Which equation has no solution?

a. 2.3y + 2 + 3.1y = 4.3y + 1.6 + 1.1y + 0.4

b. 32x + 25 - 21x = 10x

c. 1/3 + 1/7y = 3/7y

d.

Step-by-step explanation:

A.

2.3y + 2 + 3.1y = 4.3y + 1.6 + 1.1y + 0.4              combine like terms

(2.3y + 3.1y) + 2 = (4.3y + 1.1y) + (1.6 + 0.4)

5.4y + 2 = 5.4y + 2              subtract 5.4y from both sides

2 = 2   TRUE → infinitely many solutions

B.

32x + 25 - 21x = 10x          combine like terms

(32x - 21x) + 25 = 10x

11x + 25 = 10x           subtract 11x from both sides

25 = -x       change the signs

-25 = x → x = -25   One solution

C.

1/3 + 1/7y = 3/7y              subtract 1/7y from both sides

1/3 = 2/7y             multiply both sides by 7

7/3 = 2y      divide both sides by 2

7/6 = y → y = 7/6       One solution

D. ?

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.