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3 years ago

Given a rectangle with a perimeter of 24 inches, why dimensions maximize the area?

Mathematics

1 answer:

Pepsi [2]3 years ago

5 0

Answer:

The dimensions are 6 by 6

Step-by-step explanation:

Calculus answer:

2x +2y= 24

xy= A

2x=24-2y

x=12-y

(12-y)(y)= 12y- y^2

the Derivative is = 12-2y

Then set that equal to zero 0=12-2y

-12=-2y

y=6

Confirm that 6 is a maximum by using a wiggle graph

wiggle graph -∞<---inc--6---dec-->∞

6 is a maximum

plug into original equation

2x + 2(6)=24

2x+12=24

2x=12

x=6

----------------------------------------------------------------------------------------------------

y=6

x=6

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A swimming pool is represented on a coordinate grid with the following vertices: Vertex A is at (−2,−3) . Vertex B is at (−2,

Semmy [17]

Answer:

26 yards.

Step-by-step explanation:

We can find the distance walked by Jared by finding the distances between each of the given vertex of swimming pool. We will use distance formula to find the distances between each vertex.

$\text{Distance}=\sqrt{(x_2-x_1)^{2}+(y_2-y_1)^{2}}$

$\text{Distance between vertex A and vertex B}=\sqrt{(-2--2)^{2}+(-3-5)^{2}}$

$\text{Distance between vertex A and vertex B}=\sqrt{(-2+2)^{2}+(-8)^{2}}$

$\text{Distance between vertex A and vertex B}=\sqrt{(0)^{2}+(-8)^{2}}$

$\text{Distance between vertex A and vertex B}=\sqrt{64}=8$

Now let us find distance between vertex B and vertex C.

$\text{Distance between vertex B and vertex C}=\sqrt{(-2-3)^{2}+(5-5)^{2}}$

$\text{Distance between vertex B and vertex C}=\sqrt{(-5)^{2}+(0)^{2}}$

$\text{Distance between vertex B and vertex C}=\sqrt{25}=5$

Now let us find distance between vertex C and vertex D.

$\text{Distance between vertex C and vertex D}=\sqrt{(3-3)^{2}+(5--3)^{2}}$

$\text{Distance between vertex C and vertex D}=\sqrt{(0)^{2}+(5+3)^{2}}$

$\text{Distance between vertex C and vertex D}=\sqrt{64}=8$

Now let us find distance between vertex D and vertex A.

$\text{Distance between vertex D and vertex A}=\sqrt{(3--2)^{2}+(-3--3)^{2}}$

$\text{Distance between vertex D and vertex A}=\sqrt{(3+2)^{2}+(-3+3)^{2}}$

$\text{Distance between vertex D and vertex A}=\sqrt{(5)^{2}+(0)^{2}}$

$\text{Distance between vertex D and vertex A}=\sqrt{25}=5$

Now let us add all these distances to find the total distance walked by Jared.

$\text{Total distance walked by Jared}=8+5+8+5$

$\text{Total distance walked by Jared}=26$

Since we have been given that one unit on the grid equals 1 yard, therefore, Jared walked a distance equal to 26 yards.

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3 years ago

Together, two apples have 175 gram of fat. How many apples have a total of 4 grams of fat?

inysia [295]

I'm pretty sure if the answer accepts decimals, if two apples = 175 grams, then one apple equals 87.5 grams, and if we want an apple that equals four grams, it would be less than one apple so we would divide the grams of one apple till it equals 4, therefore 87.5/4 = 21.875

P.S. im not entirely sure this is right im just trying to help :)

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2 years ago

How many solutions does the equation 2x-6=6+2x

Alex_Xolod [135]

Answer:

2 solutions

Step-by-step explanation:

Since the equations are not equal, they provide two solutions. Negative numbers provide no solutions. If they are equal to zero, they have one solution.

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3 years ago

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Anarel [89]

Answer:

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Step2247 [10]

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