Answer:
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Step-by-step explanation:
Answer:
<h3>dn = -7^n-1</h3>
Step-by-step explanation:
Given the sequence -1,-7,-49,-343,....
We are to find the nth term of the sequence
dn = ar^n-1
a is the first term = -1
r is the common ration = -7/-1 = -49/-7 = 7
n is the number of terms
Substitute
dn = -1(7)^n-1
dn = -7^n-1
hence the nth term of the sequence is dn = -7^n-1
Let b=height of building. By similar triangles we can say:
b/44.75=3.1/1.29
b=44.75*3.1/1.29
b≈107.54
b≈108 meters (to the nearest whole meter)
- Quadratic Formula:
, with a = x^2 coefficient, b = x coefficient, and c = constant
With our equation, plug in the values:
![x=\frac{4\pm \sqrt{(-4)^2-4*1*13}}{2*1}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B4%5Cpm%20%5Csqrt%7B%28-4%29%5E2-4%2A1%2A13%7D%7D%7B2%2A1%7D)
Next, solve the exponent and multiplications:
![x=\frac{4\pm \sqrt{16-52}}{2}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B4%5Cpm%20%5Csqrt%7B16-52%7D%7D%7B2%7D)
Next, solve the subtraction:
![x=\frac{4\pm \sqrt{-36}}{2}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B4%5Cpm%20%5Csqrt%7B-36%7D%7D%7B2%7D)
Next, factor out i (i = √-1):
![x=\frac{4\pm \sqrt{36}i}{2}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B4%5Cpm%20%5Csqrt%7B36%7Di%7D%7B2%7D)
Next, solve the square root:
![x=\frac{4\pm 6i}{2}](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B4%5Cpm%206i%7D%7B2%7D)
Lastly, divide and <u>your answer is:</u>
![x=2\pm 3i](https://tex.z-dn.net/?f=x%3D2%5Cpm%203i)