Answer:
a. 45 π
b. 12 π
c. 16 π
Step-by-step explanation:
a.
If a 3×5 rectangle is revolved about one of its sides of length 5 to create a solid of revolution, we can see a cilinder with:
Radius: 3
Height: 5
Then the volume of the cylinder is:
V=π*r^{2} *h= π*(3)^{2} *(5) = π*(9)*(5)=45 π
b. If a 3-4-5 right triangle is revolved about a leg of length 4 to create a solid of revolution. We can see a cone with:
Radius: 3
Height: 4
Then the volume of the cone is:
V=(1/3)*π*r^{2} *h= (1/3)*π*(3)^{2} *(4) = (1/3)*π*(9)*(4)=12 π
c. We can answer this item using the past (b. item) and solving for the other leg revolution (3):
Then we will have:
Radius: 4
Height: 3
Then the volume of the cone is:
V=(1/3)*π*r^{2} *h= (1/3)*π*(4)^{2} *(3) = (1/3)*π*(16)*(3)=16 π
Answer:
238 miles
Step-by-step explanation:
340 miles = 5 hours
So get 1 hour by dividing by 5 on both sides
5/5 = 1 hr
340/5 = 68
So in 1 hour they travel 68 miles
You want to find 3 1/2 hours
Do 68 x 3 to get 3 hours
So it would be 68 x 3 =204
Plus the half an hour - which you get by doing 68/2 = 34
<em>68 = 1 hour, so half of that must be half an hour</em>
So to get the final distance you do 204 (3 hours) +34 (half an hour)
204 + 34 =238
Side = 8m
He increases length by 2m and reduces width by 2m
(a.) New dimensions will be -
Length = 10m and Width = 6m
(b.) Area = length x breadth (or width)
here we will use the special product (x+y) (x-y)
length = (x+y) and width = (x-y)
area = (8+2) x (8-2)
8^(2) - 2^(2)
= 60
Answer:
-3+15i
Step-by-step explanation:
Apply complex arithmetic rule: 
-3 * 3 -3 (-2) = -3
<h3>
Answer: (x-10)^2 + (y-1)^2 = 25</h3>
============================================
Explanation:
The general template of a circle is
(x-h)^2 + (y-k)^2 = r^2
Where,
- (h,k) is the center
- r is the radius
We are given (10,1) as the center so (h,k) = (10,1) meaning that h = 10 and k = 1 pair up together.
r = 5 is the given radius.
-----
Plug the values h = 10, k = 1, r = 5 into the equation to get:
(x-h)^2 + (y-k)^2 = r^2
(x-10)^2 + (y-1)^2 = 5^2
(x-10)^2 + (y-1)^2 = 25
