193703: A garden supply store charges $50 per cubic yard plus a $60 delivery fee to deliver cedar mulch. This can be described by the function C(m) = 50m + 60, where m is the amount of cedar mulch delivered, in cubic yards, and C is the cost, in dollars
Find C(3) and explain what it means in the context of the problem.
b) If a customer paid $360 to have cedar mulch delivered to his home, how much did he order?
Click here to see answer by josgarithmetic(39618)

Question 1193868: A) Let g(x) = x^2+bx+11. The point lies on (-1,8) on the graph of g. Find the value of b.
b) The graph of f(x) = x^2 is transformed to obtain the graph of g. Describe this transformation.
Click here to see answer by ikleyn(52794)

Question 1193867: Correction: An infinite geometric series has the first term u1 = a and u2 = (1/4a^2)-3a, where a > 0.
a. Find the values of a for which the sum to infinity of the series exists.
b. Find the value of a when s infinity = 76.
Click here to see answer by math_tutor2020(3817)

Question 1193866: An infinite geometric series has the first term u1 = a and u2 = 1/4a^2-3a, where a > 0.
a. Find the values of a for which the sum to infinity of the series exists.
b. Find the value of a when s infinity = 76.
Click here to see answer by ikleyn(52794)

Question 1193870: In a controlled experiment, the temperature T°C of a liquid, t hours after the start of an experiment is T = 25 + (e^0.4t), 0 < t < 12.
a) Sketch the graph of temperature T for 0 < t < 12.
https://www.desmos.com/calculator/gqqogezzcm
b) State the temperature halfway through the experiment to the nearest 0.1 °C.
Halfway through experiment is t = 6
c) Find the time at which the temperature of the liquid reaches 100 °C. Give answer in hours and minutes, to the nearest minute.
T - 100 is reached at t=10.8 hours or 10 hours and 48 minutes
Click here to see answer by t0hierry(194)

Question 1193904: Let u=−3i+j+k and v=mj+nk, where m, n∈ . Given that v is a unit vector perpendicular to u, find the possible values of m and of n.
Click here to see answer by ikleyn(52794)

Question 1193919: Three consecutive terms of a geometric sequence are x−3, 6 and x+2. Find the possible values of x.
Click here to see answer by Edwin McCravy(20056)

Question 1193921: The graph of the quadratic function y = (3k - 1)(x^2) - 6x +1 where k € R, has a positive concavity and passes through the x-axis twice. Find the range of possible values for k.
Click here to see answer by Edwin McCravy(20056)

Question 1193920: The graph of the quadratic function y = (3k - 1)x2 - 6x +1 where k € R, has a positive concavity and passes through the x-axis twice. Find the range of possible values for k.
Click here to see answer by Edwin McCravy(20056)

Question 1193928: If f(x) = 2x and g(x) = 5x + 2, what is (f • g)(x) when x = 3?
Click here to see answer by josgarithmetic(39618)

Question 1193928: If f(x) = 2x and g(x) = 5x + 2, what is (f • g)(x) when x = 3?
Click here to see answer by ikleyn(52794)

Question 1193905: Given tan theta= -9/4, where 270 degrees is less or equal than theta and less or equal than 360 degrees
a) state the other five trigonometric ratios as fractions.
b) determine the value of theta to the nearest degree.
Click here to see answer by Alan3354(69443)

Question 1194136: If third quartile = 80, what percentage of the students who took the exam scored lower than 80?
Click here to see answer by Edwin McCravy(20056)

Question 1194242: If f(x)=5sin2x calculate z(15 degrees) and explain what it means
Click here to see answer by greenestamps(13200)

Question 1194341: For a certain company, the cost for producing x items is 35x+300 and the revenue for selling x items is 75x−0.5x2 .

The profit that the company makes is how much it takes in (revenue) minus how much it spends (cost). In economic models, one typically assumes that a company wants to maximize its profit, or at least wants to make a profit!

Part a: Set up an expression for the profit from producing and selling x items. We assume that the company sells all of the items that it produces. (Hint: it is a quadratic polynomial.)

Part b: Find two values of x that will create a profit of $300 .

The field below accepts a list of numbers or formulas separated by semicolons (e.g. 2;4;6 or x+1;x−1 ). The order of the list does not matter. To enter a−−√ , type sqrt(a).
Click here to see answer by math_tutor2020(3817)

Question 1194580: 1. A right triangle has one leg one fourth as long as the other. Find a function that models its perimeter P in terms of the length s of the shorter leg only (ie P(s) =....).
The legs of a right triangle are the two sides that form the right angle.
You may want to draw a diagram for this, but we want P as a function of s only.

2. Find the Domain and Range of the function f(x) = LaTeX: \frac{x-1}{x+3}.
You will need to find the inverse function f-1(x) in order to get your answer.
a) Domain of f. Explain why.
b) Range of f. Explain why.
c) What would be the Range of f-1(x)? Explain why.
Click here to see answer by ikleyn(52794)

Question 1194808: Given the function y = 2cos(3x) + 1, determine the three functions f(x), g(x), and h (x) so that f°g°h(x) = 2cos(3x) + 1. b) Consider the functions f(x) = 2x — 1 and g(x) = x2. For what value(s) of x does f°g(x) =g°f(x)?

Click here to see answer by ikleyn(52794)

Question 1194875: Given the function
g(x) = 2 − x2,
evaluate
g(x + h) − g(x)
h
, h ≠ 0
Click here to see answer by Boreal(15235)

Question 1194962: what would nightly profit equal if Average attendance is 7500 per night ?
Click here to see answer by MathLover1(20850)

Question 1194961: if the civic arena has a goal of clearing 15000 each night how many tickets must be sold ?
Click here to see answer by MathLover1(20850)

Question 1194994: For all x,y element in Q
x*y= (x+y) / 2
* is the "mean" operation on Q
a.Does (Q,*) have a neutral element?
b.Is(Q,*) associative?
-Yes.
-No. For example:
c. Does it have the cancellation property?
-Yes.
-No. For example:
Click here to see answer by ikleyn(52794)

Question 1195024: Is it possible to determine whether (Z,*) (* could be any operation) is associative solely on the base that it is invertible, and has the cancelation property?
Please provide an example. I am struggling to understand this.
Click here to see answer by ikleyn(52794)

Question 1195227: Suppose a function is such that for every x≠0(x that does not equal 0). Find .
Click here to see answer by ikleyn(52794)

Question 1195270: Suppose the demand price for selling out a production run of x DVDs is given by p(x)=-0.0005x^2+60 dollars per DVD. Further suppose the weekly cost of producing these DVDs is given by C(x)=-0.001x^2+18x+4000 dollars to produce that many DVDs.

(i) Write the Revenue function R(x). And be sure to state its DOMAIN.
(ii) Use (i) to write the profit function P(x). Again, be sure to state its DOMAIN.

I am very confused as to how to get the domain in these problems because initially I thought it was (-infinity, infinity) for both revenue function and profit function, but my professor said that mathematically this is correct, but since we're talking about the real world it would be something else and it wouldn't make sense to have negative infinity, and I would like an explanation as to how to get the domain. Would the interval be (0, infinity) for both, or is there a method to figuring out the domain in this situation.

Click here to see answer by MathLover1(20850)

Question 1195269: If the perimeter of the square is given as P = 4s, then find the domain.
Click here to see answer by MathLover1(20850)

Question 1195269: If the perimeter of the square is given as P = 4s, then find the domain.
Click here to see answer by ikleyn(52794)

Question 1195289: If f(x)=3x+1 and g(x)=2x-1, then g(f(x))
Click here to see answer by josgarithmetic(39618)

Question 1195289: If f(x)=3x+1 and g(x)=2x-1, then g(f(x))
Click here to see answer by math_tutor2020(3817)

Question 1195289: If f(x)=3x+1 and g(x)=2x-1, then g(f(x))
Click here to see answer by MathLover1(20850)

Question 1195888: Each set of ordered pairs represents a function. Write a rule that represents the function.
(2,5), (4,9), (5,11), (7,15), (10,21)
Click here to see answer by MathLover1(20850)

Question 1195888: Each set of ordered pairs represents a function. Write a rule that represents the function.
(2,5), (4,9), (5,11), (7,15), (10,21)
Click here to see answer by ikleyn(52794)

Question 1195887: Each set of ordered pairs represents a function. Write a rule that represents the function.
(2,10), (4,20), (5,25), (7, 35), (9, 45)
Click here to see answer by MathLover1(20850)

Question 1195884: Read the description of the below relation and decide whether it is a function.
Steven does yard work for his neighbors. He earns $10 for every lawn that he mows plus $3.50 for raking leaves.
Click here to see answer by josgarithmetic(39618)

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