CalculatorUser

What does the C stand for, just making sure.

I plugged your equation into a calculator and it didn't work

C(14)=1.182+2.216*In(14) = {}

What are you solving for?

1.)

\(\text{If you want to figure out }(x-y)^2\text{, You can expand it to }x^2-2xy+y^2\)

\(\text{Notice how }xy=6\text{ now that means we can place it into our } x^2-2xy+y^2\text{ equation}\)

\(\text{So we have: }x^2-2xy+y^2\Rightarrow{x^2}-2(6)+y^2\Rightarrow{\color{green}x^2+y^2-12}\)

\(\text{Now consider one of the equations we were given: }(x+y)^2=31\)

\(\text{We can now expand the following: } (x+y)^2=31\Rightarrow{\color{red}x^2+2xy+y^2=31}\)

\(\text{Now we place }xy=6\text{ into the red equation}\)

\(x^2+2xy+y^2=31\rightarrow{x^2}+2(6)+y^2=31\rightarrow{\color{red}x^2+y^2=19}\)

\(\text{Now we combine the new red equation and the green equation together for the answer}\)

\({\color{red}x^2+y^2=19}\text{ and }{\color{green}x^2+y^2-12}\Rightarrow{19-12}=\boxed{7}\)

I do not have time to answer the other questions, but I am sure that the all involve expanding special cases and combining equations!

did it tell you why the h-value was wrong?

Im going to answer number 4 because i have no time I need to go.

Newton's third law states: For every action there is an equal and opposite force

So examples of third law

Jumping, you apply force to the ground,  ground applies an opposite force to you which makes you go higher.

Your welcome!

.I literally just watched a video on how to do this, this is a learning process for me too 

I am assuming that you learned the trig vocabulary for this as you asking these problems

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Lets first do a cosine graph cuz its easier

This is the base equation for a cosine graph:

\(y=A\cos{b}(x-h)+c\)

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So first find the amplitude, which is the height of the waves of the graph. (using y-values)

\(\text{Amplitude}=|\frac{\text{Max}-\text{Min}}{2}|\)

\(|\frac{-5-(-4)}{2}|\)

\(|\frac{-1}{2}|\)

\(\text{Amplitude}=\frac{1}{2}\)

Now we have the "A" value

\(y=\frac{1}{2}\cos{b}(x-h)+c\)

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Ok now we have to find the period

We first find the positive difference of the x values to find the horizontal distance.

\(|-1-3.5|=4.5\)

Then we double what we got

\(9\)

Then we solve for the b-value

\(9=\frac{2\pi}{b}\rightarrow9b=2pi\rightarrow{b}=\frac{2pi}{9}\)

Now we have

\(y=\frac{1}{2}\cos{\frac{2pi}{9}}(x-h)+c\)

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Now we have to find the phase shift (h-value)

Since it has shifted -1,                          ( coordinate (-1, -5) tells us that. )

We now have:

\(y=\frac{1}{2}\cos{\frac{2pi}{9}}(x+1)+c\)

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Now we have to find the vertical shift (c-value)

Formula for that is 

\(c=\frac{\text{Maximum}}{2}\)

\(c=\frac{-5+(-4)}{2}\)

\(c=-4.5\)

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So the equation of the sinusoidal graph is

\(y=\frac{1}{2}\cos{\frac{2pi}{9}}(x+1)-4.5\)

This is the cosine graph.

Just to make sure

Is it b^3 , or is it b^2?

This is my HINT for the last question:

Find the area of the triangle

Find the area of the pizza sections (non-shaded)

The angles of a equilateral triangle are always 60 degrees.

That means one of the pizza sections is 1/6 of an entire circle/

Now I will leave the rest up to you.

Its ok, you seem like you need practice

You are incorrect,

that is the percentage of US drinkers