Let us denote the number of boys in the glee club with X and the number of girls with Y.There are 84 students in the glee club, which means that the following equation can be written:X+Y=84We also now that there are 12 more boys than girls, so:X=Y+12We can rewrite the first equation like:(Y+12)+Y=842Y+12=842Y=62Y=62/2=31X=31+12=43So, the ratio of the number of girls to the number of boys is: Y/X=31/43
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The largest possible volume of the given box is; 96.28 ft³
<h3>How to maximize volume of a box?</h3>
Let b be the length and the width of the base (length and width are the same since the base is square).
Let h be the height of the box.
The surface area of the box is;
S = b² + 4bh
We are given S = 100 ft². Thus;
b² + 4bh = 100
h = (100 - b²)/4b
Volume of the box in terms of b will be;
V(b) = b²h = b² * (100 - b²)/4b
V(b) = 25b - b³/4
The volume is maximum when dV/db = 0. Thus;
dV/db = 25 - 3b²/4
25 - 3b²/4 = 0
√(100/3) = b
b = 5.77 ft
Thus;
h = (100 - (√(100/3)²)/4(5.77)
h = 2.8885 ft
Thus;
Largest volume = [√(100/3)]² * 2.8885
Largest Volume = 96.28 ft³
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Answer:
Step-by-step explanation:
Answer:
(-5,1)
Step-by-step explanation:
Answer:
1) slope 3/2, y-intercept 7/2
2y-3x=7
2) slope 1/5, y-intercept 3
5y-x=15
3) slope 1/5, y-intercept 4/5
-x+5y=4
4) slope 5/2, y-intercept 7/2
2y=5x+7
Step by step explanation:
1) 2y-3x=7
2y=3x+7
y=3/2y+7/2
2)5y-x=15
5y=x+15
y=1/5x+3
3)-x+5y=4
5y=x+4
y=1/5x+4/5
4)2y=5x+7
y=5/2x+7/2
