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3 years ago

Which is the greater rate of change? -1/2 4/1

1 answer:

mote1985 [20]3 years ago

3 0

4/1 is a greater rate of change because it is the same as 4. A whole number will always be greater than a fraction and also the fraction is negative which makes it even smaller than a regular fraction. I hope this answers your question! :)

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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

Solve the absolute value equation. | 4 - 8x | = 40 Select the correct choice below and fill in any answer boxes in your choice.

Step2247 [10]

Answer:

A. x = 5,5 , -4,5 are the TWO SOLUTIONS of | 4 - 8 x | = 40

Step-by-step explanation:

Here, the given expression is: | 4 - 8 x | = 40

Now, here firstly we need the find the range where (4-8 x) is NEGATIVE and where (4-8x) is POSITIVE.

To find CRITICAL POINT, put (4-8 x) = 0

⇒ 4 = 8x or x = 4/8 = 1/2

⇒ x = 1/2 is the CRITICAL POINT.

CASE - 1 : For x > 1/2, ( 4-8x) < 0 ( negative)

⇒ for x > 1/2 , | 4 - 8 x | = 40 is -(4- 8x) = 40 ( for a < 0, IaI = -a)

or, -4 + 8 x = 40

or, 8 x = 44 , or x = 44/8 = 5.5

⇒ for x > 1/2, x = 5.5 is the solution of | 4 - 8 x | = 40

CASE - 1 : For x ≤ 1/2, ( 4- 8 x) ≥ 0 ( positive)

⇒ for x ≤ 1/2 , | 4 - 8 x | = 40 is (4- 8x) = 40 ( for a > 0, IaI = a)

or, 4 - 8 x = 40

or, 8 x =4 - 40 , or 8 x = -36 or, x = -36/8 = -4.5

⇒ for x ≤ 1/2, x = -4.5 is the solution of | 4 - 8 x | = 40

Hence, x = 5,5 , -4,5 are the TWO POSSIBLE SOLUTIONS of | 4 - 8 x | = 40

5 0

3 years ago

Find the measure of the missing angles <br> b=<br> c=

Vesnalui [34]

Answer:

b=20

c=160

Step-by-step explanation:

b has the same measurement as the other angle that is across from it. c is 160 because the line that c is on is a straight line so it is 180 degrees, you subtract the other angle on the line,20, then you get the answer.

8 0

3 years ago

Read 2 more answers

Solve The Following Problems Write your Answer in Your Notebook

aleksandrvk [35]

Answer:

its either 3 or 4

Step-by-step explanation:

4 0

3 years ago

Please brainliest <br> And happy Halloween

Vaselesa [24]