Direct variation is y = kx, where k is the constant of variation.
But now it says y varies directly with x2 (or 2x), so now the x in the equation is 2x.
The equation is y = k(2x)
Now you find k.
y = 96 when x = 4.
(96) = k(2*4)
96 = k(8)
k = 12
The equation is now y = 12(2x)
To find the value of y when x=2, plug 2 into the equation you made.
y = 12(2*2)
y = 48
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Now it's with a "quadratic variation," which is the same thing except x is squared.
The equation is y = kx^2
But y varies directly with x2 (same thing as 2x), so now it's y = k(2x)^2.
Now you find k by substituting y and x values that were given.
y = 180 when x = 6
(180) = k(2*6)^2
180 = k(12)^2
180 = k(144)
k = 1.25
k, 1.25, is the constant of variation.
The figure attached has <DEF which is an inscribed angle. An inscribed angle is an angle with its vertex on the circle which is formed by two intersecting chords. According to formulas, the measurement of arc DF is twice the measurement of ∡DEF. Arc DF is equal to 360-248 or 112. Hence <span>∡DEF is equal to 56 degrees.</span>
All four sides of the original square have length s.
Adding 3 to s results in s+3, the length of the resulting rectangle.
Subtracting 3 from s results in s-3, the width of the rectangle.
The area of the rectangle is (s+3)(s-3) = s^2 - 9 = 27,
and therefore s^2 = 36, and s = 6 square units.
