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3 years ago

15

What is the rate of change between the interval of x = 3 pi over 2 and x = 2π?

2 answers:

galina1969 [7]3 years ago

5 0

Check the picture below.

$\bf slope = m = \cfrac{rise}{run} \implies 
\cfrac{ f(x_2) - f(x_1)}{ x_2 - x_1}\impliedby 
\begin{array}{llll}
average~rate\\
of~change
\end{array}\\\\
-------------------------------\\\\
\begin{cases}
x_1=\frac{3\pi }{2}\\
x_2=2\pi 
\end{cases}\implies \cfrac{f(2\pi )-f\left( \frac{3\pi }{2} \right)}{2\pi -\frac{3\pi }{2} }\implies \cfrac{3-1}{\frac{4\pi -3\pi }{2}}\implies \cfrac{2}{\quad \frac{\pi}{2}\quad }\implies \cfrac{4}{\pi }$

Sati [7]3 years ago

3 0

Answer:

The answer is 4/pi

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2 years ago

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3 years ago

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3 years ago

1) State the amplitude, period, phase shift, vertical shift and graph

bogdanovich [222]

Answer:

See answers and explanations below (along with a visual graph)

Step-by-step explanation:

For the function $y=acos(b(x+c))+d$ :

Amplitude: $|a|$

Period: $\frac{2\pi}{|b|}$

Phase shift: $\frac{-c}{b}$

Vertical shift: $d$

Therefore, for $y=2cos(\frac{2}{3}(\theta+\pi))-1$ :

Amplitude: $|a|=|2|=2$ , which is 2 units above and below the midline (see d)

Period: $\frac{2\pi}{|b|}=\frac{2\pi}{|\frac{2}{3}|}=\frac{2\pi}{\frac{2}{3}}=3\pi$ , so the cycle will repeat every 3π units

Phase shift: $\frac{-c}{b}=\frac{-\frac{2\pi}{3} }{\frac{2}{3} }=-\pi$ , or π units to the left

Vertical shift: $d=-1$ , or 1 unit down

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2 years ago

. The Empire State Building is a 102-story skyscraper. Its height is 1,250 ft. from the ground to the roof. The length and width

Aleks [24]

Answer: a) Dimensions of miniature is 0.17 × 0.08 × 0.5, b) 0.006 ft³.

Step-by-step explanation:

Since we have given that

Height of building = 1250 feet

Length of building = 424 ft

Width of building = 187 ft

Now, we know that The miniature version is just 1/ 2500 of the size of the original.

So, Height of miniature would be

$\dfrac{1250}{2500}=0.5\ ft$

Length of miniature would be

$\dfrac{424}{2500}=0.17\ ft$

Width of miniature would be

$\dfrac{187}{2500}=0.08\ ft$

a) What are the dimensions of the miniature Empire State Building?

Dimensions of miniature is 0.17 × 0.08 × 0.5

b. Determine the volume of the miniature building. Explain how you determined the volume.

$Volume=0.5\times 0.08\times 0.17=0.006\ ft^3$

Hence, a) Dimensions of miniature is 0.17 × 0.08 × 0.5, b) 0.006 ft³.

6 0

3 years ago