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Ad libitum [116K]

1 year ago

15

MONEY Dinner and admission tickets to the aquarium costs $180 for three ladults. If two people each pay $70, how much will the t

hird person have
to pay?

1 answer:

EastWind [94]1 year ago

6 0

if three ladult where having $180,and two adults out of the three pay$70 each

the third person Will pay $40

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A cone has a volume of 942 in.³ and a height of 9 inches what is the radius of the cone use 3.14 for pie

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r = 51.96 inches

Step-by-step explanation:

$V_{cone} = \pi {r}^{2} h \\ \\ \implies \: r^{2} = \frac{V_{cone}}{\pi h } \\ \\ \implies \: r^{2} = \frac{942}{3.14 {(9) } }\\ \\ \implies \: r^{2} = \frac{942}{3.14 {(9) } } \\ \\ \implies \: r^{2} =2700 \\ \\ \implies \: r= \sqrt{2700} \\ \\ \implies \: r=51.96 \: inches$

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A geometric series has second term 375 and fifth term 81 . find the sum to infinity of series .

Eduardwww [97]

Answer: $\bold{S_{\infty}=\dfrac{3125}{2}=1562.5}$

<u>Step-by-step explanation:</u>

a₁, 375, a₃, a₄, 81

First, let's find the ratio (r). There are three multiple from 375 to 81.

$375r^3=81\\\\r^3=\dfrac{81}{375}\\\\\\r^3=\dfrac{27}{125}\qquad \leftarrow simplied\\\\\\\sqrt[3]{r^3} =\sqrt[3]{\dfrac{27}{125}}\\ \\\\r=\dfrac{3}{5}$

Next, let's find a₁

$a_1\bigg(\dfrac{3}{5}\bigg)=375\\\\\\a_1=375\bigg(\dfrac{5}{3}\bigg)\\\\\\a_1=125(5)\\\\\\a_1=625$

Lastly, Use the Infinite Geometric Sum Formula to find the sum:

$S_{\infty}=\dfrac{a_1}{1-r}\\\\\\.\quad =\dfrac{625}{1-\frac{3}{5}}\\\\\\.\quad =\dfrac{625}{\frac{2}{5}}\\\\\\.\quad = \dfrac{625(5)}{2}\\\\\\.\quad = \large\boxed{\dfrac{3125}{2}}$

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