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3 years ago

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How is g(x) = (x - 1)^2 related to the graph of f(x) = x^2

1 answer:

Setler79 [48]3 years ago

3 0

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A cylindrical can without a top is made to contain 25 3 cm of liquid. What are the dimensions of the can that will minimize the

Basile [38]

Answer:

Therefore the radius of the can is 1.71 cm and height of the can is 2.72 cm.

Step-by-step explanation:

Given that, the volume of cylindrical can with out top is 25 cm³.

Consider the height of the can be h and radius be r.

The volume of the can is V= $\pi r^2h$

According to the problem,

$\pi r^2 h=25$

$\Rightarrow h=\frac{25}{\pi r^2}$

The surface area of the base of the can is = $\pi r^2$

The metal for the bottom will cost $2.00 per cm²

The metal cost for the base is =$(2.00× $\pi r^2$ )

The lateral surface area of the can is = $2\pi rh$

The metal for the side will cost $1.25 per cm²

The metal cost for the base is =$(1.25× $2\pi rh$ )

$=\$2.5 \pi r h$

Total cost of metal is C= 2.00 $\pi r^2$ + $2.5 \pi r h$

Putting $h=\frac{25}{\pi r^2}$

$\therefore C=2\pi r^2+2.5 \pi r \times \frac{25}{\pi r^2}$

$\Rightarrow C=2\pi r^2+ \frac{62.5}{ r}$

Differentiating with respect to r

$C'=4\pi r- \frac{62.5}{ r^2}$

Again differentiating with respect to r

$C''=4\pi + \frac{125}{ r^3}$

To find the minimize cost, we set C'=0

$4\pi r- \frac{62.5}{ r^2}=0$

$\Rightarrow 4\pi r=\frac{62.5}{ r^2}$

$\Rightarrow r^3=\frac{62.5}{ 4\pi}$

⇒r=1.71

Now,

$\left C''\right|_{x=1.71}=4\pi +\frac{125}{1.71^3}>0$

When r=1.71 cm, the metal cost will be minimum.

Therefore,

$h=\frac{25}{\pi\times 1.71^2}$

⇒h=2.72 cm

Therefore the radius of the can is 1.71 cm and height of the can is 2.72 cm.

6 0

3 years ago

Find the value of x when the area of a triangle is 22 in2 and has a base of 3x-1 and height of x.

Virty [35]

The formula for the area of a triangle is (1/2)bh = A
when we plug in the numbers, we get (1/2)(3x-1)x = A
using the distributive property we get (1.5x - .5)x = A
Then its 1.5x^2 - .5x = A
then if we factor out 0.5x we get 0.5x(3x-1) = A
then with the zero product property, 0.5x can equal 0 and x would need to equal 0.
if 3x-1 = 0 , then 3x = 1 then x = 1/3. so our answer would be 1/3 I'm pretty sure because a length cannot be 0

5 0

3 years ago

Find the exact value of cos210 using the unit circle

Eduardwww [97]

Cos 210° = cos ( 180° + 30° ) - cos 30° = - √3/2

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3 years ago

Simplify the expression 30x^6/3x^-2

Ne4ueva [31]

Answer:

$30x^{4}$

Step-by-step explanation:

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3 years ago

How do you write -4 1/5 as an improper fraction

jekas [21]

-21/5

Multiply 4 and 5, add 1

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3 years ago

Read 2 more answers