We can use the pythagorean theorem to solve this
The pythagorean theorem = a^2 + b^2 = c^2, while
a = one leg
b = the second leg
c = the hypotenuse
In this problem,
a = 3
b = 15
c = ?
Let's plug our values into the pythagorean theorem
(3)^2 + (15)^2 = c^2
9 + 225 = c^2
Add together the left side
234 = c^2
Take the sqrt of both sides
sqrt(234) = c
The length of BC = sqrt(234)
Answer:
The difference in the amount of wax needed is 84.78 in³ (84.78 cubic inches)
Step-by-step explanation:
Given
<em>Cylinder</em>
Radius = 3 inches
Height = 7 inches
<em>Sphere</em>
Radius = 3 inches
Required
The difference in the amount of wax needed to make a candle from each of these molds
The quantity or amount required to make a wax of candle from each molds can be calculated by getting the volume of both molds
The volume of a cylinder is calculated using
<em>V₁ = πr²h</em>
where r and h are the radius and the height of the cylinder, respectively.
r = 3 in and h = 7 in
The volume of a sphere is calculated using
![V_{2} = \frac{4}{3}\pi r^3](https://tex.z-dn.net/?f=V_%7B2%7D%20%3D%20%5Cfrac%7B4%7D%7B3%7D%5Cpi%20r%5E3)
where r is the radius of the sphere
r = 3 in
Calculating V₁
V₁ = πr²h
V₁ = π * 3² * 7
V₁ = π * 9 * 7
V₁ = π * 63
V₁ = 63π
Calculating V₂
![V_{2} = \frac{4}{3}\pi r^3](https://tex.z-dn.net/?f=V_%7B2%7D%20%3D%20%5Cfrac%7B4%7D%7B3%7D%5Cpi%20r%5E3)
![V_{2} = \frac{4}{3} * \pi * 3^3](https://tex.z-dn.net/?f=V_%7B2%7D%20%3D%20%5Cfrac%7B4%7D%7B3%7D%20%2A%20%5Cpi%20%2A%203%5E3)
![V_{2} = \frac{4}{3} * \pi * 27](https://tex.z-dn.net/?f=V_%7B2%7D%20%3D%20%5Cfrac%7B4%7D%7B3%7D%20%2A%20%5Cpi%20%2A%2027)
![V_{2} = \frac{108}{3} * \pi](https://tex.z-dn.net/?f=V_%7B2%7D%20%3D%20%5Cfrac%7B108%7D%7B3%7D%20%2A%20%5Cpi)
V₂ = 36π
Having calculated the volume of each molds, the difference in the amount of wax needed can then be calculated.
Difference = V₁ - V₂
Substituting 63π for V₁ and 36π for V₂
Difference = 63π - 36π
Difference = 27π
<em>(Taking π = 3.14)</em>
Difference = 27 * 3.14
Difference = 84.78
Hence, difference in the amount of wax needed is 84.78 in³
Yes.
It's a proportional relationship because when graphing this problem on the graph the line goes through (0,0). Therefor it is a proportional relationship. Some problems like these won't be a proportional relationship because it's not going through (0,0).
Answer:
Given the equation 2y-40=-18 to simplify the equation further we need to first add 40 to both sides of the equation thereby justifying the addition property as shown;
2y-40 + 40 =-18+40
2y = 40-18
2y = 22
We will also apply the division property here. Division property is used when both sides of an equation is divided by a number without affecting the equality rule.
Dividing the resulting equation by 2:
2y/2 = 22/2
y = 11
Step-by-step explanation:
Answer:
552 miles :)
Step-by-step explanation:
138 times 4 = 552
552/4 = 138