Answer:
Average rate of change is <u>0.80.</u>
Step-by-step explanation:
Given:
The two points given are (5, 6) and (15, 14).
Average rate of change is the ratio of the overall change in 'y' and overall change in 'x'. If the overall change in 'y' is positive with 'x', then average rate of change is also positive and vice-versa.
The average rate of change for two points is given as:
Plug in and solve for 'R'. This gives,
Therefore, the average rate of change for the points (5, 6) and (15, 14) is 0.80.
First integral:
Use the rational exponent to represent roots. You have
And from here you can use the rule
to derive
Second integral:
Simply split the fraction:
So, the integral of the sum becomes the sum of three immediate integrals:
So, the answer is the sum of the three pieces:
Third integral:
Again, you can split the integral of the sum in the sum of the integrals. The antiderivative of the cosine is the sine, because . So, you have
First, you try to make sure that both the denominators are the same. In order to do this, you multiply both fractions' numerator and denominator by the other fraction's denominator. Next, you combine like terms in the numerator, and then you simplify the fraction.
Let the volume of prism A be X. Then the volume of prism B is 2X. The combined volume could be described like this:
432 = X + 2X
Solving the equation,
432 = 3X
432/3=X
144=X
The volume of A is 144 cubic feet, while the volume of B is 288 cubic feet.