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worty [1.4K]
3 years ago
15

What is the rate of change for f(x) =7 sin x-1 on the interval from x=0 to x=piover 2

Mathematics
1 answer:
Oksi-84 [34.3K]3 years ago
7 0
\bf slope = {{ m}}= \cfrac{rise}{run} \implies 
\cfrac{{{ f(x_2)}}-{{ f(x_1)}}}{{{ x_2}}-{{ x_1}}}\impliedby 
\begin{array}{llll}
average\ rate\\
of\ change
\end{array}\\\\
-------------------------------

\bf f(x)= 7sin(x)-1  \qquad 
\begin{cases}
x_1=0\\
x_2=\frac{\pi }{2}
\end{cases}\implies \cfrac{f\left( \frac{\pi }{2} \right)-f(0)}{\frac{\pi }{2}-0}
\\\\\\
\cfrac{[7\cdot 1-1]~-~[7\cdot 0-1]}{\frac{\pi }{2}}\implies \cfrac{6-(-1)}{\frac{\pi }{2}}\implies \cfrac{6+1}{\frac{\pi }{2}}\implies \cfrac{7}{\frac{\pi }{2}}\implies \cfrac{14}{\pi }
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The answer is 5.13 in²

Step 1. Calculate the diameter of the circle (d).
Step 2. Calculate the radius of the circle (r).
Step 3. Calculate the area of the circle (A1).
Step 4. Calculate the area of the square (A2).
Step 5. Calculate the difference between two areas (A1 - A2) and divide it by 4 (because there are total 4 segments) to get <span>the area of one segment formed by a square with sides of 6" inscribed in a circle.
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Step 1:
The diameter (d) of the circle is actually the diagonal (D) of the square inscribed in the circle. The diagonal (D) of the square with side a is:
D = a√2            (ratio of 1:1:√2 means side a : side a : diagonal D = 1 : 1 : √2)
If a = 6 in, then D = 6√2 in.
d = D = 6√2 in

Step 2.
The radius (r) of the circle is half of its diameter (d):
r = d/2 = 6√2 / 2 = 3√2 in

Step 3.
The area of the circle (A1) is:
A = π * r²
A = 3.14 * (3√2)² = 3.14 * 3² * (√2)² = 3.14 * 9 * 2 = 56.52 in²

Step 4.
The area of the square (A2) is:
A2 = a²
A2 = 6² = 36 in²

Step 5:
(A1 - A2)/4 = (56.52 - 36)/4 = 20.52/4 =  5.13 in²
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2 years ago
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Based on the 2017 season, the Houston Astros have a winning percentage of 623. Use the binomial
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Step-by-step explanation:

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Step-by-step explanation:

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For current or former high-achieving, overachiever, perfectionist, and hard-working students: What are three things you wish you
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Drag a reason to each box to complete this proof.
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Given: 5x – 4 + 13x = 5

Combine like terms in the given expression.

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