Can you show the mentioned diagram?
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 (
), in cubic centimeters, and surface area (
), in square centimeters, formulas for the candle are described below:
(1)
(2)
Where:
- Radius, in centimeters.
- Height, in centimeters.
By (1) we have an expression of the height in terms of the volume and the radius of the candle:

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


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



![r = \sqrt[3]{\frac{V}{2\pi} }](https://tex.z-dn.net/?f=r%20%3D%20%5Csqrt%5B3%5D%7B%5Cfrac%7BV%7D%7B2%5Cpi%7D%20%7D)
There is just one result, since volume is a positive variable.
Second Derivative Test

If
:

(which means that the critical value leads to a minimum)
If we know that
, then the dimensions for the minimum amount of plastic are:
![r = \sqrt[3]{\frac{V}{2\pi} }](https://tex.z-dn.net/?f=r%20%3D%20%5Csqrt%5B3%5D%7B%5Cfrac%7BV%7D%7B2%5Cpi%7D%20%7D)
![r = \sqrt[3]{\frac{3217\,cm^{3}}{2\pi}}](https://tex.z-dn.net/?f=r%20%3D%20%5Csqrt%5B3%5D%7B%5Cfrac%7B3217%5C%2Ccm%5E%7B3%7D%7D%7B2%5Cpi%7D%7D)




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



The candle has a radius of 8 centimeters and 16 centimeters and uses an amount of approximately 1206.372 square centimeters.
Answer:
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The constant of proportionality is 1.25 and its meaning is the soup price per can
Step-by-step explanation:
The diagram below shows a proportional relationship between the number of cans of soup and the price.
1st:
$3.75 for 3 cans
per can
2nd:
$6.25 for 5 cans
per can
If x is the number of cans and y is the price of x cans, then
This means the constant of proportionality is 1.25 and its meaning is the soup price per can
Answer:
- a) 2x -y = -5; A=2, B=-1, C=-5
- b) y = 2x +5
Step-by-step explanation:
a) Standard Form is ...
Ax + By = C
where A > 0 and A, B, C are mutually prime.
To get that form, we can add 2x-5 to both sides of the equation:
(2x -5) -2x = (2x -5) -y +5
-5 = 2x -y
Then we can swap sides of the equal sign:
2x -y = -5 . . . . . . standard form
Matching this to the generic standard form equation, we find ...
A = 2
B = -1
C = -5
__
b) We can solve for y by adding 2x+y to both sides of the equation:
(2x +y) -2x = (2x +y) -y +5
y = 2x +5 . . . . . . slope-intercept form