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2 years ago

An athlethics track is 400 m long. Anna ran 7 1/2 laps for a race at a school athlethics event. How many kilometers did she run.

Mathematics

2 answers:

Softa [21]2 years ago

8 0

Anna has run 3 kilometers. The math is the following:
7.5 x 400 = 3000
3,000 / 1,000 = 3
3 Kilometers

saul85 [17]2 years ago

5 0

7.5 times 400 is 3000. Every Kilometer is 1000 meters. Therefore, she ran three kilometers.

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a solid consists of cylinder surmounted by a right circular cone. The height of the cone is 2h. If the volume of the solid is 3

Mademuasel [1]

Answer:

height of cylinder = 4/3 h

Step-by-step explanation:

The solid has a cylinder surmounted with a cone .Therefore, the volume of the solid is the sum of the cone and the cylinder.

volume of the solid = volume of cylinder + volume of cone

volume of the solid = πr²h + 1/3πr²h

let

height of the cylinder = H

recall

the height of the cone = 2h

volume of the solid = πr²h + 1/3πr²h

3(1/3πr²2h) = πr²H + 1/3πr²2h

2πr²h = πr²H + 2/3 πr²h

πr²(2h) = πr²(H + 2/3 h)

divide both sides by πr²

2h = H + 2/3 h

2h - 2/3h = H

H = 6h - 2h/3

H = 4/3 h

height of cylinder = 4/3 h

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2 years ago

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3 years ago

A geometric sequence is defined by the equation an = (3)3 − n.

Delvig [45]

PART A

The geometric sequence is defined by the equation

$a_{n}=3^{3-n}$

To find the first three terms, we put n=1,2,3

When n=1,

$a_{1}=3^{3-1}$

$a_{1}=3^{2}$

$a_{1}=9$
When n=2,

$a_{2}=3^{3-2}$
$a_{2}=3^{1}$

$a_{2}=3$

When n=3

$a_{3}=3^{3-3}$

$a_{3}=3^{0}$
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PART B

The common ratio can be found using any two consecutive terms.

The common ratio is given by,
$r= \frac{a_{2}}{a_{1}}$
$r = \frac{3}{9}$

$r = \frac{1}{3}$

PART C

To find
$a_{11}$

We substitute n=11 into the equation of the geometric sequence.

$a_{11} = {3}^{3 - 11}$

This implies that,

$a_{11} = {3}^{ - 8}$

$a_{11} = \frac{1}{ {3}^{8} }$

$a_{11}=\frac{1}{6561}$

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