Answer:
The answer is 48 units³
Step-by-step explanation:
If we simply draw out the region on the x-y plane enclosed between these lines we realize that,if we evaluate the integral the limits all in all cannot be constants since one side of the triangular region is slanted whose equation is given by y=x. So the one of the limit of one of the integrals in the double integral we need to evaluate must be a variable. We choose x part of the integral to have a variable limit, we could well have chosen y's limits as non constant, but it wouldn't make any difference. So the double integral we need to evaluate is given by,
Please note that the order of integration is very important here.We cannot evaluate an integral with variable limit last, we have to evaluate it first.after performing the elementary x integral we get,
After performing the elementary y integral we obtain the desired volume as below,
First, some housekeeping:
cos = 12/13 is incomplete; "cos" must have an argument (input).
cos x = 12/13 is fine; here "cos" has the argument (input) x.
Given that cos x = 12/13, find sin x. To do this, we'll need to find the length of the opposite side, given that the hypo length is 13 and the adj. side length is 12.
12^2 + opp^2 = 13^2, or opp^2 = 169-144 = 25.
Then the opp side could be either 5 or -5. Let's assume that it's +5, and that angle x is in the first quadrant.
Then sin x = opp / hyp = 5/13 (answer)
cos 2 is an entirely different kind of problem. Here you are told what the argument (input) to the cosine function is (it is 2, which here means 2 radians).
Using a calculator: cos 2 = -0.416. Note that the angle 2 rad is in QII, which is why the "adjacent side" is negative and also why the cos of 2 is negative.
Answer:
a. z = 2.00
Step-by-step explanation:
Hello!
The study variable is "Points per game of a high school team"
The hypothesis is that the average score per game is greater than before, so the parameter to test is the population mean (μ)
The hypothesis is:
H₀: μ ≤ 99
H₁: μ > 99
α: 0.01
There is no information about the variable distribution, I'll apply the Central Limit Theorem and approximate the sample mean (X[bar]) to normal since whether you use a Z or t-test, you need your variable to be at least approximately normal. Considering the sample size (n=36) I'd rather use a Z-test than a t-test.
The statistic value under the null hypothesis is:
Z= X[bar] - μ = 101 - 99 = 2
σ/√n 6/√36
I don't have σ, but since this is an approximation I can use the value of S instead.
I hope it helps!
Answer: the circumference is the perimeter of a circle or ellipse. That is, the circumference would be the arc length of the circle, as if it were opened up and straightened out to a line segment. More generally, the perimeter is the curve length around any closed figure.
Given:
The equation is:
To find:
The next step in simplifying the equation by using distributive property.
Solution:
Distributive property: According to this property if a, b and c are three real numbers, then
We have,
Using the distributive property, we get
It can be written as:
Therefore, the next step of the simplification is .
