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

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Question 1172181: 3.h(t)=−4.9t2+8t+5 represents Jeremiah's height (h) in meters above the water t seconds after he leaves the diving board. Show clear solutions thanksss!
a. What is the initial height of the diving board?
b. At what time did Jeremiah reach his maximum height?
c. What was Jeremiah’s maximum height?
d. How long was Jeremiah in the air

Click here to see answer by Boreal(15235)

Question 1172180: 2. A toy rocket is fired into the air from the top of a barn. Its height (h) above the ground in yards after t seconds is given by the function h(t)=−5t2+10t+20. Show clear solutions thanksss!
a. What was the maximum height of the rocket?
b. How long was the rocket in the air before hitting the ground?
Click here to see answer by Boreal(15235)

Question 1172179: 1. A projectile that is fired vertically into the air with an initial velocity of 120 ft. per second can be modeled by the equation s = 120t - 16t2. In the equation, s is the distance in feet of the projectile above the ground after t seconds. Show clear solutions thanksss!

a. How long will it take for a projectile to reach 216 feet?
b. Is it possible for the projectile to reach 900 feet? Justify your answer.

Click here to see answer by Alan3354(69443)

Question 1172212: 4. A rock is thrown off a 75-meter-high cliff into some water. The height of the rock relative to the cliff after t seconds is given by h(t)=−5t2+20t. Show clear solutions thanksss!
a. Where will the rock be after five seconds?
b. How long before the rock reaches its maximum height?
c. When will the rock hit the water?

Click here to see answer by Boreal(15235)

Question 1172408: Find a family of fuctions such that f(xy)=f(x)f(y). Explain please.
Click here to see answer by Edwin McCravy(20054)

Question 1172412: could you please help me arrange these functions in decreasing order of their periods.
1. y=-3cos(x+2π)
2. y=2/3cot(x/4)+6
3. y=-1/2tan(5x/6+π)
4. y= 5csc(3x)+6
5. y= -10sin(x/5-2π)
thanks in advance for helping me
Click here to see answer by Solver92311(821)

Question 1172396: If f(x) is continuous and differentiable real valued function defined on open interval (-1, 4) such that f(3) = 5 and derivative of f(x) >= -1 for all x. Find the greatest possible value of function f(x) at x = 0?
Click here to see answer by ikleyn(52747)

Question 1172441: GetThere Airlines currently charges 200 dollars per ticket and sells 40,000 tickets a week. For every 10 dollars they increase the ticket price, they sell 800 fewer tickets a week. How many dollars should they charge to maximize their total revenue?
I have gotten the answer of $300 by doing these steps. What have I done wrong?
Number of tickets = 40000 - 1000 * (P - 200)/10
Revenue = (40000 - 1000 * (P - 200)/10) * P
= 60000 P - 100 P^2
60000 - 200 P = 0
P = 300
Thanks
Click here to see answer by math_tutor2020(3816)

Question 1172442: Find the range of the function
f(x) = {x^2 + 14x + 9}/{x^2 + 2x + 3}, as x varies over all real numbers.
Thanks!
Click here to see answer by ikleyn(52747)

Question 1172442: Find the range of the function
f(x) = {x^2 + 14x + 9}/{x^2 + 2x + 3}, as x varies over all real numbers.
Thanks!
Click here to see answer by math_tutor2020(3816)

Question 1172537: f(x)=5x-7 from x=-3 to x=7

Click here to see answer by Alan3354(69443)

Question 1172599: The drama club is putting on a play, but they have to rent the auditorium for $500 in order to put on the show. In order to make a profit from the show, the club decides to charge $12 per ticket. How do I write and equation to represent the profit the club will make as a function of the number of tickets they will sell?
Click here to see answer by ankor@dixie-net.com(22740)

Question 1172629: 4. Sketch the graph of f(x) = 2x^2 / (x^2+2x -3) and give its domain, intercepts and asymptotes.
Click here to see answer by ewatrrr(24785)

Question 1172624: Joe's Taxi Service charges a flat rate plus an additional $0.45 per mile. If someone takes one of Joe's taxis for 13 miles and is charged $12.35, determine the
following:
a: What does Joe charge for the flat rate?
b: Write an equation that represents the total cost of riding in Joe's taxi as a function of the number of miles driven.
c: If someone rides in one of Joe's taxis and pays $23.15, how many miles did he travel?
Click here to see answer by Boreal(15235)

Question 1172973: The two congruent squares are removed from one of a rectangular 10 in by 20 in a piece of cardboard. Two congruent rectangles are removed from the other end. Determine the equation of the volume of the resulting box as a function of x. What is the domain of the function?
Click here to see answer by ikleyn(52747)

Question 1172972: The two congruent squares are removed from one of a rectangular 10 in by 20 in a piece of cardboard. Two congruent rectangles are removed from the other end. Determine the equation of the volume of the resulting box as a function of x. What is the domain of the function?
Click here to see answer by ikleyn(52747)

Question 1173099: What is the slope of the line that passes through the points (-5,-7) and (4,-1)
Write your answer in simplest form
Click here to see answer by ewatrrr(24785)

Question 1173224: find the domain of f(x)=3 outside of the square root on the square root line and then x-5 inside the square root
Click here to see answer by ikleyn(52747)

Question 1173514: If a box of Tipas Hopia costs Php50.00, how much are 2 boxes? 3 boxes? 4 boxes? and 5
boxes?
1. Express this relation by graphing.
2. Through the vertical line test, determine if it describes a function.
3. Identify the dependent and independent variables
Click here to see answer by ikleyn(52747)

Question 1173526: If a box of cookies costs Php50.00, how much are 2 boxes? 3 boxes? 4 boxes? and 5
boxes?
1. Express this relation by graphing.
2. Through the vertical line test, determine if it describes a function.
3. Identify the dependent and independent variables

Click here to see answer by ewatrrr(24785)

Question 1173567: Is the formula an = −4n(n − 1) is explicit or recursive? Find the first five terms of the sequence.
a. recursive; 1, - 4, 16, - 64, 256 c. explicit; 1, - 4, 16, - 64, 256
b. recursive; 0, - 16, - 24, - 48, - 80 d. explicit; 0, - 8, - 24, - 48, - 80

Click here to see answer by ikleyn(52747)

Question 1173594: Given that f(x) and g(x)are functions f(x)=x/x-5 and g(x)=x-2 find f(-10)
Click here to see answer by math_helper(2461)

Question 1173594: Given that f(x) and g(x)are functions f(x)=x/x-5 and g(x)=x-2 find f(-10)
Click here to see answer by MathTherapy(10549)

Question 1173687: Jorge bought a mechanical pencil for $8. A
lead and eraser refill pack costs $2. Write a
linear function to describe the cost of using
the pencil as a function of the number of
refill packs.
A. 𝐶(𝑟) = 8𝑟 − 2
B. 𝐶(𝑟) = 2𝑟 + 8
C. 𝐶(𝑟) = 2𝑟
D. 𝐶(𝑟) = 8𝑟 + 2
Click here to see answer by ewatrrr(24785)

Question 1173686: If 𝑓(1) = 3 and 𝑓(𝑛) = −2𝑓(𝑛 − 1) + 1,
then 𝑓(5) =
A. -5
B. 11
C. 21
D. 43
Click here to see answer by mila nedic(19)

Question 1173793: 1. 1. Let f(x) = √ x + 1 − 1/4−x^(2) . Compute the following:
i. f(0)
ii. f(-3)
iii. f(2)
iv. f(-1)
v. f(3)
vi. Domain(f(x))
2. (a) Let f( x/x−2 ) = 3x + 4 find f(x).
(b) Compute difference quotient of the function g(x) = √ x^(2) − 9, and simplify your answer.
3. Let f(x) = 1 − x, g(x) = x2 + bx + c. find b and c such that fog(x) = −x^(2)+ 5x + 4. + bx + c. find b and c such that fog(x) = −x^(2)+ 5x + 4.
Click here to see answer by ikleyn(52747)

Question 1173791: which of the following relations does not represent a function?
A) {(-3,1), (2,1),(4,5)}
B) {(-4,1), (-4,3),(2,-3)}
C) {(0,1), (1,1), (2,1)}
D) {( -1,1), (0,2), (1,-1)
Click here to see answer by ewatrrr(24785)

Question 1173858: 1. Let f(x) = - x - 5 and g(x) = 4x + 2 Find g(x) + f(x)
Click here to see answer by greenestamps(13195)

Question 1173856: 3. Let f(x) = 2x + 1 and g(x) = x ^ 4 - 2x Find f(x) - g(x)
Click here to see answer by greenestamps(13195)

Question 1173942: Find the domain of the function. (Enter your answer using interval notation.)
f(x) =
5x3 − 2
x2 + 3x − 18

Click here to see answer by josgarithmetic(39613)

Question 1173920: Given h(x) = cos sqrt(3x^2-7), determine f(x) and g(x) in two different ways, such that h(x) = (f o g)(x) where f(x) is not equal to x or g(x) is not equal to x. For each option, show that h(x) = (f o g)(x).
f(x) = ? g(x) = ?
f(x) = ? g(x) = ?

Click here to see answer by greenestamps(13195)

Question 1173960: If f = {(-2,5),(1,4),(3,9),(11,3)} and g = {(0,15),(5,-5),(7,10),(9,-1), what is (g o f)(3)?
Click here to see answer by math_tutor2020(3816)

Question 1173977: does the following rule defines y as a function of x or no
x=|y+10|
Click here to see answer by ikleyn(52747)

Question 1173887: 1. (b) Compute difference quotient of the function g(x) = √x^(2) − 9, and simplify answer.

Click here to see answer by Solver92311(821)

Question 1173792: 1. Find the equation of the line passes through the point (3, −2) and is perpendicular to the line 3x − 2y = 4.
2. An environmental study of a certain community suggests that the average daily level of pollution in the air will be Q(p) = √ 0.6p + 20 units when the population is p thousand. It is estimated that after t years the population will be p(t) = 9 + 0.5t^(2) thousand.
(a) Express the level of pollution in the air as a function of time.
(b) compute the level of pollution after 5 years from now.
(c) When will the pollution level reach 10 units?
Click here to see answer by Boreal(15235)

Question 1174173: the output for the graph y=-2x+6 when the input value is 4

Click here to see answer by ikleyn(52747)

Question 1174192: 10. 4 cubic feet of air at a pressure of 18 pounds per square inch were compressed to a volume of 3 cubic feet. At the same time, the air was heated from an absolute temperature of 288° to one of 308° (from 59° to 95° F). What was its pressure then? (show the solutions with variations thanks!)
Click here to see answer by Theo(13342)

Question 1174323: Point P(u, v) is in the first quadrant on the
graph of the line connecting the points (0,4)
and (4,0). A shaded triangular region is
shown in the diagram. For what point P will
the area of the shaded triangular region be a
maximum?
I tried to get a formula for finding the area for the triangle inside. I got 1/2(4-u)(4-v) but I'm not sure where to go from there.
There was also a similar question on the site with the diagram since I can't seem to post it on here
https://www.algebra.com/cgi-bin/display-illustration.mpl?tutor=lolxcry&illustration_name=Math

Click here to see answer by ikleyn(52747)

Question 1174342: A ball is thrown in the air from the top of a building. Its height, in meters above the ground, as a function of time in seconds, is given by
h(t) = −4.9t² + 24t + 8
How long does it take to reach the maximum height?
I'd appreciate a detailed written version of this problem, It's a bit confusing for me.
Click here to see answer by ikleyn(52747)

Question 1174552: Function f satisfies f(x)+2f(5-x)=x for all real numbers x. What is the value of f(1)?
Click here to see answer by ikleyn(52747)

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