Percent: 80%
Fraction: 12/15
Decimal: 0.8. hope that helped.
Answer:
a. 80.83 ft b. 40.42 ft
Step-by-step explanation:
Let h = height of pole = 70 ft, L = length of cable and x = distance of cable on ground to pole and Ф = angle between cable and ground.
a) How long is the cable?
Since L, h and x form a right-angled triangle with angle Ф and h being the opposite side to Ф and L being the hypotenuse side, by trigonometric ratios,
sinФ = h/L
L = h/sinФ
L = 70 ft/sin60°
L = 70 ft/0.8660
L = 80.83 ft
b) How far from the pole should the cable be attached to the ground?
Since L, h and x form a right-angled triangle with angle Ф and h being the opposite side to Ф and x being the adjacent side, by trigonometric ratios,
tanФ = h/x
x = h/tanФ
x = 70 ft/tan60°
x = 70 ft/1.7321
x = 40.42 ft
Using the conversion of exponent to power, the equivalent expression is given as follows:
![\frac{\sqrt{x}}{\sqrt[4]{y}z^2}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Csqrt%7Bx%7D%7D%7B%5Csqrt%5B4%5D%7By%7Dz%5E2%7D)
<h3>How to transform an exponent to a power?</h3>
It happens according to the following rule, with the denominator as the root and the numerator as the exponent:
![a^{\frac{n}{m}} = \sqrt[m]{a^n}](https://tex.z-dn.net/?f=a%5E%7B%5Cfrac%7Bn%7D%7Bm%7D%7D%20%3D%20%5Csqrt%5Bm%5D%7Ba%5En%7D)
In this problem, we are given the following expression:

Negative exponents go to the denominator, hence the <em>equivalent expression</em> is given by:
![\frac{\sqrt{x}}{\sqrt[4]{y}z^2}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Csqrt%7Bx%7D%7D%7B%5Csqrt%5B4%5D%7By%7Dz%5E2%7D)
More can be learned about the conversion of exponent to power at brainly.com/question/2020414
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The asymptote of the function f(x) = aˣ is y = 0.
The domain of the function f(x) = aˣ is x ∈ R.
The range of the function f(x) = aˣ is y > 0.
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f(x - n) - shifting the graph by n units to the right
f(x + n) - shifting the graph by n units to the left
f(x) - n - shifting the graph by n units down
f(x) + n - shifting the graph by n units up
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We have 
- shifting the graph of f(x) = 6ˣ, 4 units to the right. Therefore
Domain - no change
Range - no change
Asymptote - no change
Answer:
The asymptote is y = 0. The domain is x ∈ R. The range is y > 0.
If
, therefore
- shifting the graph of f(x) = 6ˣ, 4 units down.
Therefore, yor answer is:
Domain - no change (x ∈ R)
Range - change → y > -4
Asymptote - change → y = -4