Can you me figure out this 2 (4²+3)-66/11

Hello from MrBillDoesMath!

-17 or 32, depending upon the value of the symbol before "11".

First answer (-17) if symbol interpreted as +; second answer (32) if symbol interpreted as "/"

Discussion:

The equation you wrote uses a division sign. The original, I believe, uses a plus sign instead. Not sure which one to use so let's solve both of them.

Interpretation 1:

2 (4^2 + 3) - 66 + 11  =

2( 16+3) - 66 + 11 =

2(19) -66 + 11 =

38 -66 + 11 =

= -17

Interpretation 2:

2 (4^2 + 3) - 66 \ 11 =                    => order of operation, "\" before "

2(19) - 6   =

38 - 6 =

32

Thank you,

MrB

hello from mrbilldoesmath!

answer:

the domain is the set { -2, 0, 2, 3}

discussion:

the domain is the set of x values in the ordered pairs (x,y). taking the x, or first component, of each ordered pair gives   -2, 0, 2, 3.

you,

mrb

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.