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mestny [16]
3 years ago
8

An experimental model for a suspension bridge is built in the shape of a parabolic arch. In one section, cable runs from the top

of one tower down to the roadway, just touching it there, and up again to the top of a second tower. The towers are both 9 inches tall and stand 60 inches apart. Find the vertical distance from the roadway to the cable at a point on the road 12 inches from the lowest point of the cable.
Mathematics
1 answer:
Temka [501]3 years ago
6 0
First find the function of the form ax^2+bx+c...

We have the points (-30,9),(0,0),(30,9) so we know c=0 then we have:

900a-30b=9
900a+30b=9  adding these together

1800a=18, a=1/100 then 900a-30b=9 becomes:

9-30b=9

-30b=0 so b=0 so the parabola is just:

y(x)=x^2/100

y(12)=144/100=36/25

y(12)=1.44 in
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Jacob consumes an energy drink that contains caffeine. After consuming the energy drink, the amount of caffeine in Jacob's body
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Answer: 0.87400mg of caffeine.

Step-by-step explanation:

You have

N(t)=N0(e^−rt)(1)

as a general Exponential decay equation where N0 is the amount at t=0, N(t) is the amount remaining at time t and r is the exponential decay constant. You're specifically given that after 10 hours, the decay factor is 0.2601, i.e.,

N(10)/N(0)=N0(e^−10r)/N0(e^0)= e^−10r=0.2601 . .(2)

Taking the last 2 parts of (2) to the power of 0.1t gives

e^−rt=0.2601^.1t . .(3)

This means that

N(t)=N0(e^−rt)=N0(0.2601^.1t). .(4)

Also,

N(2.56)N(1.56)=N0(0.2601.1(2.56))N0(0.2601.1(1.56))=0.2601.1(2.56−1.56)=0.2601^.1

= 0.87400mg of caffeine.

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