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stiv31 [10]
3 years ago
5

The equation of line r is y = -12 1 2 x - 4. If line s runs perpendicular to line r and passes through (4, -3), what would be th

e equation of line s?
Mathematics
2 answers:
vovangra [49]3 years ago
8 0

Answer:

I believe that she wants to write "The equation of line r is y = -1/2x - 4. If line s runs perpendicular to line r and passes through (4, -3), what would be the equation of line s?"

Step-by-step explanation:

N76 [4]3 years ago
3 0
Can you please retype the equation for line r? I don’t understand
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Solve y=f(x) for x. Then find the input when the output is -3.
DochEvi [55]

Answer:

Please check the explanation

Step-by-step explanation:

Given the function

f\left(x\right)\:=\:\left(x-5\right)^3-1

Given that the output = -3

i.e. y = -3

now substituting the value y=-3 and solve for x to determine the input 'x'

\:\:y=\:\left(x-5\right)^3-1

-3\:=\:\left(x-5\right)^3-1\:\:\:

switch sides

\left(x-5\right)^3-1=-3

Add 1 to both sides

\left(x-5\right)^3-1+1=-3+1

\left(x-5\right)^3=-2

\mathrm{For\:}g^3\left(x\right)=f\left(a\right)\mathrm{\:the\:solutions\:are\:}g\left(x\right)=\sqrt[3]{f\left(a\right)},\:\sqrt[3]{f\left(a\right)}\frac{-1-\sqrt{3}i}{2},\:\sqrt[3]{f\left(a\right)}\frac{-1+\sqrt{3}i}{2}

Thus, the input values are:

x=-\sqrt[3]{2}+5,\:x=\frac{\sqrt[3]{2}\left(1+5\cdot \:2^{\frac{2}{3}}\right)}{2}-i\frac{\sqrt[3]{2}\sqrt{3}}{2},\:x=\frac{\sqrt[3]{2}\left(1+5\cdot \:2^{\frac{2}{3}}\right)}{2}+i\frac{\sqrt[3]{2}\sqrt{3}}{2}

And the real input is:

x=-\sqrt[3]{2}+5

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