Answer:
See proof below
Step-by-step explanation
cot^2(x) - csc^2(x) = -1
In trigonometry identity
cot^2x = cos²x/sin²x
Csc²x = 1/sin²x
Substitute into the original expression
cos²x/sin²x - 1/sin²x
Find the LCM
(Cos²x-1)/sin²x .... *
Recall that sin²x+cos²x = 1
Sin²x = 1-cos²x
-sin²x = -1+cos²x
-sin²x = cos²x-1 .... **
Substitute ** into *
(Cos²x-1)/sin²x
-sin²x/sin²x
= -1 (RHS)
Therefore cot^2(x) - csc^2(x) = -1 (Proved!)
<u>Given</u>:
The given inequality is
We need to determine the graph that fits the inequality.
<u>Graph of the inequality:</u>
The inequality means that x is greater than 4. This means that the end value 4 is not included.
To graph the inequality " > " a dashed line is used.
The inequality does not contain any y - value in it.
Hence, it has only one vertical line at and is shaded for all values of x greater than 4.
Therefore, the graph that fits the inequality is a vertical dashed line, shaded to the right of the line.
Thus, Option d is the correct answer.
To get the volume of water in gallons we proceed as follows:
volume=length*width*height
the dimension of the pool is:
50m by 25m by 1.5 m
thus the volume will be:
50×25×1.5
=1,875 m^3
but 1 m^3= 1000 liters
therefore:
1,875 m^3=(1875x1000)=1,875,000 liters
converting the above into gallons we get:
1 gallon= 3.786 L
therefore:
1,875,000 L=1,875,000/3.786 gallons
=495,245.6418 gallons
Answer:
The actual area is 44,825 mi², and the actual population density of Ohio is 282.3 people per square mile. I can't answer the estimate part because I don't know what your estimate was. But you can say my estimate was greater than the actual number or less than the actual number. And you can say your estimate was greater/less than the actual population density because I didn't know so many people were in each square mile because a square mile isn't that large.
Step-by-step explanation:
Can't really explain this type of question. :v