P(1,-3) Q(5,2) exact distance

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

What is the solution to the inequality shown below?

lesantik [10]

To solve the inequality, you need to isolate/get the variable "p" by itself in the inequality:

5p + 26 < 72 Subtract 26 on both sides

5p + 26 - 26 < 72 - 26

5p < 46 Divide 5 on both sides to get "p" by itself

$\frac{5p}{5}$

$p$

p < 9.2 Your answer is A

8 0

3 years ago

Can you answer this please

hjlf

I think it’s 155in 2

6 0

3 years ago

write the equation if the line in slope- intercept form that passes through (7,-4) with a slope of -1.

QveST [7]

9514 1404 393

Answer:

y = -x +3

Step-by-step explanation:

The point-slope form can be a useful place to start.

y -k = m(x -h) . . . . . line with slope m through point (h, k)

You require the line ...

y -(-4) = -1(x -7)

y = -x +7 -4 . . . . . . . . eliminate parentheses, add -4

y = -x +3 . . . . . . . . . slope-intercept form

7 0

3 years ago

What is the length of AB?<br> O A. 9<br> O B. 18<br> O C. 48<br> D. 6

insens350 [35]

<h3>Answer: A. 9</h3>

=====================================================

Explanation:

Draw in the segments AO and OC.

Triangle ABO is congruent to triangle CBO. We can prove this through the use of the HL theorem. HL stands for hypotenuse leg.

Since the triangles are congruent, this means the corresponding pieces AB and BC are the same length.

Then we can say:

AB+BC = AC .... segment addition postulate

AB+AB = AC .... plug in BC = AB

2*AB = AC

2*AB = 18

AB = 18/2 .... divide both sides by 2

AB = 9

In short, the chord AC is bisected by the perpendicular radius drawn in the diagram. So all we do is cut AC = 18 in half to get AB = 9.

6 0

2 years ago

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