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3 years ago

Express the following in exponential notation: (3p) x (3p) x (3p)

Mathematics

1 answer:

Flauer [41]3 years ago

7 0

27 p3 is the simple forum

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A rectangular box is to have a square base and a volume of 72 ft3. If the material for the base costs $0.62/ft2, the material fo

Igoryamba

Answer:

a. length = 0.7211 ft

b. width = 0.7211 ft

c. height = 140.3846 ft

Step-by-step explanation:

This is an optimiztion with restriction problem.

We have to minimize the cost, with the restriction of the volume being equal to 72 ft3.

As the cost for the sides is constant, we know that length and width are equal.

Then, we can express the volume as:

$V=x\cdot y\cdot z=x^2z=73$

being x: length and z: height

We can express the height in function of the length as:

$x^2z=73\\\\z=73x^{-2}$

Then, the cost of the box can be expressed as:

$C=0.62(x^2)+4*0.15(xz)+0.18(x^2)=(0.62+0.18)x^2+0.60xz\\\\C=0.8x^2+0.60x*x^{-2}=0.8x^2+0.6x^{-1}$

To optimize C, we derive and equal to zero

$\dfrac{dC}{dx}=\dfrac{d}{dx}[0.8x^2+0.6x^{-1}]=1.6x-0.6x^{-2}=0\\\\\\1.6x=0.6x^{-2}\\\\x^{1+2}=0.6/1.6=0.375\\\\x=\sqrt[3]{0.375} =0.7211$

The height z is then

$z=73x^{-2}=\dfrac{73}{0.7211^2}=\dfrac{73}{0.52}=140.3846$

6 0

3 years ago

What’s is the answer to these two problems?

Len [333]

Answer:

Step-by-step explanation:

8 0

3 years ago

Help!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Roman55 [17]

Answer:

Answer =C

Step-by-step explanation:

F= 9

So teh answer is 9

6 0

3 years ago

What is the perimeter of the polygon shown below?

yKpoI14uk [10]

Answer:

I don't see the polygon but all you need to do is add up all the sides.

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3 years ago

30-60-90 Angle Triangle- Geometry

AlexFokin [52]

Answer:

perimeter = 42 units

Step-by-step explanation:

7 0

2 years ago