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3 years ago

8

In a fruit cocktail for every 100ml Orange juice you need 12ml Apple juice and 8ml of coconut milk what is the ratio of Apple ju

ice to coconut milk to orange juice expressed in its simplest form

1 answer:

Kisachek [45]3 years ago

7 0

100:12:8 can be simplified to 25:3:2

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Step-by-step explanation:

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2 years ago

(15-16) Consider the Infinite Geometric Series:

vodka [1.7K]

15 Answer: S₁ = 1 S₂ = 4 S₃ = 13 S₄ = 40 Sum = NO

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

1 + 3 + 9 + 27 + ... $\implies\sum^{\infty}_{n=1}3^{n-1}\implies\sum^{\infty}_{n=1}\dfrac{3^n}{3}\\\\\bullet S_1=1\\\bullet S_2=1+3=4\\\bullet S_3=1+3+9=13\\\bullet S=1+3+9+27=40\\\\\\ \lim_{n \to \infty} \dfrac{3^n}{3} \implies\dfrac{3^{\infty}}{3}\implies\infty\\\\\text{The series diverges so there is no sum.}$

16 Answer: $\bold{S_1=\dfrac{1}{2}\qquad S_2=\dfrac{2}{3}\qquad S_3=\dfrac{13}{18}\qquad S_4=\dfrac{39}{54}\qquad Sum=YES}$

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

$\dfrac{1}{2}+\dfrac{1}{6}+\dfrac{1}{18}+\dfrac{1}{54}+\dfrac{1}{162}+...\implies \sum^{\infty}_{n=1}\dfrac{1}{2}\bigg(\dfrac{1}{3}\bigg)^{n-1}\\\\\\\bullet S_1=\dfrac{1}{2}\\\\\bullet S_2=\dfrac{1}{2}+\dfrac{1}{6}=\dfrac{2}{3}\\\\\bullet S_3=\dfrac{1}{2}+\dfrac{1}{6}+\dfrac{1}{18}=\dfrac{13}{18}\\\\\bullet S_4=\dfrac{1}{2}+\dfrac{1}{6}+\dfrac{1}{18}+\dfrac{1}{54}=\dfrac{39}{54}$

$\lim_{n \to \infty} \dfrac{1}{2}\bigg(\dfrac{1}{3}\bigg)^{n-1}\implies \dfrac{1}{2}\lim_{n \to \infty} \dfrac{1}{3^{\infty-1}}\implies \dfrac{1}{\infty}=0\\\\\\\text{The series converges so it does have a sum.}$

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3 years ago

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seropon [69]

Answer:

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Step-by-step explanation:

Factor each half of the expression separately:

$4k^2(7k-6)+7(7k-6)$

Since both 4k² and 7 are being multiplied by (7k-6), we can combine them to get:

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