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3 years ago

Find the value of the unknown side length for the given perimeter P. P = 14 m A. 3 m B. 4 m C. 14 m D. 25 m

Mathematics

1 answer:

koban [17]3 years ago

5 0

If the perimeter is 14. Add 2,4, and 5 which is 11. Then find out how many meters does it take to get from 11 to 14. In this case the answer is 3

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3 years ago

A box with a square base and open top must have a volume of 157216 cm3. We wish to find the dimensions of the box that minimize

shepuryov [24]

Answer:

Base Length of 68cm
Height of 34 cm.

Step-by-step explanation:

Given a box with a square base and an open top which must have a volume of 157216 cubic centimetre. We want to minimize the amount of material used.

Step 1:

Let the side length of the base =x

Let the height of the box =h

Since the box has a square base

Volume $=x^2h=157216$

$h=\dfrac{157216}{x^2}$

Surface Area of the box = Base Area + Area of 4 sides

$A(x,h)=x^2+4xh\\$Substitute h=\dfrac{157216}{x^2}\\A(x)=x^2+4x\left(\dfrac{157216}{x^2}\right)\\A(x)=\dfrac{x^3+628864}{x}$

Step 2: Find the derivative of A(x)

$If\:A(x)=\dfrac{x^3+628864}{x}\\A'(x)=\dfrac{2x^3-628864}{x^2}$

Step 3: Set A'(x)=0 and solve for x

$A'(x)=\dfrac{2x^3-628864}{x^2}=0\\2x^3-628864=0\\2x^3=628864\\x^3=314432\\x=\sqrt[3]{314432}\\ x=68$

Step 4: Verify that x=68 is a minimum value

We use the second derivative test

$If\:A(x)=\dfrac{x^3+628864}{x}\\A''(x)=\dfrac{2x^3+1257728}{x^3}\\$When x=68\\A''(x)=6$

Since the second derivative is positive at x=68, then it is a minimum point.

Recall:

$h=\dfrac{157216}{x^2}\\h=\dfrac{157216}{68^2}=34$

Therefore, the dimensions that minimizes the box surface area are:

Base Length of 68cm
Height of 34 cm.

3 0

3 years ago

Needed quickly like asap

Artemon [7]

It is 18/20 and in simplest form it is 9/10.

Steps:
1.You have to add all the shirts, 2+7+11. This is 20, this will become your denominator

2. See what portion is NOT BLACK, the non black at 7 and 11, once you add these it becomes 18. 18 is now your numerator.

3. You now have the fraction 18/20 which you can simplify into 9/10

Hope this helps :)

4 0

3 years ago