Answer:
The answer is below
Step-by-step explanation:
Let x be the diameter of the semicircle. radius = x/2
The window is a combination of a rectangle and semicircle.
Width of window = diameter = x, let length of the window = y.
Perimeter of semicircle = πr = πx/2
Perimeter of window = x + y + y + πx/2
20 = x + 2y + πx/2
2y + x + πx/2 = 20
2y = 20 - x(1 - π/2)
y = 10 - x(1 - π/2)/2
Area of semicircle = (1/2)πr² = (1/2)π(x/2)²
Area of window = xy + (1/2)π(x/2)²
A = x(10 - x(1 - π/2)/2) + πx²/8
A = 10x - x² - πx²/4 + πx²/8
A = 10x - x² - πx²/8
The maximum area is at dA / dx = 0
dA / dx = 10 - 2x - 2πx/8
0 = 10 - 2x - πx / 4
2x + πx / 4 = 10
2.785x = 10
x = 3.59 feet
Maximum area = 10x - x² - πx²/8 = 10(3.59) - 3.59² - π(3.59²) / 8
Maximum area = 17.95 feet²
Answer:
Step-by-step explanation:
let price of one pretzel=x
price of one soda=y
3x+4y=11.25 ...(1)
5x+2y=8.25 ...(2)
multiply by 2
10x+4y=16.50 ...(3)
(3)-(1) gives
7x=5.25
x=0.75
from (1)
3(0.75)+4y=11.25
2.25+4y=11.25
4y=11.25-2.25
4y=9
y=9/4=2.25
cost of one pretzel=$0.75
cost of one soda=$2.25
Answer:
12/7
Step-by-step explanation:
Answer:
The probability is 0.05 or 5%
Step-by-step explanation:
Of 6 cars the probability of 3 being a lemon is:
[tex]frac{{3!3!}{6!}} [\tex]
Picking the first one a lemon is [tex]frac{{3}{6}} [\tex] , the second one also lemon [tex]frac{{2}{5}} [\tex] and the third one [tex]frac{{1}{4}} [\tex].
[tex]frac{{3*2*1}{6*5*4}} [\tex] can be rearanged as
[tex]frac{{3!3!}{6!}} [\tex]
