Answer:
√5.
Step-by-step explanation:
Tan A = 1/2 means that the right triangle containing angle A has legs of length 1 and 2 units. So the hypotenuse = √(1^2 + 2^2) = √5 (using the Pythagoras theorem). The side opposite to < A = 1 unit and the adjacent side = 2 (as tan = opposite / adjacent).
so cos A = adjacent / hypotenuse = 2/√5.
and sin A = opposite / hypotenuse = 1 / √5
cos A / sin A = 2/√5 / 1/ √5 = 2.
sin A / (1 + cos A) = 1/√5 (1 + 2/ √5)
= 1 / √5 ( (√5 + 2) /√5)
= 1 / (√5 + 2)
So the answer is:
2 + 1 /(√5 + 2).
We can simplify it further by multiplying top and bottom of the fraction by the complement of √5 + 2 which is √5 - 2.
2 + 1 / (√5 + 2)
= 2(√5 + 2) + 1 / (√5 + 2 )
= { 2(√5 + 2) + 1 } / (√5 + 2)
Multiplying this by √5 - 2 / √5 - 2 we get:
(2(5 - 4) + √5 - 2) / (5 -4)
= 2 + √5 - 2 / 1
= √5.
Considering the conversion from exponent to radical, the equation that justifies why the expression ![9^{\frac{1}{3}} = \sqrt[3]{9}](https://tex.z-dn.net/?f=9%5E%7B%5Cfrac%7B1%7D%7B3%7D%7D%20%3D%20%5Csqrt%5B3%5D%7B9%7D)
is correct is.
<h3>How is the conversion from exponent to radical realized?</h3>
The conversion of rational exponents to radical notation is modeled by:
![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, the expression is:
And the equation that shows that this is correct is:
More can be learned about the conversion from exponent to radical at brainly.com/question/19627260
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1/4 mile in 1/32 hr
unit rate would be x miles in 1 hour.
A complex fraction is a fraction that has a fraction in the numerator OR denominator OR both.
(1/4) / (1/32) =(1/4) * (32/1) = 8 miles in 1 hour
