Answer:
[4, 6]
Step-by-step explanation:
∑ₙ₌₁°° (x − 5)ⁿ / n²
Use ratio test.
lim(n→∞)│aₙ₊₁ / aₙ│< 1
lim(n→∞)│[(x − 5)ⁿ⁺¹ / (n+1)²] / [(x − 5)ⁿ / n²]│< 1
lim(n→∞)│[(x − 5) n² / (n+1)²│< 1
│x − 5│< 1
-1 < x − 5 < 1
4 < x < 6
If x = 4, ∑ₙ₌₁°° (4 − 5)ⁿ / n² = ∑ₙ₌₁°° (-1)ⁿ / n², which converges.
If x = 6, ∑ₙ₌₁°° (6 − 5)ⁿ / n² = ∑ₙ₌₁°° 1 / n², which converges.
So the interval of convergence is [4, 6].
The value of x is 7 and the lengths of the sides are 16, 11 and 8
<h3>How to determine the values of x and each side?</h3>
The complete question is added as an attachment
The perimeter is calculated as:
P = 3x - 5 + 2x-3 + 15 - x
Evaluate
P = 4x + 7
The perimeter is 35.
So, we have
4x + 7 = 35
This gives
4x = 28
Divide by 4
x = 7
Substitute x = 7 in 3x - 5, 2x-3 and 15 - x
3x - 5 = 3* 7 - 5 =16
2x-3 = 2* 7 - 3 = 11
15 - x= 15 - 7 = 8
Hence, the value of x is 7 and the lengths of the sides are 16, 11 and 8
Read more about perimeter at:
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Answer:
x= 36
Step-by-step explanation:
both angles together are supplementary and will form 180
Therefore, you know the missing angle can be found by substracting 108 from 180
180 - 108 = 72
72 = 2x
If +15 is also a a part of the power of 216 there will be no solution:
216^(-1.5t)=1-15
216^(-1.5t)=-14
-1.5t= 216 base log -14 as log with negative value(-14 in this problem) has no solution so,
I guess it is 216^(-1.5t+15)=1 right?
216^-1.5t+15=1
-1.5t+15=216 base log 1
-1.5t+15=0(Any log with value 1 of anybase has no value which is peopwely 0)
-1.5t=-15
t=15/1.5
t=10
Answer:
k = 15
Step-by-step explanation:
12/4/5 = 4/5/4/5 k
15 = k
OR
5/4 (12) = 4/5 (5/4) k (multiply by the reciprocal)
15 = k
