Answer:
4pi in^2
Step-by-step explanation:
Lateral surface area of a cylinder = 2πrh
π = pi
r = radius
h = height
Let me illustrate with an example
A cylinder has the following dimensions
r = radius = 20
h = height = 10
lateral area = 2 x π x 20 x 10 = 400π
If dimensions are reduced to one-fifth their original length, new dimensions are
r = radius = 20 x 1/5 = 4
h = height = 10 x 1/5 = 2
New lateral area = 2 x 4 x 2 x π = 16π
change in lateral area = 400π / 16π = 25
If dimensions are reduced by 1/5, lateral area would reduce by 25
100 pi / 25 = 4
Answer:
Let x = total number of apples picked by the prince
x=44
Step-by-step explanation:
1st troll payment
x-(0.5x+2)
x-0.5x-2
0.5x-2 (that is the amount of apples left after 1st troll payment)
2nd troll payment
(0.5x-2)-(0.5(0.5x-2)+2)
Simplifying,
(0.5x-2)-(0.25x-1+2)
(0.5x-2)-(0.25x+1)
0.5x-2-0.25x-1
0.25x-3 (apples remaining after 2nd troll payment)
3rd troll payment
(0.25x-3)-(0.5(0.25x-3)+2)=2
(0.25x-3)-(0.125x-1.5+2)=2
(0.25x-3)-(0.125x+0.5)=2
0.25x-3- 0.125x-0.5=2
0.125x-3.5=2
0.125x =2+3.5
0.125x=5.5
x=5.5/0.125 (divide both sides by 0.125)
=44 apples
Therefore total number of apples picked by the prince, x=44
The numbers are 9 and 17 cause 9+17 is 26 and 9+8 is 17
Midpoint of the segment connecting the points (5,3)and (7,-2)is (6,1/2)
Answer:
The APR at which the money is borrowed, is approximately 651.79%
Step-by-step explanation:
The amount which one wishes to borrow for two weeks, P = $600
The amount of interest that one must pay back = $25 per $100 borrowed
Therefore;
The total interest on the $600 loan (borrowed) for two weeks = 25/100× $600 = $150
The number of days for which the amount was borrowed = 2 weeks = 14 days
The Annual Percentage Rate, APR is given as follows;
![APR = \left (\dfrac{\left (\dfrac{Interest \ Paid \ for \ the \ Loan \ duration}{The \ amount \ borrowed} \right )}{The \ number \ of \ days \ the \ amount \ was \ borrowed } \right ) \times 365 \times 100](https://tex.z-dn.net/?f=APR%20%3D%20%5Cleft%20%28%5Cdfrac%7B%5Cleft%20%28%5Cdfrac%7BInterest%20%5C%20Paid%20%5C%20for%20%5C%20the%20%20%5C%20Loan%20%5C%20duration%7D%7BThe%20%5C%20amount%20%5C%20borrowed%7D%20%5Cright%20%29%7D%7BThe%20%5C%20number%20%5C%20of%20%5C%20days%20%5C%20the%20%5C%20amount%20%5C%20was%20%20%5C%20borrowed%20%7D%20%5Cright%20%29%20%5Ctimes%20365%20%5Ctimes%20100)
Therefore, we get
![APR = \left (\dfrac{\left (\dfrac{150}{600} \right )}{14 } \right ) \times 365 \times 100 \approx 651.79 \%](https://tex.z-dn.net/?f=APR%20%3D%20%5Cleft%20%28%5Cdfrac%7B%5Cleft%20%28%5Cdfrac%7B150%7D%7B600%7D%20%5Cright%20%29%7D%7B14%20%7D%20%5Cright%20%29%20%5Ctimes%20365%20%5Ctimes%20100%20%20%5Capprox%20651.79%20%5C%25)
The annual rate at which the money is borrowed, APR ≈ 651.79%.