Using properties of the logarithm, you can rearrange the integrand as
Then recall that the integral of 
is
(or you can find that out by integrating by parts) and so
Answer: 144 Cubic Feet
Explanation: Multiply all of your numbers together to get your volume.
<u>Numbers</u> : Length(12) x Width(3) x Height(4) = 144 cubic feet.
I hope this helps you! :)
Answer:
Step-by-step explanation:
The angles remain right angles if you are reflecting over the x axis.
Answer:
Step-by-step explanation:
The cotangent function can be rewritten by trigonometric relations, that is:
(1)
By taking approach the periodicity properties of the cosine and sine function (both functions have a period of 360°), we use the following equivalencies:
(2)
(3)
By (2) and (3) in (1), we have following expression:
If we know that 
and 
, then the result of the trigonometric expression is:
1. We assume, that the number 40 is 100% - because it's the output value of the task.
2. We assume, that x is the value we are looking for.
3. If 100% equals 40, so we can write it down as 100%=40.
4. We know, that x% equals 21 of the output value, so we can write it down as x%=21.
5. Now we have two simple equations:
1) 100%=40
2) x%=21
where left sides of both of them have the same units, and both right sides have the same units, so we can do something like that:
100%/x%=40/21
6. Now we just have to solve the simple equation, and we will get the solution we are looking for.
7. Solution for 21 is what percent of 40
100%/x%=40/21
(100/x)*x=(40/21)*x - we multiply both sides of the equation by x
100=1.90476190476*x - we divide both sides of the equation by (1.90476190476) to get x
100/1.90476190476=x
52.5=x
x=52.5
now we have:
21 is 52.5% of 40
