Answer:
w=6
Step-by-step explanation:
P=2(L)+2(w)
48= 2(18)+2w
48=36+2w
12=2w
w=6
checking;
48= 2(18)+2(6)
48= 36+12
48= 48
We know that the total number of students is 180, so 180 is the 100 precent of the students, now we can set up a proportion and solve
180/100=135/x
x=135 times 100 over 180
x=75%
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Answer: 216 in ^3
Explanation:
18 x 3 x 12 = 648
648 / 3 = 216 in ^3
I hope this helped!
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- Zack Slocum
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Longer leg = x + 4
Shorter leg = x
Hypotenuse = x + 8
Using Pythagorean Theorem:
a^2 + b^2 = c^2
(x + 4)^2 + x^2 = (x + 8)^2
x^2 + 8x + 16 + x^2 = x^2 + 16x + 64
2x^2 + 8x + 16 = x^2 + 16x + 64
2x^2 +8x = x^2 + 16x + 48
2x^2 - 8x = x^2 + 48
x^2 - 8x = 48
x^2 - 8x - 48 = 0
You can complete the square from here or use the quadratic formula.
Completing the square:
x^2 - 8x = 48
x^2 - 8x + (-8/2)^2 = 48 + (-8/2)^2
x^2 - 8x + 16 = 48 + 16
(x - 4)(x - 4) = 64 or (x - 4)^2 = 64
x - 4 = +√64 OR x - 4 = -√64
x - 4 = +8 OR x - 4 = -8
x = 12 OR x = -4
However, you can't use negative 4 as a length because your length needs to be a positive.
So x will be 12.
Shorter leg: 12
Longer leg: 12 + 4
Hypotenuse: 12 + 8
Answer:
1. y = sin(x²+C)
2. see below
Step-by-step explanation:
1. 
separation of variables

integration both sides
you should get :
remember constant of integration!!
2. y = sin(x²+C)
3 = sin(0+C)
y(0) = 3 does not have a solution because our sin graph is not shifted vertically or multiplied by a factor whose absolute value is greater than 1, so our range is [-1,1] and 3 is not part of this range