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2 years ago

What is the distance from (−4, 0) to (2, 5)? round your answer to the nearest hundredth. 7.81 8.17 8.58 10.4

Mathematics

1 answer:

Arlecino [84]2 years ago

6 0

The correct answer would be 7.81

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The graph of a sinusoidal function has a minimum point at (0, - 10) and then has a maximum point at (2, - 4) Write the formula o

AleksAgata [21]

Answer: $\bold{y=3sin\bigg(\dfrac{\pi}{2}x-\dfrac{\pi}{2}\bigg)-7}$

<u>Step-by-step explanation:</u>

Minimum: (0, -10)

Maximum: (2, -4)

y = A sin (Bx - C) + D

Amplitude (A) = (Max - Min)/2
Period = 2π/B → B = 2π/Period
Phase Shift = C/B → C = B × Phase Shift
Midline (D) = (Max + Min)/2

$A=\dfrac{-4-(-10)}{2}\quad =\dfrac{-4+10}{2}\quad =\dfrac{6}{2}\quad =\large\boxed{3}$

$\text{x-value of Max minus x-value of Min}= \dfrac{1}{2}\text{Period}\\\\2 - 0 = \dfrac{1}{2}P\quad \rightarrow \quad P=4\\\\\\B=\dfrac{2\pi}{P}\quad =\dfrac{2\pi}{4}\quad =\large\boxed{\dfrac{\pi}{2}}\\$

$D = \dfrac{\text{Max + Min}}{2}\quad = \dfrac{-4+(-10)}{2}\quad =\dfrac{-14}{2}\quad =\large\boxed{-7}$

Sin usually starts at (0, 0). For this graph, the midline touches 0 when x = 1 so the Phase Shift = 1.

$C = B \times \text{Phase Shift}\quad = \dfrac{\pi}{2}\times 1\quad =\large\boxed{\dfrac{\pi}{2}}$

$A=3, \quad B=\dfrac{\pi}{2}, \quad C=\dfrac{\pi}{2},\quad D=-7\\\\\rightarrow \quad \large\boxed{y=3\sin \bigg(\dfrac{\pi}{2}x-\dfrac{\pi}{2}\bigg)-7}$

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2 years ago

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6/7 * 6/7 equals please help

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Answer:

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Step-by-step explanation:

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2 years ago

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The function c = 100 + 0.30m represents the cost c (in dollars) of renting a car after driving m miles. What would the cost be t

aleksley [76]

Answer:

c = $130

Step-by-step explanation:

Given:

c = 100 + 0.30m

Where,

c = cost of renting a car (in dollars)

m = number of miles driven (in miles)

If m = 100 miles

c = 100 + 0.30m

= 100 + 0.30(100)

= 100 + 30

= 130

c = $130

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2 years ago

Which rectangle if translated 3 units left and 10 units down and then reflected over the line x = -5 will result in rectangle E?

aev [14]

Answer:

Rectangle C

Step-by-step explanation:

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3 years ago