The number of months overcharged for 1 gallon of leaky water = 1 1/3
= 4/3
Let us assume the quantity of water overcharged = w
Let us assume the time in months = t
Then, the equation modelling this direct variation is
w = (3/4)t
When w = 5, then
5 = (3/4) * t
20 = 3t
t = 20/3
= 6 2/3
From the above deduction, we can conclude that the first option or option "A" is the correct option. I hope the answer helps you.
We can solve this by distributing
![4(8x+5)](https://tex.z-dn.net/?f=4%288x%2B5%29)
Now, distribute the 4 to both 8x and 5.
![32x+20](https://tex.z-dn.net/?f=32x%2B20)
That's your answer!
Answer:
The Volume of large cone is 19.545
greater than the smaller cone
Step-by-step explanation:
Given:
Size of the small cone = 3.5 inches
Diameter of the small cone = 3 inches
Size of the large cone = 3.5 inches
Diameter of the small cone = 3 inches
To Find:
How much greater, to the nearest tenth of a cubic inch, is the volume of the larger cone than the volume of the smaller cone = ?
Solution:
Volume of the small cone :
Radius = ![\frac{diameter}{2}](https://tex.z-dn.net/?f=%5Cfrac%7Bdiameter%7D%7B2%7D)
Radius = ![\frac{3}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B3%7D%7B2%7D)
Radius = 1.5 inches
volume of the cone =![\pi rl](https://tex.z-dn.net/?f=%5Cpi%20rl)
substituting the values,
=>![\pi (1.5)(3.5)](https://tex.z-dn.net/?f=%5Cpi%20%281.5%29%283.5%29)
=>![\pi(5.25)](https://tex.z-dn.net/?f=%5Cpi%285.25%29)
=> 16.485 ![inches^3](https://tex.z-dn.net/?f=inches%5E3)
Volume of the large cone :
Volume of the large cone :
Radius = ![\frac{diameter}{2}](https://tex.z-dn.net/?f=%5Cfrac%7Bdiameter%7D%7B2%7D)
Radius = ![\frac{4.5}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B4.5%7D%7B2%7D)
Radius = 2.25 inches
volume of the cone =![\pi rl](https://tex.z-dn.net/?f=%5Cpi%20rl)
substituting the values,
=>![\pi (2.25)(5.1)](https://tex.z-dn.net/?f=%5Cpi%20%282.25%29%285.1%29)
=>![\pi(11.475)](https://tex.z-dn.net/?f=%5Cpi%2811.475%29)
=>36.06 ![inches^3](https://tex.z-dn.net/?f=inches%5E3)
Now ,
volume of small cone - volume of large cone
=>36.06 - 16.485
=>19.545 ![inches^3](https://tex.z-dn.net/?f=inches%5E3)
Answer:
22.6°
Step-by-step explanation:
Reference angle = <FDE
Side opposite to <FDE = 5
Hypotenuse = 13
The trigonometric ratios to apply is:
![sin(\theta) = \frac{opp}{hyp}](https://tex.z-dn.net/?f=%20sin%28%5Ctheta%29%20%3D%20%5Cfrac%7Bopp%7D%7Bhyp%7D%20)
Plug in the values
![sin(\angle FDE) = \frac{5}{13}](https://tex.z-dn.net/?f=%20sin%28%5Cangle%20FDE%29%20%3D%20%5Cfrac%7B5%7D%7B13%7D%20)
![sin(\angle FDE) = 0.3846](https://tex.z-dn.net/?f=%20sin%28%5Cangle%20FDE%29%20%3D%200.3846%20)
![\angle FDE = sin^{-1}(0.3846)](https://tex.z-dn.net/?f=%20%5Cangle%20FDE%20%3D%20sin%5E%7B-1%7D%280.3846%29%20)
(nearest tenth)
It’s rise over run so 3/2