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3 years ago

Ms. Geronimo has a $10 gift certificate to her local bakery.

Mathematics

1 answer:

avanturin [10]3 years ago

5 0

Answer: a) 13 macaroons

b) 6 cookies

Step-by-step explanation: Total = $10

a) $2.20/slice of pie

$0.60/macaroon

10 - 2.20 = 7.80

7.80/0.6 = 13

b) $4.60/loaf

cookies = 1 1/2*macaroons = (1 + 0.5)*0.6 = 1,5 * 0.6 = 0.90

cookies = $0.90

10 - 4.60 = 5.40

5.40/0.9 = 6

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A spring has natural length 0.75 m and a 5 kg mass. A force of 8 N is needed to keep the spring stretched to a length of 0.85 m.

I am Lyosha [343]

Use Hooke's law to find the spring constant. If it takes 8N to stretch the spring by 0.1m, then

$8\text{ N}=k(0.1\text{ m})\implies k=80\dfrac{\text N}{\text m}$

I'm going to assume the spring is fixed to a ceiling, and that any stretching in the downward direction counts as movement in the positive direction. The spring's motion is then modeled by

$y''(t)+80y(t)=0$

where $y(t)$ is the position of the spring's free end as it moves up and down. Solving this is easy enough: the characteristic solution will be

$y(t)=C_1\cos4\sqrt5t+C_2\sin4\sqrt5t$

Given that the spring is stretched to a length of 1m (a difference of 0.25m from its natural length), and is released with no external pushing or pulling, we have the two initial conditions $y(0)=\dfrac14$ and $y'(0)=0$ .

$y(0)=\dfrac14\implies\dfrac14=C_1\cos0+C_2\sin0\implies C_1=\dfrac14$
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So the spring's motion is dictated by the function

$y(t)=\dfrac14\cos4\sqrt5t$

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3 years ago

If the track makes 30 miles in 25 minutes, find the time it will need to cover 25 miles

dimulka [17.4K]

Answer:

About 21 min

Explanation:

Distance and time are directly related, meaning that distance / time = constant.

In this case the constant is the rate or speed.

Thus you can write:

speed = distance / time

And, given that covering 30 miles requires 25 minutes, to calculate the time needed to cover 25 miles, you can set this proportion:

30 miles / 25 min = 25 miles / t

To clear t you do cross multiplication:

t × 30 miles = 25 miles × 25 min

Divide both sides by 30 miles:

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Scorpion4ik [409]

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Archy [21]

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