Evaluate the expression 5(7 − 4)2 ÷ 3 + 11.

The expression 5(7 − 4)2 ÷ 3 + 11 is equal to 20.9

Solution:

Given expression is 5(7 − 4)2 ÷ 3 + 11

We need to evaluate the given expression

Let us use "BODMAS" rule

BODMAS means sequence of operations which are Brackets, Order, Division, Multiplication, Addition and then Subtraction.

Now solve the given expression

5(7 − 4)2 ÷ 3 + 11

First "brackets" are to be solved as per BODMAS

5(3)2 ÷ 3 + 11

Now division is performed, 2 is divided by 3 to give 0.66

Now "brackets" is solved

Now multiplication is performed

9.9 + 11

Atlast, addition is performed

20.9

Hence 5(7 − 4)2 ÷ 3 + 11 is equal to 20.9

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.