Find the 93rd term of the arithmetic sequence -11, -7, -3
1 answer:
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Answer:
209.43951 round to the nearest tenth is 209.44
Step-by-step explanation:
A cone with a base radius of 5 units and a height of 8 units has a volume of 209.44 cubed units.
If a cone has a flat bottom, meaning the height and radius meet at right angles, then this formula can be used to find of volume ('V') of that cone (also know as a right circular cone):
V = 1/3(PI*r squared * h )
The volume of a cone can be calculated by taking one-third of the result of the radius squared, multiplied by the height, multiplied by the mathematical constant pi.
Here is a step-by-step case that illustrates how to find to volume of a cone with a radius of 2 feet and a height of 3 feet. Note that in order to save space (and because pi cannot be determine precisely) a limited number of decimal places are used, the symbol ~ denotes that this answer is an approximation.
V = 1/3(pi * r^2 * h)
= 1/3(pi * 2^2 * 3)
= 1/3(pi * 12)
= 1/3(37.7)
~ 12.6 cubic feet
Hope this helps!!
Answer:
(x, y, z) = (1, -3, 1)
Step-by-step explanation:
Any number of calculators and/or web sites can be used to solve this system of equations. It can be helpful to familiarize yourself with your graphing calculator's capabilities in this area. The solution from one such site is shown below:
(x, y, z) = (1, -3, 1)
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Both y and z show up in these equations with coefficients that have a magnitude of 1. This means you can easily use one of those equations to create a substitution for y or for z.
Using the first equation to write an expression for z, we have ...
z = 4x +3y +6
Substituting that into the second and third equations gives ...
6x -y +3(4x +3y +6) = 12 ⇒ 18x +8y = -6
8x +2y +4(4x +3y +6) = 6 ⇒ 24x +14y = -18
Now, we can subtract 4 times the first equation from 3 times the second to eliminate x:
3(24x +14y) -4(18x +8y) = 3(-18) -4(-6)
10y = -30
y = -3
Substituting into the first equation (of the equations in x and y), we have ...
18x +8(-3) = -6
18x = 18
x = 1
Finally, substituting into the equation for z gives ...
z = 4(1) +3(-3) +6 = 1
The solution is (x, y, z) = (1, -3, 1).
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The equations can also be solved using Cramer's rule, elimination, matrix methods, and other means. When solving by hand, the method of choice will often depend on what you're familiar with and what the coefficients are.
