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Darya [45]
3 years ago
7

Dan and Jake have new stamp collecting books. Dan puts 5 stamps in his book every day, and Jake puts 6 stamps in his book every

day. How many stamps will Dan have when Jake has 30 in his book?
Mathematics
1 answer:
Ghella [55]3 years ago
4 0
Jake puts 6 stamps in his book every day.

30/6= 5 

Jake put stamps in the book for 5 days.

So, Dan puts 5 stamps in the book every day.

5*5= 25

Dan has 25 stamps when Jake has 30.

I hope this helps!
~kaikers


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Why?

To solve the problem, we need to remember that if we derivate the position function, we will get the velocity function, and if we derivate the velocity function, we will get the acceleration function. So, we will need to derivate two times.

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s(t)=2t^{3}-21t^{2}+60t+3

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v(t)=\frac{ds}{dt}=(2t^{3}-21t^{2}+60t+3)\\\\v(t)=3*2t^{2}-2*21t+60*1+0\\\\v(t)=6t^{2}-42t+60

Now, making the function equal to 0, to find the times when the particle reversed its direction, we have:

v(t)=6t^{2}-42t+60\\\\0=6t^{2}-42t+60\\\\0=t^{2}-7t+10\\(t-5)*(t-2)=0\\\\t_{1}=5s\\t_{2}=2s

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a(t)=\frac{dv}{dt}=6t^{2}-42t+60\\\\a(t)=12t-42

Now, substituting the times to calculate the accelerations, we have:

a(t_1)=a(2s)=12*2-42=-18\frac{ft}{s^{2}}\\ \\a(t_2)=a(5s)=12*5-42=18\frac{ft}{s^{2}}

Now, substitutitng the times to calculate the positions, we have:

s(t_1)=2*(2)^{3}-21*(2)^{2}+60*2+3=16-84+120+3=55ft\\\\s(t_2)=2*(5)^{3}-21*(5)^{2}+60*5+3=250-525+300+3=28ft

Have a nice day!

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