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2 years ago

Describe the series of rigid transformations that maps pqs onto p’’’q ’’’s ’’’ .explain.

Mathematics

1 answer:

Masteriza [31]2 years ago

7 0

It’s triangular your welcome hint q

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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))

8 0

2 years ago

When two computers are working together, they can finish updating software in 9 minutes. How long would they take individually t

tensa zangetsu [6.8K]

First computer takes x min. For 1 min it does 1/x part of work.

Second computer takes (x+24) min. For one min it does 1/(x+24) part of work.

Both computers for one min do (1/x+1/(x+24)) part of work.

At the same time, both computers for one min do 1/9 part of work.

$\frac{1}{x} + \frac{1}{x+24} = \frac{1}{9} 
\\ \\ \frac{x+24+x}{x(x+24)} = \frac{1}{9} 
\\ \\9(2x+24)=x^{2} +24x
\\ \\ 18x+216=x^{2} +24x
\\ \\ x^{2}+6x-216=0
\\ \\ D=b^{2}-4ac=36+4*216 = 900
\\ \\ x= \frac{-b+/- \sqrt{D} }{2a} = \frac{-6+/-30}{2} 
\\ \\ x_{1}=-18, x_{2}=12

We can use only positive number here. So, 

for the first computer x=12 min,

 for second computer x+24=12+24= 36 min

Answer 12 min and 36 min.$

7 0

3 years ago

If you stand next to a wall on a frictionless skateboard and push the wall with a force of 36 N, how hard does the wall push on

VARVARA [1.3K]

The wall pushes back with an equal and opposite force. So it pushes with a force of 36N in the opposite direction of the push. This allows you to move away from the wall.

7 0

3 years ago

If you are given the graph of g (x) = log2 x, how could you graph f (x) = log2 x + 5?

Klio2033 [76]

You move the original graph
5
to the left.

3 0

3 years ago

How to solve (<br> 7•6-4^2)+4

Anuta_ua [19.1K]

Answer:

Step-by-step explanation:

3 0

3 years ago

Read 2 more answers