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Rina8888 [55]
2 years ago
10

Amanda travels to work from home in 60

SAT
1 answer:
vodomira [7]2 years ago
4 0

Answer:

50 minutes

Explanation:

We can set this up as a rate * time = distance problem. We can set the rate at which Amanda travels to work to be x, since that quantity is unknown. The time it takes is given to be 60 minutes. This means that the total distance she travels to get to work is 60x. On the other hand, the way back home has more unknown quantities. The exact rate is unknown, but we do know that it is 20% more than the rate at which Amanda travels to work. This means that the rate is x + .20x, or 1.2x. We can set the time to be y, which means the total distance she travels to get back home is 1.2xy. We are told that Amanda uses the same route to get to and from work, which means 60x = 1.2xy. All we have to do now is solve this equation:

60x=1.2xy\\60=1.2y\\y=50

If we divide through by x and then isolate y, we get that it takes Amanda 50 minutes to get home

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the height of a bottle rocket, in meters, is given by the function s(t)=−9t2+103t+403. find the average velocity of the bottle r
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The average velocity of the bottle rocket are two given time intervals is 30 m/s and 20 m/s respectively, while the instantaneous velocity at 4.5 seconds is 22 m/s.

The given parameters;

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  • time interval (4.499, 4.5), and (4.5, 4.501)

The average velocity of the bottle rocket over the intervals is calculated as follows;

when the interval = [<em>4.499, 4.5</em>]

s(4.499)= -9(4.499)^2  + 103(4.499) + 403 = 684.22 \ m\\\\s(4.5) =  -9(4.5)^2  + 103(4.5) + 403 = 684.25 \ m

v = \frac{\Delta \ s}{\Delta \ t} = \frac{684.25 - 684.22}{4.5 - 4.499} = 30 \ m/s

when the interval = [<em>4.5, 4.501</em>]

s(4.5) = -9(4.5)^2 + 103(4.5) + 403 = 684.25 \ m\\\\s(4.501) = -9(4.501)^2 + 103(4.501) + 403 =684.27 \ m\\\\v= \frac{684.27 - 684.25}{4.501-4.5} \\\\v = 20 \ m/s

The instantaneous velocity of the bottle rocket at time t=4.5;

v = \frac{d \ s(t)}{dt} = -18t + 103\\\\v(4.5) = -18(4.5) + 103\\\\v(4.5) = 22 \ m/s

Thus, the average velocity of the bottle rocket are two given time intervals is 30 m/s and 20 m/s respectively, while the instantaneous velocity at 4.5 seconds is 22 m/s.

Learn more here: brainly.com/question/25009886

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