![36 \int\limits^1_0 { \frac{1}{(2 x + 1) ^{3} } } \, dx =](https://tex.z-dn.net/?f=36%20%5Cint%5Climits%5E1_0%20%7B%20%5Cfrac%7B1%7D%7B%282%20x%20%2B%201%29%20%5E%7B3%7D%20%7D%20%7D%20%5C%2C%20dx%20%3D)
u = 2 x + 1, d u = 2 d x, d x = d u / 2
![36*1/2 \int\limits^1_0 {u ^{-3} } \, du = 18 * t ^{-2}/(-2) = \\ - 9 * t^{-2}= \\ -9 * ( 2 x + 1 ) ^{-2}](https://tex.z-dn.net/?f=36%2A1%2F2%20%5Cint%5Climits%5E1_0%20%7Bu%20%5E%7B-3%7D%20%7D%20%5C%2C%20du%20%3D%2018%20%2A%20t%20%5E%7B-2%7D%2F%28-2%29%20%3D%20%5C%5C%20-%209%20%2A%20t%5E%7B-2%7D%3D%20%5C%5C%20-9%20%2A%20%28%202%20x%20%2B%201%20%29%20%5E%7B-2%7D%20%20%20%20)
- 9 / ( 2 + 1 )² - ( - 9 / ( 0 + 1 )² =
- 9 / 9 + 9 = - 1 + 9 =
8
1/4 of a slice since the pizza is 5/4 and only 5 people need a slice
Answer:
∴73,563 calls are made between two cities with populations of 100,000 and 160,000 that are 435 miles apart.
Step-by-step explanation:
Given that,
The number of phone calls between two cities (N )
- directly proportional as the value of populations
and
of two cities. - Inversely varies as the magnitude of distance (d).
![N\propto\frac{p_1p_2}{d}](https://tex.z-dn.net/?f=N%5Cpropto%5Cfrac%7Bp_1p_2%7D%7Bd%7D)
![N=k.\frac{p_1p_2}{d}](https://tex.z-dn.net/?f=N%3Dk.%5Cfrac%7Bp_1p_2%7D%7Bd%7D)
Given that,
N=18,000, d=310 miles,
=15,500 and
=180,000
![18,000=k.\frac{15,500\times 180,000}{310}](https://tex.z-dn.net/?f=18%2C000%3Dk.%5Cfrac%7B15%2C500%5Ctimes%20180%2C000%7D%7B310%7D)
![\Rightarrow k=\frac{18,000\times310}{15,500\times 180,000}](https://tex.z-dn.net/?f=%5CRightarrow%20k%3D%5Cfrac%7B18%2C000%5Ctimes310%7D%7B15%2C500%5Ctimes%20180%2C000%7D)
![\Rightarrow k=\frac{31}{15,500}](https://tex.z-dn.net/?f=%5CRightarrow%20k%3D%5Cfrac%7B31%7D%7B15%2C500%7D)
Now,
N=? , d=435 miles,
=100,500 and
=160,000
![N=\frac{31}{15,500}.\frac{100,000\times 160,000}{435}](https://tex.z-dn.net/?f=N%3D%5Cfrac%7B31%7D%7B15%2C500%7D.%5Cfrac%7B100%2C000%5Ctimes%20160%2C000%7D%7B435%7D)
![\Rightarrow N\approx 73,563](https://tex.z-dn.net/?f=%5CRightarrow%20N%5Capprox%2073%2C563)
∴73,563 calls are made between two cities with populations of 100,000 and 160,000 that are 435 miles apart.
Answer:
Carlota is not correct
Step-by-step explanation:
A ratio represents relationship between of two or more things.
Ratio of minutes to gallons of water flowing through a garden hose ![=2:12](https://tex.z-dn.net/?f=%3D2%3A12)
Here,
![2:12=1:6](https://tex.z-dn.net/?f=2%3A12%3D1%3A6)
Also,
It's given that an equivalent ratio of minutes to gallons is ![6:1](https://tex.z-dn.net/?f=6%3A1)
Now,
![1:6\neq 6:1](https://tex.z-dn.net/?f=1%3A6%5Cneq%206%3A1)
Therefore,
Carlota is not correct
Answer: d) 3/8
there's 8 things in the spinner which means the denominator will be 8. there's 3 of the number 2 on the spinner. that gives you a fraction of 3/8 - and that's your probability
hope this helps :)