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3 years ago

Write the explicit formula for the geometric sequence.

1 answer:

8 0

We are given the series of <span>a1 = -5 a2 = 20 a3 = -80. In this case, we can see that this is a geometric sequence with a geometric ratio equal to 20/-5 = -80/ 20 or equal to 4. Hence, r is equal to 4, a1 is equal to -5.

The geometric sequence formula is an = a1*r^(n-1) = -5 * (-4)^ (n-1) where n is an integer. Answer is B.</span>

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A. A 5in radius ball is in a

abruzzese [7]

Answer:

52.33%

Step-by-step explanation:

Since, all six sides of the box are touching the ball.

So, all the three dimensions of the box are equal.

Hence, it is a cubical box.

Side length of the box (l)

= diameter of the ball

= 2*radius of the ball

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= 10 In.

$V_{ball} = \frac{4}{3} \pi r^3$

$V_{ball} = \frac{4}{3} \times 3.14(5)^3$

$V_{ball} = \frac{4}{3} \times 3.14\times 125$

$V_{ball} = \frac{1,570}{3}\: In^3$

$V_{box} =l^3$

$V_{box} =(10)^3$

$V_{box} =1000\: In^3$

Percentage of the space in the box occupied by the ball

$= \frac{V_{ball}}{V_{box} } \times 100$

$= \frac{\frac{1,570}{3}}{1000} \times 100$

$= \frac{1570}{3000} \times 100$

$= \frac{157}{3}$

$= 52.33\%$

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