What is the coordinate of the vertex?

Please help me with this it is about how wide the patio doors will be

Tcecarenko [31]

9 centimetres is probably most accurate

3 0

3 years ago

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

A triangular prism and its dimensions are snown in the diagram.

stealth61 [152]

A.......................... is the answering to this

6 0

3 years ago

a rectangular fish tank hold 12 fish, A round fish tank hold 3 fish. How many times as many fish dose the rectangular tank hold

ch4aika [34]

Answer:

4 times

Step-by-step explanation:

You divide 12 by 3

5 0

3 years ago

(8,5) and (x, -1); slope: -6

Aliun [14]

Answer:

9 = x; (9, -1)

Step-by-step explanation:

-y₁ + y₂\-x₁ + x₂ = m

-5 - 1\-8 + x

-8 + x = 1

+8 + 8

_________

x = 9

The denominator is set to equal one because the numerator already equals negative six, and all we have to do is divide it by a POSITIVE one to stay at negative six.

I am joyous to assist you anytime.

3 0

4 years ago