Please help me with the question below! its due in 10 minutes!
thank you sm!
Answers
Answer:
To find the composite function (f ◦ g)(x), we need to substitute g(x) into f(x) and simplify.
Given:
f(x) = x
g(x) = -2x + 3
To find (f ◦ g)(x), we substitute g(x) into f(x):
(f ◦ g)(x) = f(g(x))
Substituting g(x) into f(x), we get:
(f ◦ g)(x) = f(-2x + 3)
Since f(x) = x, we replace f(-2x + 3) with (-2x + 3):
(f ◦ g)(x) = -2x + 3
Therefore, the composite function (f ◦ g)(x) is -2x + 3.
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The Nguyen family spent $48 on entrance fees to the county fair. Each ticket for an adult cost $12. Each ticket for a child cost $5. Each senior citizen paid $2. There were six people in the group. There were 2 fewer tickets purchased for senior citizens than adult tickets. How many adult tickets were purchased?
Please help me answer this question
The main tank at an aquarium is a cylinder with diameter 203 ft and height 25 ft. Using 3.14 for pi, find the volume of the tank to the nearest cubic foot.
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Final answer:
The absolute maximum and minimum of a function on a given interval can be found by calculating the function's critical points and evaluating the function at these points and the interval endpoints, then comparing these values.
Explanation:
In order to find the absolute maximum and absolute minimum values of a function on a given interval, you must first find the critical points of the function within the interval. Critical points occur where the derivative of the function is equal to zero or is undefined. In this case, the derivative of f(t) = 9t + 9 cot(t/2) is f'(t) = 9 - (9/2) csc2(t/2). Set this to zero and solve for t to find the critical points. Additionally, the endpoints of the interval, π/4 and 7π/4, could be the absolute maximum or minimum, so these should be evaluated as well. Once you have found the values of the function at these points and the endpoints, compare them to determine the absolute maximum and minimum values.
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Final answer:
To find the absolute maximum and minimum values of a function, we find the critical points and endpoints. Evaluating the function at these points gives the maximum and minimum values.
Explanation:
To find the absolute maximum and absolute minimum values of a function on a given interval, we need to find the critical points and endpoints of the interval.
To find the critical points of f, we need to find where the derivative of f is equal to zero or undefined. The derivative of f(t) = 9t + 9cot(t/2) is f'(t) = 9 - 9csc^2(t/2).
Setting f'(t) = 0, we have 9 - 9csc^2(t/2) = 0. Solving this equation, we get csc^2(t/2) = 1, which means sin^2(t/2) = 1. This gives us sin(t/2) = ±1. The critical points occur when t/2 = π/2 or t/2 = 3π/2. Solving for t, we get t = π or t = 3π as the critical points.
The endpoints of the interval are π/4 and 7π/4.
Now we evaluate the function f at the critical points and endpoints:
- f(π/4) = 9(π/4) + 9cot(π/8) ≈ 6.566
- f(π) = 9π + 9cot(π/2) = 9π
- f(3π) = 9(3π) + 9cot(3π/2) = 27π
- f(7π/4) = 9(7π/4) + 9cot(7π/8) ≈ 46.607
From these evaluations, we can see that the absolute maximum value occurs at t = 7π/4 and is approximately 46.607, while the absolute minimum value occurs at t = π/4 and is approximately 6.566.
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Answers
28M=12(4+M)
28M=48+12M
28K−12M=48
(28−12)M=48
16K=48
M=4816
M=3So Marna can clean the chimney alone in 3 hours
Final answer:
To find the time it takes for Marna to clean a 20-foot chimney by herself, we first determine the combined and individual rates of Marna and Kalon. We then subtract Kalon's rate from the combined rate to find Marna's rate and subsequently her individual cleaning time which is 3 hours.
Explanation:
The subject of this question is Mathematics, specifically dealing with the concept of rates and time. To solve this problem, we first need to express the combined rate of Kalon and Marna working together. The combined rate is expressed as 1 job per 1 5/7 hours, which simplifies to 7/12 of a chimney per hour.
Kalon's individual rate is 1 job per 4 hours, this simplifies to 1/4 of a chimney per hour. The formula we'll use is (1/Marna's time) = combined rate - Kalon's rate. Therefore, Marna's rate will be (7/12 - 1/4), simplified to 1/3 of a chimney per hour. Hence, Marna would require 3 hours to clean a 20-foot chimney by herself.
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Answers
Answer:
,
and
, where
.
Step-by-step explanation:
An exponential growth function that represents exponential decay has ,
and
, where
.
It is the same function. In the case of growth, b represents a number greater than zero, but in decay, it represents a number between 0 and 1.
Answers
Also please explain. Thanks!
Answers
(1/2+1/4)x= 12
3/4x =12
by multiple both sides by 4/3
so x = 16
Find the LCD, which is 4.
2x/4 + x/4 = 12
3x/4 = 12
Multiply both sides by 4 to remove the fraction.
3x/4 • 4 = 12 • 4
3x = 48
To find x, divide both sides by the coefficient of x, which is 3.
3x/3 = 48/3
x = 16
Check:
16/2 + 16/4 = 12
2(16)/4 + 16/4 = 12
32/4 + 16/4 = 12
8 + 4 = 12
12 = 12
Thus, the answer to x is 16.
Answers
Answer:
15 cats
Step-by-step explanation:
because 5:2 is equivalent to 15:12