The parabola is opens upward.
a = (8 – 5)
= 3
Using the standard form:
(x – h)^2 = 4a(y – k)
(x -5)^2 = 12( y – 4)
In general form
x^2 -10x +25 =12y – 48
x^2 -10x -12y + 73 =0
(1-cos^2(x)) csc^2(x)=1
one of the trigonometry rules is sin^2(x) + cos^2(x) = 1 if you rearrange this you realize that sin^2= 1-cos^2(x)
we also know that csc^2(x)= 1/sin^2(x) so now you can rewrite your equation as:
sin^2(x) x 1/sin^2(x) = 1
sin^2(x)/sin^2(x) =1
the LHS (left hand side) can cancel down to 1 because the numerator and denominator are the same
so then 1=1 Therefore LHS=RHS
Hope this helps
For volume of a prism, the general rule is multiply the area of the base by the area of the height. For example, for a triangular prism, the volume would be (1/2)b*h*a if you set a = height of the prism and h = height of the triangle from the formula (1/2)bh, which is the area of a triangle.
5x - 7 < 2x - 1
Take away 2x from both sides:
3x - 7 < -1
Add 7 to both sides:
3x < 6
Divide by 3 on both sides :
x < 2
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Answer: x < 2
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