Sinα=h/L
α=arcsin(h/L)° we are told that h=18 and L=20 so
α=arcsin(9/10)°
α≈64° (to nearest whole degree)
Problem 1
Answer: Direct variation; k = 1/4
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Explanation:
We can rewrite the given equation y = x/4 into y = (1/4)x. Then note how it's in the form y = kx. In this case, k = 1/4. In decimal form, this is k = 0.25
All direct variation equations are in the form y = kx. The value of k is the constant of variation.
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Problem 2
Answer: Inverse variation; k = 9
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Explanation:
The equation 9/y = x rearranges to xy = 9.
We can then solve for y to get y = 9/x
This is in the form y = k/x, where k = 9
All inverse variation equations are in the form y = k/x, with k as the constant of variation.
Let us assume the width of the rectangle = x meters
Then
Length of the rectangle = 2x + 2
Perimeter of the rectangle = 16 meters
Then
Perimeter = 2 (Length + width)
16 = 2(2x + 2 + x)
16 = 2(3x + 2)
16 = 6x + 4
6x = 16 - 4
6x = 12
x = 2
Then
Length of the side of the rectangle = 2x + 2
= (2 * 2) + 2
= 6
I hope that the procedure is clear enough for you to understand and this is the answer that you were looking for.
Answer:
Girls to boys = 1:2
Girls to students = 1:3
Boys to students = 2:3
Step-by-step explanation:
So, let's subtract the number of girls from the number of students in the class:
60 - 20 = 40
This means that for every 20 girls there are 40 boys in the ratio of girls to boys:
20:40
This can be simplified down by factoring, here we can divide by 20:
(20 ÷ 20) : (40 ÷ 20)
1:2
So the ratio of girls to boys is 1:2
The ratio of boys to students can be calculated via:
40:60
This can be simplified by dividing by 20 again:
(40 ÷ 20) : (60 ÷ 20)
2:3
So the ratio of boys to students is 2:3
The ratio of girls to students can be put in a ratio of:
20 : 60
This can be simplified down by dividing by 20:
(20 ÷ 20) : (60 ÷ 20)
1:3
So the ratio of girls to students is 1:3
Hope this helps!
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