13. If AC = 16, DE = 8 and BE = 6, find AE. Please show all work
1 answer:
Answer:
AE = 4
Step-by-step explanation:
Use the formula
AE*EC = DE*EB
Since we don't know AE or EC, let AE = x and then EC will = 16 - x. The formula then becomes
x(16 - x) = 8(6)
Getting everything on one side and setting it equal to 0 will allow us to factor for x:
Factoring that gives you that
x = 4 and x = 12. That means that one of those sements has a length of 4 and the other has a length of 12. AE is shorter so it's 4 and EC = 12
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We will conclude that:
- The domain of the exponential function is equal to the range of the logarithmic function.
- The domain of the logarithmic function is equal to the range of the exponential function.
<h3>Comparing the domains and ranges.</h3>
Let's study the two functions.
The exponential function is given by:
f(x) = A*e^x
You can input any value of x in that function, so the domain is the set of all real numbers. And the value of x can't change the sign of the function, so, for example, if A is positive, the range will be:
y > 0.
For the logarithmic function we have:
g(x) = A*ln(x).
As you may know, only positive values can be used as arguments for the logarithmic function, while we know that:
So the range of the logarithmic function is the set of all real numbers.
<h3>So what we can conclude?</h3>- The domain of the exponential function is equal to the range of the logarithmic function.
- The domain of the logarithmic function is equal to the range of the exponential function.
If you want to learn more about domains and ranges, you can read: