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Katena32 [7]
3 years ago
12

You did the ball bounce activity. From the ball bounce activity you noticed that the ball bounces up from the floor at a shorter

height each time. If you stood on a ladder and dropped a ball from a height of 10 feet and though experimentation found that the ball rebounds 0.7 of its previous height
What height will the ball bounce up to after it hits the ground a 2nd time

Write an explicit formula for how high it will bounce after it hits the floor the 9th time

Write a recursive formula for how high it will bounce after it hits the floor for the 9th time

How many times does the ball have to strike the floor before it bounces back less then 7 inches

What is the total distance the ball had traveled when it hits the floor the 5th time
Mathematics
2 answers:
yuradex [85]3 years ago
7 0

Answer:

Step-by-step explanation:

wait so each one of them are questions right?

Nimfa-mama [501]3 years ago
7 0

Answer:

MOOOOOOOOOAAAAAAAAAAANNNNNN

Step-by-step explanation:

MOOOOOOOOOOOOOOAAAAAANNNNNN

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Write the first four terms in the following sequences. A(n+1)=12 A(n) for n≥1 and A(1)=4 .
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Find the length of the curve. R(t) = cos(8t) i + sin(8t) j + 8 ln cos t k, 0 ≤ t ≤ π/4
arsen [322]

we are given

R(t)=cos(8t)i+sin(8t)j+8ln(cos(t))k

now, we can find x , y and z components

x=cos(8t),y=sin(8t),z=8ln(cos(t))

Arc length calculation:

we can use formula

L=\int\limits^a_b {\sqrt{(x')^2+(y')^2+(z')^2} } \, dt

x'=-8sin(8t),y=8cos(8t),z=-8tan(t)

now, we can plug these values

L=\int _0^{\frac{\pi }{4}}\sqrt{(-8sin(8t))^2+(8cos(8t))^2+(-8tan(t))^2} dt

now, we can simplify it

L=\int _0^{\frac{\pi }{4}}\sqrt{64+64tan^2(t)} dt

L=\int _0^{\frac{\pi }{4}}8\sqrt{1+tan^2(t)} dt

L=\int _0^{\frac{\pi }{4}}8\sqrt{sec^2(t)} dt

L=\int _0^{\frac{\pi }{4}}8sec(t) dt

now, we can solve integral

\int \:8\sec \left(t\right)dt

=8\ln \left|\tan \left(t\right)+\sec \left(t\right)\right|

now, we can plug bounds

and we get

=8\ln \left(\sqrt{2}+1\right)-0

so,

L=8\ln \left(1+\sqrt{2}\right)..............Answer

5 0
3 years ago
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