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.
We are tasked to solve the value of p(8a) in the expression p(x)=3x^2-4.
This means that what would find the value of the expression when x=8a. To solve this, we simply substitute the value of x in the expression.
p(x)=3x^2-4
p(8a)=3(8a)^2-4
p(8a)=3(64a^2)-4
p(8a)=192a^2-4
A term is a number or variable in a math sentence (such as an expression or equation).
Example:
a + 2b + c + 5
5 is a constant; a,b, c are all variables.
One way is by comparing the weather for today as compared to the rest of the week or month.
2.5x + 4x = 39
6.5x = 39
x = 39 / 6.5
x = 6
