The quantity of a number and 3 all divided by 4 equals -2

strojnjashka [21]

Answer:

The candle has a radius of 8 centimeters and 16 centimeters and uses an amount of approximately 1206.372 square centimeters.

Step-by-step explanation:

The volume ( $V$ ), in cubic centimeters, and surface area ( $A_{s}$ ), in square centimeters, formulas for the candle are described below:

$V = \pi\cdot r^{2}\cdot h$ (1)

$A_{s} = 2\pi\cdot r^{2} + 2\pi\cdot r \cdot h$ (2)

Where:

$r$ - Radius, in centimeters.

$h$ - Height, in centimeters.

By (1) we have an expression of the height in terms of the volume and the radius of the candle:

$h = \frac{V}{\pi\cdot r^{2}}$

By substitution in (2) we get the following formula:

$A_{s} = 2\pi \cdot r^{2} + 2\pi\cdot r\cdot \left(\frac{V}{\pi\cdot r^{2}} \right)$

$A_{s} = 2\pi \cdot r^{2} +\frac{2\cdot V}{r}$

Then, we derive the formulas for the First and Second Derivative Tests:

First Derivative Test

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

$4\pi\cdot r^{3} - 2\cdot V = 0$

$2\pi\cdot r^{3} = V$

$r = \sqrt[3]{\frac{V}{2\pi} }$

There is just one result, since volume is a positive variable.

Second Derivative Test

$A_{s}'' = 4\pi + \frac{4\cdot V}{r^{3}}$

If $\left(r = \sqrt[3]{\frac{V}{2\pi}}\right)$ :

$A_{s} = 4\pi + \frac{4\cdot V}{\frac{V}{2\pi} }$

$A_{s} = 12\pi$ (which means that the critical value leads to a minimum)

If we know that $V = 3217\,cm^{3}$ , then the dimensions for the minimum amount of plastic are:

$r = \sqrt[3]{\frac{V}{2\pi} }$

$r = \sqrt[3]{\frac{3217\,cm^{3}}{2\pi}}$

$r = 8\,cm$

$h = \frac{V}{\pi\cdot r^{2}}$

$h = \frac{3217\,cm^{3}}{\pi\cdot (8\,cm)^{2}}$

$h = 16\,cm$

And the amount of plastic needed to cover the outside of the candle for packaging is:

$A_{s} = 2\pi\cdot r^{2} + 2\pi\cdot r \cdot h$

$A_{s} = 2\pi\cdot (8\,cm)^{2} + 2\pi\cdot (8\,cm)\cdot (16\,cm)$

$A_{s} \approx 1206.372\,cm^{2}$

The candle has a radius of 8 centimeters and 16 centimeters and uses an amount of approximately 1206.372 square centimeters.

3 0

2 years ago

Seven and thirty twp hundreths plus two and one tenth times two and seven tenths minus 18a

alexdok [17]

Answer: Write the expression as:

" 70 $\frac{32}{100}$ +
2 $\frac{1}{10}$ * 2 $\frac{7}{10$ − 18a " ;
______________________________________________________
or; write as:
______________________________________________________
" 70.32 + (2.1) * (2.7) − 18a " ;
______________________________________________________

To simplify:
______________________________________________________

Using "PEDMAS" (the "order of operations") ;

the "multiplication" comes first;

So: → "(2.1) * (2.7) = 5.67 " .

And rewrite:
______________________________________________________
" 70.32 + 5.67 − 18a " .

Now: " 70.32 + 5.67 = 75.99 " ;

So, we can the final simplified expression as:
______________________________________________________
" 75.99 − 18a " ;

or; write as: " 75 $\frac{99}{100}$ − 18a " .
______________________________________________________

7 0

2 years ago

Find the equation of a line that passes through points (1,8) and (4,4).

daser333 [38]

Step-by-step explanation: Using the equation, y = mx + b, the slope-intercept form, plug in the values you have and solve for b. (m is the slope.) You have y = -8 and x = 4 and m = 1/2.

3 0

1 year ago

Find the volume of the prism

hichkok12 [17]

Answer:

do you have an image for that?

Step-by-step explanation:

4 0

2 years ago

Solve for p. 21 + p = 44 HELP THIS IS URGENT

Scorpion4ik [409]

P= 41-21
The final result is P= 20