Find the volume of the solid generated when the region bounded by y=4x and y=16x is revolved about the x-axis. A coordinate system has an unlabeled horizontal x-axis and an unlabeled vertical y-axis. From left to right, a curve labeled y equals 16 StartRoot x EndRoot starts on the origin and rises at a decreasing rate in quadrant 1. A line labeled y equals 4 x starts at the origin and rises from left to right, intersecting the curve at the origin and in quadrant 1. The region above the line and below the curve is shaded and labeled R. A curved arrow is rotated about the x-axis. x y y=16x y=4x R

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step-by-step explanation:

you have 6 cupcakes

5x + 3y = - 4

step-by-step explanation:

the equation of a line in standard form is

ax + by = c ( a is a positive integer and b, c are integers )

express the line first of all in slope- intercept form

y = mx + c ( m is the slope and c the y-intercept )

to calculate m use the gradient formula

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

with (x₁, y₁ ) = (7, - 3) and (x₂, y₂ ) = (4, - 8)

m = = -

y = - x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (4, - 8 ), then

- 8 = - + c ⇒ c = -

y = - x - ← in slope-intercept form

multiply all terms by 3 to eliminate the fractions

3y = - 5x - 4 ( add 5x to both sides )

5x + 3y = - 4 ← in standard form

x is the total time in minutes for the free response

you are given number of questions as 15 - m and time per item as 8 minutes

to find x multiply the two givens together:

x = 8 * (15-m) = 8(15-m)