Answer:
<u>The sum of the first 5 terms of the series is 77.</u>
Step-by-step explanation:
1. Let's review the information provided to us for solving the sum of the first 5 terms of the series:
1st term = 7
2nd term = - 14
3rd term = 28
4th term = - 56
2. Let's solve the sum of the first 5 terms of the series:
Aₙ = Aₙ₋₁ * -2 ; A₁ = 7
A₁ = 7
A₂ = A₁ * -2 = 7 * - 2 = - 14
A₃ = A₂ * - 2 = -14 * - 2 = 28
A₄ = A₃ * - 2 = 28 * - 2 = - 56
A₅ = A₄ * - 2 = -56 * - 2 = 112
Sum of the first 5 terms of the series = 7 - 14 + 28 - 56 + 112
<u>Sum of the first 5 terms of the series = 77</u>
<u>Given</u><u> info</u><u>:</u><u>-</u> Find the remainder when x^5 - 3x^3 + x - 5 is divided by x - 2
<u>Solution:</u><u>-</u>
Given,
p(x) = x^5 - 3x^3 + x - 5 , g(x) = x - 2
Let g(x) = x-2 will be the factor of p(x) if p(2) = 0.
Now, p(x) = x^5 - 3x^3 + x - 5
p(2) = (2)^5 - 3(2)^3 + 2 - 5
= (2*2*2*2*2) - 3(2*2*2) + 3 - 5
= 32 - 3(8) + 3 - 5
= 32 - 24 + 3 - 5
= 31 - 24 - 2
= 31 - 26
= 5 Remainder.
Hence, when x^5 - 3x^3 + x - 5 is divided by x - 2 , we get the remainder as 5.
-√4 + √(-48) + √121 + √(-108)
= -√(2²) + √(-1 • 3 • 4²) + √(11²) + √(-1 • 2² • 3³)
= -2 + 4√3 i + 11 + 6√3 i
= 9 + 10√3 i
Answer:
The intercept is 5.
Step-by-step explanation:
Since we already have the slope of -1/6, we can use that and either point in point-slope form to get the equation in slope-intercept.
y - y1 = m(x - x1)
y - 3 = -1/6(x - 12)
y - 3 = -1/6x + 2
y = -1/6x + 5
Therefore, b= 5
