How do you write a rule for a linear function?

1 answer:

5 0

Solve linear equation as follows:
- Unknown move to one side of the equation, and the numbers on the other side of the equation,
- Multiply or divide both sides by a value in order to get the number of the unknown x,
<span>- The transfer number or unknown to the other side of the equation, change the sign to the opposite.</span>

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A cable runs along the wall from C to P at a cost of $4 per meter, and straight from P to M at a cost of $5 per meter. If M i

a_sh-v [17]

Answer:

The minimum cost of installing the cable is $156.

Step-by-step explanation:

We have an optimization problem.

We have to minimize the cost of the cable.

We will use the variable x to express the the length of cable CP and PM, accordingly to the attache picture.

The length of the cable that goes from C to P (let's call it CP) is x.

$\bar{CP}=x$

Then, the length of the cable that goes from P to M (PM) can be calcualted usign the Pithagorean theorem:

$\bar{PM}=\sqrt{(33-x)^2+9^2}$

The cost function Y is:

$Y=4*\bar{CP}+5*\bar{PM}=4x+5\sqrt{(33-x)^2+9^2}$

To optimize this cost funtion we have to derive and equal to 0:

$\dfrac{dY}{dx}=0\\\\\\\dfrac{dY}{dx}=4+5(\dfrac{1}{2})((33-x)^2+9^2)^{-1/2} *(-2)(33-x)\\\\\\\dfrac{dY}{dx}=4+5\dfrac{x-33}{\sqrt{(33-x)^2+81}}=0\\\\\\\dfrac{x-33}{\sqrt{(33-x)^2+81}}=-\dfrac{4}{5}\\\\\\(x-33)=-\dfrac{4}{5}\sqrt{(33-x)^2+81}\\\\\\(x-33)^2=(-\dfrac{4}{5})^2[(x-33)^2+81]\\\\\\(x-33)^2=\dfrac{16}{25}(x-33)^2+\dfrac{1296}{25}\\\\\\\dfrac{25-16}{25} (x-33)^2=\dfrac{1296}{25}\\\\\\9(x-33)^2=1296\\\\\\x-33=\sqrt{\dfrac{1296}{9}}=\sqrt{144}=\pm12\\\\\\x=33\pm12\\\\\\x_1=33-12=21\\\\x_2=33+12=45$

The valid solution is x=21, as x can not phisically larger than 33.

The cost then becomes:

$Y=4*\bar{CP}+5*\bar{PM}=4x+5\sqrt{(33-x)^2+9^2}\\\\\\Y=4*21+5\sqrt{(33-21)^2+81}\\\\Y=81+5\sqrt{144+81}\\\\Y=81+5\sqrt{225}\\\\Y=81+5*15\\\\Y=81+75\\\\Y=156$

6 0

3 years ago

PLEASE HELP ASAP WILL MARK BRAINLIEST

netineya [11]

For the first one a=4 cuz 4x4=16

7 0

3 years ago

Read 2 more answers

Long division 207 divided by 9 show your work

mihalych1998 [28]

You break up the 207 into smaller numbers you can work with. 9 can go into 20 a maximum of 2 times, so you subtract 2*9 or 18 from 20. Then, you bring down the 7. 9 goes into 27 exactly 3 times, so you have 9*23=207.