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Dvinal [7]
3 years ago
6

The function f(x) varies directly with x and f(x)=160 when x=40.

Mathematics
1 answer:
DaniilM [7]3 years ago
4 0
160÷40 is 4 so i think the function f multiplies x by 4.
when x is 8, 8×4=32 so the answer shld be 32
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Step-by-step explanation:

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Given that Martin throws a ball straight up in the air.

The equation h(t)=-16t^2+40t+5 gives the height of the ball, in feet, t seconds after martin releases it.

We need to determine the time that it takes the ball to hit the ground.

<u>Time taken:</u>

To determine the time 't', let us equate h(t) = 0 in the equation h(t)=-16t^2+40t+5

Thus, we have;

0=-16t^2+40t+5

Switch sides, we get;

-16 t^{2}+40 t+5=0

Now, we shall solve the equation using the quadratic formula.

Thus, we have;

t=\frac{-40 \pm \sqrt{40^{2}-4(-16) 5}}{2(-16)}

Solving, we get,

t=\frac{-40 \pm \sqrt{1600+320}}{-32}

t=\frac{-40 \pm \sqrt{1920}}{-32}

t=\frac{-40 \pm 8\sqrt{30}}{-32}

t=\frac{8(-5 \pm \sqrt{30})}{-32}

Cancelling the common terms, we get,

t=\frac{-5 \pm \sqrt{30}}{-4}

Thus, the roots of the equation t=\frac{-5 + \sqrt{30}}{-4} and t=\frac{-5 - \sqrt{30}}{-4}

Simplifying the roots, we get,

t=\frac{-5 +5.477}{-4}   and   t=\frac{-5 -5.477}{-4}

t=-0.119   and   t=2.619

Since, t cannot take negative values, then t=2.619

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