Check the picture below.
notice the midpoint of the diameter segment, is just 1,9.
also, recall the radius is half the diameter, notice how long the radius is, just 4 units.
Answer:
Step-by-step explanation:
<u>We can observe general terms of n:</u>
- aₙ = n + 1 + 2n + 2 + 3n + 3 + ... + (n - 1)n + (n - 1)
<u>Rewrite it as:</u>
- aₙ = (n + 1) + 2(n + 1) + 3(n + 1) + ... (n - 1)(n + 1) =
- (n + 1)(1 + 2 + 3 + ... + n - 1) =
- (n + 1)(1 + n - 1)(n - 1)/2 =
- (n - 1)n(n + 1)/2
<u>We need to find the least n for which aₙ > 500:</u>
- (n - 1)n(n + 1)/2 > 500 ⇒ (n - 1)n(n + 1) > 1000
<u>If n = 10:</u>
- a₁₀ = 9*10*11 = 990 < 1000
<u>If n = 11:</u>
- a₁₁ = 10*11*12 = 1320 > 1000
So the least n is 11
Answer:
8
Step-by-step explanation:
1) luckily, this equation is in standard form of a circle:
(x – h)^2+ (y – k)^2 = r^2
where r=radius
to find the radius by itself remove the square by taking the square root of r
square root of 64=8
8 is the radius
hope this helps!
Answer:
y>3/5x−1.5
Step-by-step explanation:
Problem One
Call the radius of the second can = r
Call the height of the second can = h
Then the radius of the first can = 1/3 r
The height of the first can = 3*h
A1 / A2 = (2*pi*(1/3r)*(3h)] / [2*pi * r * h]
Here's what will cancel. The twos on the right will cancel. The 3 and 1/3 will multiply to one. The 2 r's will cancel. The h's will cancel. Finally, the pis will cancel
Result A1 / A2 = 1/1
The labels will be shaped differently, but they will occupy the same area.
Problem Two
It seems like the writer of the problem put some lids on the new solid that were not implied by the question.
If I understand the problem correctly, looking at it from the top you are sweeping out a circle for the lid on top and bottom, plus the center core of the cylinder.
One lid would be pi r^2 = pi w^2 and so 2 of them would be 2 pi w^2
The region between the lids would be 2 pi r h for the surface area which is 2pi w h
Put the 2 regions together and you get
Area = 2 pi w^2 + 2 pi w h
Answer: Upper left corner <<<<< Answer