100 POINTS AND BRAINLIST CAN SOMEONE PLEASE HELP ME WITH THIS IVE BEEN ASKING FOR 3 DAYS AND I GOT AN Answer EARLIER BUT VENUS1234 DELETED MY ENTIRE QUESTION FOR NO REASON AND I REALLY NEED TO PASS THIS TEXT I WILL GIVE BRAINLIST AND EXTRA POINTS IF ASKED Question 3 (Essay Worth 10 points) (04.03 MC) A point Q on a segment with endpoints A (2, −1) and C (4, 2) partitions the segment in a 4:1 ratio. Find Q. You must show all work to receive credit. Question 4 (Essay Worth 10 points) (04.03 MC) Find the area of the following shape. You must show all work to receive credit. shape with vertices located at negative 4 comma 0, 0 comma 4, 2 comma 2, 1 comma 2, and 1 comma 0

Q=(3.6,1.4)

Step By Step:

A point Q on a segment with endpoints A (2, −1) and C (4, 2) partitions the segment in a 4:1 ratio.

A=(x_1,y_1)=(2,-1)

B=(x_2,y_2)=(4,2)

m:n = 4:1

Let (x,y) be the coordinates of Q

Section formula : x=mx_2+nx_1/m+n, y=my_2+ny_1/m+n

Substitute the values in the formula:

x=4(4)+2/4+1, y=4(2)-1/4+1

x=18/5,y=7/5

x=3.6, y=1.4

Hence Q=(3.6,1.4)

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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.