Write an equation of the line parallel to y=3x−7 that passes through point (2, 4).
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divide total paid by number of pencils for price of 1 pencil
4.50 / 18 = 0.25 for 1
so you would put a dot at (1, 0.25) (2,0.5) (3,0.75) etc and draw a line through the dots
see attached picture:
The two boundary curves y = √(6x + 4) and y = 2x meet at
√(6x + 4) = 2x
6x + 4 = 4x²
2x² - 3x - 2 = 0
(x - 2) (2x + 1) = 0
⇒ x = -1/2 and x = 2
R is bounded to the left by the y-axis (x = 0), so R is the set
R = {(x, y) : 0 ≤ x ≤ 2 and 2x ≤ y ≤ √(6x + 4)}
Using the shell method, the volume is made up of cylindrical shells of radius x and height √(6x + 4) - 2x. So each shell of thickness ∆x contributes a volume of
2π (radius) (height) ∆x = 2π x (√(6x + 4) - 2x) ∆x
and as we let ∆x approach zero, the total volume of the solid is given by the definite integral