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3 years ago

The difference of 3x and 23 is 40

Mathematics

1 answer:

Tamiku [17]3 years ago

4 0

Answer:

x = 21

Step-by-step explanation:

3x - 23 = 40

Collect like terms

3x = 40 + 23

3x = 63

Divide through by 3

3x/3 = 63/3

x = 21

Check

3x - 23 = 40

since x = 21

3(21) - 23 = 40

63 - 23 = 40

40 = 40

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3 years ago

Among all rectangles that have a perimeter of 182, find the dimensions of the one whose area is largest.

Evgen [1.6K]

Answer:

<em>The largest rectangle of perimeter 182 is a square of side 45.5</em>

Step-by-step explanation:

<u>Maximization Using Derivatives</u>

The procedure consists in finding an appropriate function that depends on only one variable. Then, the first derivative of the function will be found, equated to 0 and find the maximum or minimum values.

Suppose we have a rectangle of dimensions x and y. The area of that rectangle is:

$A=x.y$

And the perimeter is

$P=2x+2y$

We know the perimeter is 182, thus

$2x+2y=182$

Simplifying

$x+y=91$

Solving for y

$y=91-x$

The area is

$A=x.(91-x)=91x-x^2$

Taking the derivative:

$A'=91-2x$

Equating to 0

$91-2x=0$

Solving

$x=91/2=45.5$

Finding y

$y=91-x=45.5$

The largest rectangle of perimeter 182 is a square of side 45.5

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3 years ago