The sum of two numbers is 27. One number is 2 times as large as the other. What are the numbers? Larger number:
Smaller number: ​

Let x be the larger number, and y be the smaller number.  

The sum of two numbers is 27. So the equation would be:

x+y=27

The larger number is 3 more than the smaller number. So:  

larger number = smaller number + 3  

or  

x=y+3

Now, we want to get rid of x and solve for y first. Since x=y+3, we can substitute y+3 for x in the equation x+y=27.  

Therefore:

(y + 3) + y = 27  

Combine like terms:

2y + 3 = 27  

Subtract 3 on both sides:

2y = 24  

Divide both sides by 2:

y = 12  

So the smaller number is 12. The larger number is 3 more than the smaller number, so:  

x = 12 + 3

x = 15  

The 2 numbers are 12 and 15. Check:  

12 + 15 = 27

I'm not 100% sure of which equation so I used both.

Step-by-step explanation:

a + b = 27

20 + 7 = 27

(a × 2) + b = 27

(6.75 × 2) + 13.5 = 27

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.

13cm

step-by-step explanation:

(apex)