Write an equation that is parallel to the line y = −5x + 2 and passes through the point (0, 3).
a) y = 5x + 3
b) y = −5x + 3
c) y = 15x + 3
d) y = −15x + 3

option B

ANSWER:

The equation that is parallel to the line y = −5x + 2 and passes through the point (0, 3) is y = -5x + 3  

SOLUTION:

We need to find Write an equation that is parallel to the line y = −5x + 2 and passes through the point (0, 3).

Given, Equation is y = -5x + 3   ----- eqn (1)    

Given point P(0,3)

The above equation is in slope intercept form y = mx + c, Where m is slope and c is intercept made on x-axis.

Comparing equation 1 with y = mx + c we get m =-5 and c =3

Two parallel equations will always has the same slope.  

So the required equation slope is also -5 that is m=-5 and it passes through the point p

Now, by using point slope form  ---- eqn(2),

where m is slope and point on that line.

Put and m =-5 in eqn  (2)

y – 3 = -5(x – 0)

y – 3 = -5x

y = -5x +3

Hence the equation that is parallel to the line y = −5x + 2 and passes through the point (0, 3) is y = -5x + 3, i.e. option B

d

step-by-step explanation:

answer: ratio of volume of cone (with 3 times the height and equal diameter) to volume of cylinder is 2 to 1. the value of π is not used.

step-by-step explanation:

radius is diameter/2 = 4.

area of circle is π r^2.

volume of cylinder is height × area of base = hπr^2 = 3(4^2) π = 48π cubic inches.

not knowing the formula for volume of cone, i calculate it using calculus (which is for calculating things).

volume of cone is integral 0 to h area(y) dy. area(y) is π r(y)^2. r(y) runs r to zero as y runs zero to h, r(0) = r, r(h) = 0.

r(y) = r - r/h y

area(y) = π (r - r/h y)^2 = π (r^2 - 2r^2y/h + r^2y^2/h^2) = π r^2(1-2y/h+y^2/h^2)

antiderivative area(y) = π r^2 (y-y^2/h+y^3/(3h^2))

integral 0 to h = π r^2(h-h^2/h+h^3/(3h^2) - (0)) = π r^2(h - h + h/3) = π r^2(h/3) = π/3 r^2 h

volume of this cone is π/3(4^2)18 cubic inches.

= 6 16 π = 96π cubic inches.

cone has twice the volume, 96/48.

cone height is 6 times the cylinder.

ratio of volume formula: π r^2 cancels.

cone over cylinder ratio is 6h/3 to h, 2 to 1.