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3 years ago

Points (-21, ) and (-7, y) have a slope of 5. Find the y coordinate of the point.

Mathematics

1 answer:

Ira Lisetskai [31]3 years ago

5 0

Answer:

girl bye you forgot the y coordinate in the first pair sorry lollll

Step-by-step explanation:

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3 years ago

A carpentry shop currently sells 66000 decoy ducks per year at a cost of 16 dollars each. In the previous year when they raised

Rus_ich [418]

Answer:

19 dollars

Step-by-step explanation:

<h2>Buckle up! This is a good one!</h2>

First we have to find the line that goes trough the two points. And it has the form :

$y=mx+b$

<em>m is often called the slope.</em>

Given the two points (66000, 16) and (51000, 21) we find m with this formula:

$m=\frac{y_{2} -y_{1} }{x_{2} -x_{1} }\\m=\frac{21-16}{51000-66000} \\m=-\frac{5}{15000} \\m=-\frac{1}{3000}$

We pick the point (51000,21) and plug it into the equation of the line and we find b:

$y= mx + b\\21=(-\frac{1}{3000} )(51000)+b\\21=-17+b\\21+17=b=38$

<h3>And we have got our line equation</h3>

$y= -\frac{1}{3000}x + 38\\$

<u>Where x represents the quantity and y represents the price.</u>

<u />

<h2>The revenue</h2>

The revenue is price times quantity, since price is y and quantity is x, we get

$y=-\frac{1}{3000} x+38\\y*x=x*(-\frac{1}{3000} x+38)\\yx=-\frac{1}{3000} x^2+38x\\R(x)=-\frac{1}{3000} x^2+38x$

<h3>to maximize the revenue, we get the first derivative:</h3>

$R(x)=-\frac{1}{3000} x^2+38x\\R'(x)=-(2)\frac{1}{3000} x+38\\R'(x)=-\frac{2}{3000} x+38\\\\R'(x)=-\frac{1}{1500} x+38\\\\$

$R'(x)=-\frac{1}{1500} x+38=0\\38=\frac{1}{1500} x\\38*1500=x=57000$

So the quantity that maximizes revenue is 57000,

<h3>let's find out the price by plugging it into the equation:</h3>

$y= -\frac{1}{3000}x + 38\\y= -\frac{1}{3000}(57000) + 38\\y= -19 + 38\\y=19$

<h2>And there you go! 19 dollars is the price the carpentry shop should charge per decoy duck.</h2>

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3 years ago