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3 years ago

8

The given amount of annual interest is earned from a total of $13,000 invested in two funds paying simple interest. Write and so

lve a system of equations to find the amount invested at each given rate.

1 answer:

stiks02 [169]3 years ago

5 0

Answer:

because it just is this is not the actual answer

Step-by-step explanation:

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In a survey of 150 students at Kennedy Middle School, 48% said

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3 years ago

Identify the median and IQR of the data set below.20222426283032Your answerWhich dota

Dennis_Churaev [7]

We are given a boxplot that contains some data. We will use the information below to analyze the given question.

STEP 1: Median

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STEP 2: Interquartile range

The interquartile range is the difference between the third quartile and the first quartile.

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4 0

1 year ago

Please help solve this system of equations

stepan [7]

Make a substitution:

$\begin{cases}u=2x+y\\v=2x-y\end{cases}$

Then the system becomes

$\begin{cases}\dfrac{2\sqrt[3]{u}}{u-v}+\dfrac{2\sqrt[3]{u}}{u+v}=\dfrac{81}{182}\\\\\dfrac{2\sqrt[3]{v}}{u-v}-\dfrac{2\sqrt[3]{v}}{u+v}=\dfrac1{182}\end{cases}$

Simplifying the equations gives

$\begin{cases}\dfrac{4\sqrt[3]{u^4}}{u^2-v^2}=\dfrac{81}{182}\\\\\dfrac{4\sqrt[3]{v^4}}{u^2-v^2}=\dfrac1{182}\end{cases}$

which is to say,

$\dfrac{4\sqrt[3]{u^4}}{u^2-v^2}=\dfrac{81\times4\sqrt[3]{v^4}}{u^2-v^2}$

$\implies\sqrt[3]{\left(\dfrac uv\right)^4}=81$

$\implies\dfrac uv=\pm27$

$\implies u=\pm27v$

Substituting this into the new system gives

$\dfrac{4\sqrt[3]{v^4}}{(\pm27v)^2-v^2}=\dfrac1{182}\implies\dfrac1{v^2}=1\implies v=\pm1$

$\implies u=\pm27$

Then

$\begin{cases}x=\dfrac{u+v}4\\\\y=\dfrac{u-v}2}\end{cases}\implies x=\pm7,y=\pm13$

(meaning two solutions are (7, 13) and (-7, -13))

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3 years ago