Answer:
8^4
Step-by-step explanation:
Here we have:
8^6 · 8³
-------------
8^5
That's multiplication in the numerator. The appropriate rule of exponents states that:
8^a·8^b = 8^(a+b), so the numerator is equivalent to 8^(6 + 3) = 8^9.
Now we have
8^9
------
8^5
and the appropriate rule for division here is
8^a / 8^b = 8^(a - b)
So our:
8^9
--------- 8^(9-5) = 8^4
8^5
Answer:
15foot
Step-by-step explanation:
The set up will give a right angled triangle.
The length of the shadow will be the hypotenuse = 16foot
The height of the tree will be the opposite = x
The angle of elevation = 70°
Using the SOH CAH TOA trig identity
Sin theta = opposite/hypotenuse
Sin 70 = x/16
x=16sin70
x = 15.04feet
Hence the height of the tree to the nearest whole foot is 15foot
2x+1=10 2x=9 x=9/2
-2x-1=10 -2x=11 x=-11/2
The answer is C
Answer:
The sum of the first 8 terms in the series is 65535.
Step-by-step explanation:
We have,
The common ratio in a geometric series, r = 4
First term of GP is, a = 3
It is required to find the sum of the first 8 terms in the series. The sum of first n terms of a GP is given by :
![S_n=\dfrac{a(r^n-1)}{r-1}, r>1](https://tex.z-dn.net/?f=S_n%3D%5Cdfrac%7Ba%28r%5En-1%29%7D%7Br-1%7D%2C%20r%3E1)
Here, n = 8
![S_8=\dfrac{3\times ((4)^8-1)}{4-1}\\\\S_8=65535](https://tex.z-dn.net/?f=S_8%3D%5Cdfrac%7B3%5Ctimes%20%28%284%29%5E8-1%29%7D%7B4-1%7D%5C%5C%5C%5CS_8%3D65535)
So, the sum of the first 8 terms in the series is 65535.