The members of the PTA are ordering pizza for a meeting. They plan to order 3 cheese pizzas for every 4 pepperoni pizzas they or
1 answer:
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Answer:
225
Step-by-step explanation:
The sum of this series is given by the formula:
Where
S_n is the sum
a is the first term (we get this by plugging in n = 1 into "2n-1", we have 2(1) - 1 = 1)
n is the number of terms (the sum is defined for n = 1 to n = 15, so 15 terms)
d is the common different (the difference is successive terms. Here, 2nd term would be 2(2) - 1 = 3, and first term was 1, so d = 3 -1 = 2)
<em>plugging in the info, we will get the sum:</em>
<em></em>
<em>The sum is 225</em>
Answer:
The volume of the solid is 714.887 units³
Step-by-step explanation:
* Lets talk about the shell method
- The shell method is to finding the volume by decomposing
a solid of revolution into cylindrical shells
- Consider a region in the plane that is divided into thin vertical
rectangle
- If each vertical rectangle is revolved about the y-axis, we
obtain a cylindrical shell, with the top and bottom removed.
- The resulting volume of the cylindrical shell is the surface area
of the cylinder times the thickness of the cylinder
- The formula for the volume will be: V = ,
where 2πx · f(x) is the surface area of the cylinder shell and
dx is its thickness
* Lets solve the problem
∵ y =
∵ The plane region is revolving about the y-axis
∵ y = 32 and x = 0
- Lets find the volume by the shell method
- The definite integral are x = 0 and the value of x when y = 32
- Lets find the value of x when y = 0
∵
∵ y = 32
∴
- We will use this rule to find x, if , where c
is a constant
∴
∴ The definite integral are x = 0 , x = 4
- Now we will use the rule
∵
∵ y = f(x) = x^(5/2) , a = 4 , b = 0
∴
- simplify x(x^5/2) by adding their power
∴
- The rule of integration of
∴ from x = 0 to x = 4
∴ from x = 0 to x = 4
- Substitute x = 4 and x = 0
∴
∴
* The volume of the solid is 714.887 units³