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3 years ago

What is the nth term of a geometric sequence that has a common ratio of 6 and 24 as the third term

1 answer:

4 0

The common ratio r is 6, while the third term (ar²) is 24.
Nth term in a GP is given by the formula ar^n-1, thus the third term is ar²
ar²= 24
thus, a × 36 = 24
a =24/36
The ninth term is given by ar^8
= (24/36)× 6^8
= 1119744.

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After a baseball is hit, the height h (in feet) of the ball above the ground t seconds after it is hit can be approximated by th

lubasha [3.4K]

Answer:

The ball will take 4.05 seconds to hit the ground.

Step-by-step explanation:

we have

$h=-16t^{2}+64t+3$

This is a quadratic equation (vertical parabola) open down

The vertex is a maximum

we know that

The ball hit the ground when h=0

Solve the quadratic equation

For h=0

$-16t^{2}+64t+3=0$

The formula to solve a quadratic equation of the form

$at^{2} +bt+c=0$ is equal to

$t=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}$

in this problem we have

$-16t^{2}+64t+3=0$

$a=-16\\b=64\\c=3$

substitute in the formula

$t=\frac{-64(+/-)\sqrt{64^{2}-4(-16)(3)}} {2(-16)}$

$t=\frac{-64(+/-)\sqrt{4,288}} {-32}$

$t=\frac{64(-)\sqrt{4,288}} {32}=-0.05\ sec$ ---> the time cannot be a negative number

$t=\frac{64(+)\sqrt{4,288}} {32}=4.05\ sec$

therefore

The ball will take 4.05 seconds to hit the ground.

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3 years ago

Which expression is not a polynomial?

Lunna [17]

12 is not a polynomial

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3 years ago

As the exponent on the base 10 increases, does

trapecia [35]

Answer:

Since the exponent on 10 is positive, I know they are looking for a LARGE number, so I'll need to move the decimal point to the right, in order to make the number LARGER. Since the exponent on 10 is "12", I'll need to move the decimal point twelve places over.

First, I'll move the decimal point twelve places over. I make little loops when I count off the places, to keep track:

3.6 _ _ _ _ _ _ _ _ _ _ _ .

Then I fill in the loops with zeroes:

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In other words, the number is 3,600,000,000,000, or 3.6 trillion

Step-by-step explanation:

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4 years ago

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WARRIOR [948]

Answer:

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