A circular plot is watered by a sprinkler that rotates through it. The sprinkler only rotates through a semi-circle, or half of the whole circle.
Area of a circle: A = pi x r^2
r = 160 / 2 = 80
A = pi x 80^2
A = 6400pi / 2 = 3200pi
3200pi = 10053.0965
The area water is approximately 10,053 ft^2.
Hope this helps!! :)
<span>When creating a subset of 5 elements from 7 elements, order should not matter. Therefore, we use the combination formula over the permutation formula.
The combination formula given n elements total and r elements used is n! / [r!*(n-r)!]. Substituting 7 for n and 5 for r, we get:
7! / (5!*2!) = 7*6 / 2 = 21
21 subsets can be created</span>
Answer:
15 mph
Step-by-step explanation:
Before traffic cleared:
distance = 30 miles
average speed = s
time = t
d = st
30 = st
After traffic cleared:
distance = 176 miles
average speed = s + 29
time = 6 - t
d = st
176 = (s + 29)(6 - t)
30 = st
s = 30/t
176 = (30/t + 29)(6 - t)
176t = (30 + 29t)(6 - t)
176t = 180 - 30t + 174t - 29t^2
29t^2 + 32t - 180 = 0
(29t + 90)(t - 2) = 0
t = -90/29 or t = 2
Time must be a positive number, so we discard the solution t = -90/29.
t = 2
30 = st
30 = s * 2
s = 15
Answer: 15 mph
First, you have to find the area of the entire wall, including the window. The formula for the area of a trapezoid is:
A = (b1 + b2)/2 * h
b1 is the first base, b2 is the second base, A is the total area, and h is the height.
Plug in the numbers from the problem.
(13 + 10)/2 * 8
Simplify.
(23)/2*8
11.5*8 = 92
Now, to calculate the window's surface area, you use the formula for area of a circle.
A = 3.14*r^2
Plug in your number.
A = 3.14 * 2^2
Simplify.
A = 3.14 * 4
A = 12.56
Now, you subtract the area of the window from the total area of the wall.
92 - 12.56 = 79.44
79.44 feet
Answer: The value of the bond when Tyler's mom purchased it = $150
Step-by-step explanation:
Let x= Purchasing price of the bond.
Given: Rate of increase in its value = 4% = 0.04
Value of bond after one year = x+ 4% of x
= x+0.04x
= 1.04x
One year after it was purchased, the value of the savings bond was $156.

Hence, the value of the bond when Tyler's mom purchased it = $150