Mathematics, 26.06.2019 08:00, alandrabell9234

Ineed with this is about expinents

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How to solve exponents:

Learn the correct words and vocabulary for exponent problems. When you have an exponent, like 2^{3}, you have two simple parts. The bottom number, here a 2, is the base. The number it is raised to, here a 3, is known as the exponent or power. If you are talking about 2^{3}, you would say it is "two to the third," "two to the third power," or "two raised to the third power."
If a number is raised to the second power, like 5^{2}, you can also say that the number is squared, such as "five squared."
If a number is raised to the third power, like 10^{3}, you can also say it is cubed, such as "ten cubed."
If a number has no exponent shown, like a simple 4, it is technically to the first power and can be rewritten as 4^{1}.
If the exponent is 0, and a "non-zero number" is raised to the "zero power", then the whole thing equals 1, such as 4^{0}=1 or even something like (3/8)^{0}=1

answered: Guest

step-by-step explanation:

answered: Guest

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.

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