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RoseWind [281]
3 years ago
5

Which function has the greatest rate of change on the interval from x = 3 pi over 2 to x = 2π?

Mathematics
1 answer:
vodka [1.7K]3 years ago
4 0
The average rate of change for the function f(x) can be calculated from the following equation
\frac{f( x_{2})-f( x_{1} )}{ x_{2} - x_{1} }

By applying the last formula on the given equations 
(1) the first function f
from the table f(3π/2) = -2   and   f(2π) = 0
∴ The average rate of f = \frac{f(2 \pi)-f( \frac{3 \pi}{2} )}{2 \pi -  \frac{3 \pi}{2} } =  \frac{0-(-2)}{ \frac{\pi}{2} }=  \frac{2}{ \frac{\pi}{2} }  =  \frac{4}{\pi}

(2) the second function g(x)
from the graph g(3π/2) = -2   and   g(2π) = 0
∴ The average rate of g = \frac{g(2 \pi)-g( \frac{3 \pi}{2} )}{2 
\pi -  \frac{3 \pi}{2} } =  \frac{0-(-2)}{ \frac{\pi}{2} }=  \frac{2}{ 
\frac{\pi}{2} }  =  \frac{4}{\pi}

(3) the third function h(x) = 6 sin x +1
∴ h(3π/2) = 6 sin (3π/2) + 1 = 6 *(-1) + 1 = -5
   h(2π) = 6 sin (2π) + 1 = 6 * 0 + 1 = 1
∴ The average rate of h = \frac{f(2 \pi)-f( \frac{3 \pi}{2} )}{2 
\pi -  \frac{3 \pi}{2} } =  \frac{1-(-5)}{ \frac{\pi}{2} }=  \frac{6}{ 
\frac{\pi}{2} }  =  \frac{12}{\pi}

By comparing the results, The <span>function which has the greatest rate of change is h(x)
</span>

So, the correct answer is option <span>C) h(x)</span>
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ValentinkaMS [17]
Because none of the points on the number line are above 0, we know that the points will be negative.
This eliminates the second and third choices, as they contain positive numbers.
The first point, A, is a number less than -0.5 or -1/2
The first choice matches A with -5/16, which is less than -0.5 or -1/2
Therefore, the fourth choice must be the correct answer.
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3 years ago
Leanne Raymond Montel and Emily body gift for their soccer coach the total cost of the gift including tax was $55.80 Montel paid
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Solution: The total cost of the gift including the tax = $55.80

The amount paid by Montel = $14

The amount paid by Raymond is

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Therefore, Raymond paid $18.6

The amount paid by Emily is

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0.25 \times 55.80 = 13.95

Therefore, Emily paid $13.95

We also know that the remaining amount is paid by Leanne.

Therefore, the remaining amount is:

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7 0
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Answer: yw

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amm1812
5\cdot3\cdot4=60 - the current possible number of plates

after adding 2 letters into the 1st set:
7\cdot3\cdot4=82
after adding 2 letters into the 2nd set:
5\cdot5\cdot4=100
after adding 2 letters into the 3rd set:
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after adding 1 letter into the 1st set and 1 into the 2nd set:
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after adding 1 letter into the 1st set and 1 into the 3rd set:
6\cdot3\cdot5=90
after adding 1 letter into the 2nd set and 1 into the 3rd set:
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<span>The largest possible number of plates after adding two numbers is 100.
So, </span><span>the largest possible number of additional plates is 100-60=40</span>
7 0
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