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3 years ago

15

The equation r=3c +5 represents the values shown in the table below C- 6, 8, 12, 18 R- 23, 29, ?, 59 What is the missing value i

n the table?

2 answers:

Kipish [7]3 years ago

4 0

C: 41 is the missing value in the table

almond37 [142]3 years ago

3 0

The missing value is 53.

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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.

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3 years ago

Thompson and Thompson is a steel bolts manufacturing company. Their current steel bolts have a mean diameter of 134 millimeters,

Arisa [49]

; 134

a:8

n:44

3.6

3.6

P,ob.Z);Jlty : 1 - P(:

<z<-

[ - ]]p(-2.98 ' z ' 2.98)]

[ -]p(z ' 2.98) - p(z ' -2.98)]

[ - E0.9986 - 0.0014]

=0.0028

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3 years ago

Select the correct answer.

Anastaziya [24]

Answer:

yo

Step-by-step explanation:

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3 years ago

2y^2-10y^2+9y-45 <br> Factor polynomial completely

hammer [34]

Answer:

-8y^2+9y-45

Step-by-step explanation:

symbolab.com

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3 years ago

What is the location of the point (5, 0) translates 4 units to the down and reflected across the y-axis?

CaHeK987 [17]

STEP-BY-STEP EXPLANATION:

Given information

The given ordered point = (5, 0)

Step 1: We need to translate the point 4 units down

To translate down means we will be subtracting a value from the y--axis

Hence, we have

$\begin{gathered} (x,\text{ y) }\rightarrow\text{ (x, y-b)} \\ \text{where b = 4} \\ (5,\text{ 0) }\rightarrow\text{ (5, 0 - 4)} \\ (5,\text{ 0) }\rightarrow\text{ (5, -4)} \end{gathered}$

When translated 4 units down, we got (5, -4)

Step 2: Reflect over the y-axis

The general rule for reflecting over the y-axis is (-x, y)

This means the value of x will be negated and the value of y will remain the same

$\begin{gathered} \text{Over the y-ax}is \\ (x,\text{ y) }\rightarrow\text{ (-x, y)} \\ (5,\text{ -4) }\rightarrow\text{ (-5, -4)} \end{gathered}$

Step 3: the graph the point

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1 year ago