100 POINTS IF U GET THIS RIGHT!
2 answers:
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Answer:
The series CONVERGES with the sum being 6.25.
Step-by-step explanation:
Given that the geometric series is 10 - 6 + 3.6 - 2.16 + ....
So the first term of the geometric progression is, = 10
The second term of the geometric progression is = -6 =
× r = 10 × r
where r is the constant ratio.
Therefore r = = -0.6
The third term of the geometric progression, = 3.6 =
× r = -6 × -0.6 = 3.6
The fourth term of the geometric progression, = -2.16 =
× r = 3.6 × -0.6 = -2.16
So the above confirms that the series is indeed a geometric progression with first term, = 10 and constant ratio, r = -0.6
Now to find if the series converges or diverges we can take sum of the series from first term to infinity.
We can already infer that the series is convergent since the constant ratio, r = -0.6 which is less than 1.
So from the formula for the sum to infinity of a geometric progression, S, we get
S =
So the series is convergent with the sum being 6.25
Answer:
- 162 ft²
Step-by-step explanation:
<u>The missing side of the garden is the hypotenuse of a triangle with legs:</u>
- (80 - 70) = 10 ft and (40 - 15) = 25 ft
<u>The length of the side is:</u>
≈ 27 ft
<u>The area of the garden is:</u>
- A = 27*6 = 162 ft²
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.
