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Answer:
a = √11 and b = 6
Step-by-step explanation:
Refer to attached picture for reference
for an right triangle with angle θ
we are given
cos θ = 5/6 = length of adjacent side / length of hypotenuse
hence
adjacent length = 5 units
hypotenuse length = 6 units
the missing side is the "opposite" length which we can find with the Pythagorean equation. in our case:
hypotenuse ² = adjacent ² + opposite² (rearrange)
opposite ² = hypotenuse ² - adjacent ²
opposite ² = 6² - 5²
opposite = √ (6²-5²) = √11
sin θ = opposite length / hypotenuse (substitute values above)
sin θ = √11 / 6
hence a = √11 and b = 6
The transformed function is y = 1/3(log(x/3 + 4)) + 1
<h3>How to transform the logarithmic function?</h3>The parent logarithmic function is
y = log(x)
When shifted left by 4 units, we have:
y = log(x + 4)
When shifted up by 3 units, we have:
y = log(x + 4) + 3
When compressed vertically by 1/3, we have:
y = 1/3(log(x + 4) + 3)
This gives
y = 1/3(log(x + 4)) + 1
When stretched horizontally by 3, we have:
y = 1/3(log(x/3 + 4)) + 1
Hence, the transformed function is y = 1/3(log(x/3 + 4)) + 1
<h3>The transformation of function f(x)</h3>We have:
f(x) = log[-(x – 5)] + 4
Set the radicand greater than 0
-(x - 5) > 0
Divide by -1
x - 5 < 0
Add 5 to both sides
x < 5 -- this represents the domain
A logarithmic function can output any real number.
So, the range is
In the domain, we have:
x < 5
This means that the interval of decrease is
Rewrite as an equation
x = 5 --- this represents the equation of asymptote
Read more about logarithmic functions at:
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