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3 years ago

-2=-(n-8)= Help please!??

Mathematics

1 answer:

motikmotik3 years ago

7 0

Answer:

n = 10

Step-by-step explanation:

move all terms to the left:

-2-(-(n-8))=0

calculate terms in parentheses: -(-(n-8)), so:

-(n-8)

get rid of parentheses

-n+8

add all the numbers together, and all the variables

-1n+8

go back to the equation:

-(-1n+8)

get rid of parentheses

1n-8-2=0

add all the numbers together, and all the variables

n-10=0

move all terms containing n to the left, all other terms to the right

n=10

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Step-by-step explanation:

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3 years ago

1..A message in a bottle is floating on top of the ocean in a periodic manner. The time between periods of maximum heights is 26

statuscvo [17]

Answer:

See below for answers and explanations (along with a graph attached)

Step-by-step explanation:

Part A

The amplitude of a sinusoidal function is half the distance between the maximum and the minimum. It is given to us that the distance from the highest and lowest point is 6 feet, so our amplitude is 6/2 = 3 feet

Part B

The graph's function would be in the form of $y=acos(bx+c)+d$ where $a$ is the amplitude, $\frac{2\pi}{b}$ is the period, $-\frac{c}{b}$ is the phase/horizontal shift, and $d$ is the average/midline.

We already know our amplitude of $a=3$ from part A.

Since our period is given to us as 26 seconds, then we can use the equation $\frac{2\pi}{b}=26$ to find $b$ , which happens to be $b=\frac{\pi}{13}$ .

Since the cosine function starts at its maximum and we want it to start at the average where the bottle travels up, we would need to use the cofunction identity $sin(x)=cos(x-\frac{\pi}{2})$ which shifts the cosine graph $\frac{\pi}{2}$ units to the right. This means that $c=-\frac{\pi}{2}$ , making our phase shift $-\frac{c}{b}=-\frac{-\frac{\pi}{2}}{\frac{\pi}{13}}=6.5$ , or 6.5 feet to the right

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Part C

Using our determined function from Part B, by looking at its graph, we see that the bottle will reach its lowest height of 9 feet after 19.5 seconds (see attached graph).

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3 years ago

Read 2 more answers

Graph the line with slope 1/2 that passes through the point (-1,2).

enyata [817]

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Answer:

see the attachment for a graph

Step-by-step explanation:

With the given point and slope, the equation of the line can be written in point-slope form:

y -k = m(x -h) . . . . . line with slope m through point (h, k)

y -2 = 1/2(x +1) . . . . line with slope 1/2 through point (-1, 2)

Slope is the ratio of rise to run, so a slope of 1/2 means the line will rise 1 unit for each 2 units of run (to the right). If you're plotting this by hand, you can identify a second point that is 2 right and 1 up from the given point:

(-1 +2, 2 +1) = (1, 3).

You can draw your line through those two points.

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3 years ago