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3 years ago

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You start driving west for 5 miles, turn left, and drive south for another 8 miles. At the end of driving, what is your straight

line distance from your starting point? Round to the nearest tenth of a mile.

1 answer:

artcher [175]3 years ago

4 0

Answer: 9.4

Step-by-step explanation: plug it into Pythagorean Theorem equation

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PLEASE HELP I DO NOT UNDERSTAND AT ALL ITS PRECALC PLEASE SERIOUS ANSWERS

Elina [12.6K]

You want to end up with $A\sin(\omega t+\phi)$ . Expand this using the angle sum identity for sine:

$A\sin(\omega t+\phi)=A\sin(\omega t)\cos\phi+A\cos(\omega t)\sin\phi$

We want this to line up with $2\sin(4\pi t)+5\cos(4\pi t)$ . Right away, we know $\omega=4\pi$ .

We also need to have

$\begin{cases}A\cos\phi=2\\A\sin\phi=5\end{cases}$

Recall that $\sin^2x+\cos^2x=1$ for all $x$ ; this means

$(A\cos\phi)^2+(A\sin\phi)^2=2^2+5^2\implies A^2=29\implies A=\sqrt{29}$

Then

$\begin{cases}\cos\phi=\frac2{\sqrt{29}}\\\sin\phi=\frac5{\sqrt{29}}\end{cases}\implies\tan\phi=\dfrac{\sin\phi}{\cos\phi}=\dfrac52\implies\phi=\tan^{-1}\left(\dfrac52\right)$

So we end up with

$2\sin(4\pi t)+5\cos(4\pi t)=\sqrt{29}\sin\left(4\pi t+\tan^{-1}\left(\dfrac52\right)\right)$

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2 years ago

Read 2 more answers

To which set of numbers does the number-5 belong? select all that apply

Lelu [443]

A, C, D are the correct answers.

-5 is neither a whole number nor a natural number. This is because negative numbers are not included in these. Hope this helps! Let me know:)

4 0

2 years ago

Simplify (b^4)^3 A.B^9 B.B^3 C.B D.B^12

natulia [17]

(b^4)^3

To simplify when something is raised to two different exponents, multiply the two exponents together:

4 * 3 = 12

You now have b^12.

The answer is D.

6 0

2 years ago

I WILL GIVE BRAINLIEST

Xelga [282]

Answer:

y = 6x

Step-by-step explanation:

For a vertical stretch, you simply multiply x by the factor you want to stretch it by. 3x • 2 is 6x.

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2 years ago

Read 2 more answers

Please I need this quick!!! 15 points

professor190 [17]

Let the number be n.

Then:

n^2 + (1/n)^2 = 82/9; find n. Find the LCD; it is 9n^2.

Mult all 3 terms by 9n^2:
82*9n^2
9n^4 + 9 = (82/9)(9n^2) => 9n^4 + 9 = ------------
   9
Then 9n^4 - 82n^2 + 9 = 0

I used my graphing calculator to find that n = 3.

Let's check: is 3^2 + (1/3)^2 = 82/9?
Is 9 + 1/9 = 82/9?
Is 81 + 1 = 82? YES. So, n=3 is a solution.

7 0

2 years ago