Answer:
Step-by-step explanation:
First thing I did was graph this on my calculator to find the upper and lower bounds. They were x = 5, 9. Then I applied the disk method of integration. From this I know know I use y = x equations, x intervals, I need a value for R, and then I need a value for r. R represents the height of the representative rectangle which is perpendicular to the axis of rotation, so the height of that rectangle starts at y = 0 and meets the curve. So
Since there is no "hole" or space between the graph and the axis of rotation, r=0. Putting that into the volume formula:
![V=\pi \int\limits^9_5 {[-x^2+14x-45]^2-[0]^2} \, dx](https://tex.z-dn.net/?f=V%3D%5Cpi%20%5Cint%5Climits%5E9_5%20%7B%5B-x%5E2%2B14x-45%5D%5E2-%5B0%5D%5E2%7D%20%5C%2C%20dx)
To simplify I have to multiply that polynomial by itself. Doing that gives us:
Integrating gives us:
which we integrate from 5 to 9
Doing a bit of simplification on that:
![V=\pi [\frac{x^5}{5}-7x^4+\frac{286x^3}{3}-630x^2+2025x]](https://tex.z-dn.net/?f=V%3D%5Cpi%20%5B%5Cfrac%7Bx%5E5%7D%7B5%7D-7x%5E4%2B%5Cfrac%7B286x%5E3%7D%7B3%7D-630x%5E2%2B2025x%5D)
from 5 to 9
Applying the First Fundamental Theorem of Calculus we get that when we sub in a 9 for x then a 5 for x:
which subtracts to
Answer:
Step-by-step explanation:
f(5) = 2^8 - 5 +3
f(5) = 256-5+3
f(5) = 254
Using its concept, it is found that the probability that the lawyer will flip to a page number that is not a multiple of 4 is given by:
p=19/25
Probability is a field of mathematics that deals with the numerical description of the likelihood that an event will occur or that a statement is true. The probability of an event is a number between 0 and 1, with approximately 0 indicating the impossibility of the event and 1 indicating certainty.
A probability is given by the number of desired outcomes divided by the number of total outcomes.
In this problem, there are 50 numbers, of which 50 - (48/4) = 38 are not multiples of 4, hence the probability is given by:
p=38/50 = 19/25
Learn more about probability here:brainly.com/question/24756209
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Answer:
12
Step-by-step explanation:
1.3
20 ÷ 15 = 1.3
