Answer:
a. 3/4 inches per minute
b. -1 1/8 inches per minute
c. B is fastest; 1 1/8 is more than 3/4
Step-by-step explanation:
A <em>change</em> is a <em>difference</em>. A <em>rate of change</em> is <em>one difference divided by another</em>, usually the change in y-value divided by the change in x-value.
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<h3>a.</h3>
The change in elevation is the difference between the elevation at the end of the period (6 inches) and the elevation at the beginning of the period (3 inches). The change in time period is the difference between the end time (8 min) and the beginning time (4 min).
change in elevation per minute = (6 -3 inches)/(8 -4 min)
= (3 inches)/(4 min) = 3/4 inches/minute
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<h3>b.</h3>
Similarly, ...
change in elevation per minute = (3 -7 1/2 inches)/(18 -14 min)
= (-4 1/2 inches)/(4 min) = -1 1/8 inches/minute
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<h3>c.</h3>
We know that 3/4 is more than -1 1/8, but when we talk about the "fastest rate of change", we're generally interested in the magnitude--the value without the sign. That means we understand a rate of change of -1 1/8 inches per minute to be "faster" than a rate of change of 3/4 inches per minute.
The rate of change from Part B is fastest. 1 1/8 inches per minute is more than 3/4 inches per minute.
Yes here is an example:_
x/4 + 5/6 = 2
The LCD of 4 and 6 is 12 but we can also multiply through by 24 to clear the fractions:-
x/4 * 24 + 5/6 * 24 = 2 + 24
6x + 20 = 40
This will give us the same result if we multiplied through by 12.
Answer:
![\frac{125x^3 - 8}{5x - 2} = 25x^2 + 10x +4](https://tex.z-dn.net/?f=%5Cfrac%7B125x%5E3%20-%208%7D%7B5x%20-%202%7D%20%3D%2025x%5E2%20%2B%2010x%20%2B4)
Step-by-step explanation:
Given
![Dividend = 125x^3 - 8](https://tex.z-dn.net/?f=Dividend%20%3D%20125x%5E3%20-%208)
![Divisor = 5x - 2](https://tex.z-dn.net/?f=Divisor%20%3D%205x%20-%202)
Required
Determine the quotient
See attachment for complete process.
First, divide 125x^3 by 5x
![\frac{125x^3}{5x} =25x^2](https://tex.z-dn.net/?f=%5Cfrac%7B125x%5E3%7D%7B5x%7D%20%3D25x%5E2)
Write
at the top
Multiply
by ![25x^2](https://tex.z-dn.net/?f=25x%5E2)
![= 125x^3 - 50x^2](https://tex.z-dn.net/?f=%3D%20125x%5E3%20-%2050x%5E2)
Subtract from 125x^3 - 8
i.e.
![125x^3 - 8 - (125x^3 - 50x^2) = 50x^2 - 8](https://tex.z-dn.net/?f=125x%5E3%20-%208%20-%20%28125x%5E3%20-%2050x%5E2%29%20%3D%2050x%5E2%20-%208)
Step 2:
Divide 50x^2 by 5x
![\frac{50x^2}{5x} = 10x](https://tex.z-dn.net/?f=%5Cfrac%7B50x%5E2%7D%7B5x%7D%20%3D%2010x)
Write
at the top
Multiply
by ![10x](https://tex.z-dn.net/?f=10x)
![= 50x^2 - 20x](https://tex.z-dn.net/?f=%3D%2050x%5E2%20-%2020x)
Subtract from 50x^2 - 8
i.e.
![50x^2 - 8 - (50x^2 - 20x) = 20x - 8](https://tex.z-dn.net/?f=50x%5E2%20-%208%20-%20%2850x%5E2%20-%2020x%29%20%3D%2020x%20-%208)
Step 3:
Divide 20x by 5x
![\frac{20x}{5x} = 4](https://tex.z-dn.net/?f=%5Cfrac%7B20x%7D%7B5x%7D%20%3D%204)
Write
at the top
Multiply
by ![4](https://tex.z-dn.net/?f=4)
![= 20x - 8](https://tex.z-dn.net/?f=%3D%2020x%20-%208)
Subtract from 20x - 8
i.e.
![20x - 8 - (20x - 8) = 0](https://tex.z-dn.net/?f=20x%20-%208%20-%20%2820x%20-%208%29%20%3D%200)
Hence:
![\frac{125x^3 - 8}{5x - 2} = 25x^2 + 10x +4](https://tex.z-dn.net/?f=%5Cfrac%7B125x%5E3%20-%208%7D%7B5x%20-%202%7D%20%3D%2025x%5E2%20%2B%2010x%20%2B4)
In the case that a scientist cools three gases in an experiment, the change in temperature will be negative for the experiment. This is because cooling results in a temperature lower than the original temperature. For example, a gas originally at 25°C when cooled to 20°C has a temperature change of -5°C.
Answer: 768 ounces
Step-by-step explanation: ounces of water 48 days 16 multiply 48 x 16 you get 768