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2 years ago

11

John gained 8 pounds while on vacation, but lost 12 pounds after he returned home. Which number is the additive inverse of the c

hange in John's weight?
-12
-8
4
8

1 answer:

bonufazy [111]2 years ago

8 0

Answer: 4

Step-by-step explanation: Because he gained 8 pounds and lost 12 when he got home, the additive inverse would be 4. (additive inverse is the opposite.

Hope this helps :)

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The harmonic motion of a particle is given by f(t) = 2 cos(3t) + 3 sin(2t), 0 ≤ t ≤ 8. (a) When is the position function decreas

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For the last part, you have to find where $f'(t)$ attains its maximum over $0\le t\le8$ . We have

$f'(t)=-6\sin3t+6\cos2t$

so that

$f''(t)=-18\cos3t-12\sin2t$

with critical points at $t$ such that

$-18\cos3t-12\sin2t=0$

$3\cos3t+2\sin2t=0$

$3(\cos^3t-3\cos t\sin^2t)+4\sin t\cos t=0$

$\cos t(3\cos^2t-9\sin^2t+4\sin t)=0$

$\cos t(12\sin^2t-4\sin t-3)=0$

So either

$\cos t=0\implies t=\dfrac{(2n+1)\pi}2$

or

$12\sin^2t-4\sin t-3=0\implies\sin t=\dfrac{1\pm\sqrt{10}}6\implies t=\sin^{-1}\dfrac{1\pm\sqrt{10}}6+2n\pi$

where $n$ is any integer. We get 8 solutions over the given interval with $n=0,1,2$ from the first set of solutions, $n=0,1$ from the set of solutions where $\sin t=\dfrac{1+\sqrt{10}}6$ , and $n=1$ from the set of solutions where $\sin t=\dfrac{1-\sqrt{10}}6$ . They are approximately

$\dfrac\pi2\approx2$

$\dfrac{3\pi}2\approx5$

$\dfrac{5\pi}2\approx8$

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2 years ago

A submarine is descending to examine the seafloor 2,100 feet below the surface. It takes the submarine 2 hours to make this desc

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Answer:

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Step-by-step explanation:

I know the answer because descending means going down so 2100 is the big number and its negative to if you do -2100 divided by 2 then you will get -1050.

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2 years ago

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Solve the system using elimanation: 5x + 4y = 12. 3x -3y = 18

Scorpion4ik [409]

If you would like to solve the system of equations 5x + 4y = 12 and 3x - 3y = 18 using elimination, you can do this using the following steps:

<span>5x + 4y = 12 /*3
3x - 3y = 18 /*4
_____________
15x + 12y = 36
12x - 12y = 72
_____________
15x + 12y + 12x - 12y = 36 + 72
15x + 12x = 36 + 72
27x = 108
x = 108/27
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</span><span>3x - 3y = 18
</span>3 * 4 - 3y = 18
12 - 3y = 18
12 - 18 = 3y
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y = -6/3
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(x, y) = (4, -2)

The correct result would be: x = 4 and y = -2.

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Answer: He is paid $90 last weekend.

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If he works on Sunday, he is paid time and a half.

Amount would be

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Number of hours he worked on Saturday = 6 hours

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So, Total amount he is paid last weekend altogether is given by

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Angle 4 equals 34 degrees since angle 2 and 4 are opposite angles and opposite angles are congruent

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