Answer:
15.68$
Step-by-step explanation:
You calculate the price of one lollipop:
4.48/2= 2.24
The multiply that by 7.
2.24*7= 15.68$
Answer:
Water level in the reservoir is falling at the rate of 0.398 ft per minute.
Step-by-step explanation:
From the figure attached,
Water level in the reservoir has been given as 10 feet and radius of the reservoir is 4 feet.
Let the level of water in the reservoir after time t is h where radius of the water level becomes r.
ΔABE and ΔCDE are similar.
Therefore, their corresponding sides will be in the same ratio.
![\frac{r}{h}=\frac{4}{10}](https://tex.z-dn.net/?f=%5Cfrac%7Br%7D%7Bh%7D%3D%5Cfrac%7B4%7D%7B10%7D)
--------(1)
Now volume of the water V = ![\frac{1}{3}\pi r^{2}h](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B3%7D%5Cpi%20r%5E%7B2%7Dh)
From equation (1),
V = ![\frac{1}{3}\pi (\frac{2}{5}h)^{2} h](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B3%7D%5Cpi%20%28%5Cfrac%7B2%7D%7B5%7Dh%29%5E%7B2%7D%20h)
V = ![\frac{4\pi h^{2}\times h}{75}](https://tex.z-dn.net/?f=%5Cfrac%7B4%5Cpi%20h%5E%7B2%7D%5Ctimes%20h%7D%7B75%7D)
![\frac{dV}{dt}=\frac{4\pi }{75}\times \frac{d}{dt}(h^{3})](https://tex.z-dn.net/?f=%5Cfrac%7BdV%7D%7Bdt%7D%3D%5Cfrac%7B4%5Cpi%20%7D%7B75%7D%5Ctimes%20%5Cfrac%7Bd%7D%7Bdt%7D%28h%5E%7B3%7D%29)
![\frac{dV}{dt}=\frac{4\pi }{75}\times (3h^{2})\frac{dh}{dt}](https://tex.z-dn.net/?f=%5Cfrac%7BdV%7D%7Bdt%7D%3D%5Cfrac%7B4%5Cpi%20%7D%7B75%7D%5Ctimes%20%283h%5E%7B2%7D%29%5Cfrac%7Bdh%7D%7Bdt%7D)
![\frac{dV}{dt}=\frac{12\pi h^{2}}{75}\times \frac{dh}{dt}](https://tex.z-dn.net/?f=%5Cfrac%7BdV%7D%7Bdt%7D%3D%5Cfrac%7B12%5Cpi%20h%5E%7B2%7D%7D%7B75%7D%5Ctimes%20%5Cfrac%7Bdh%7D%7Bdt%7D)
Since
feet³ per minute and h = 5 feet
![5=\frac{12\pi (5)^{2}}{75}\times \frac{dh}{dt}](https://tex.z-dn.net/?f=5%3D%5Cfrac%7B12%5Cpi%20%285%29%5E%7B2%7D%7D%7B75%7D%5Ctimes%20%5Cfrac%7Bdh%7D%7Bdt%7D)
![5=4\pi \frac{dh}{dt}](https://tex.z-dn.net/?f=5%3D4%5Cpi%20%5Cfrac%7Bdh%7D%7Bdt%7D)
![\frac{dh}{dt}=\frac{5}{4\pi}](https://tex.z-dn.net/?f=%5Cfrac%7Bdh%7D%7Bdt%7D%3D%5Cfrac%7B5%7D%7B4%5Cpi%7D)
feet per minute
Therefore, water level in the reservoir is falling at the rate of 0.398 feet per minute.
Answer:
36 milliliters of rain.
Step-by-step explanation:
The rate at which rain accumluated in a bucket is given by the function:
![r(t)=10t-t^2](https://tex.z-dn.net/?f=r%28t%29%3D10t-t%5E2)
Where r(t) is measured in milliliters per minute.
We want to find the total accumulation of rain from <em>t</em> = 0 to <em>t</em> = 3.
We can use the Net Change Theorem. So, we will integrate function <em>r</em> from <em>t</em> = 0 to <em>t</em> = 3:
![\displaystyle \int_0^3r(t)\, dt](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cint_0%5E3r%28t%29%5C%2C%20dt)
Substitute:
![=\displaystyle \int_0^3 10t-t^2\, dt](https://tex.z-dn.net/?f=%3D%5Cdisplaystyle%20%5Cint_0%5E3%2010t-t%5E2%5C%2C%20dt)
Integrate:
![\displaystyle =5t^2-\frac{1}{3}t^3\Big|_0^3](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%3D5t%5E2-%5Cfrac%7B1%7D%7B3%7Dt%5E3%5CBig%7C_0%5E3)
Evaluate:
![\displaystyle =(5(3)^2-\frac{1}{3}(3)^3)-(5(0)^2-\frac{1}{3}(0)^3)=36\text{ milliliters}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%3D%285%283%29%5E2-%5Cfrac%7B1%7D%7B3%7D%283%29%5E3%29-%285%280%29%5E2-%5Cfrac%7B1%7D%7B3%7D%280%29%5E3%29%3D36%5Ctext%7B%20milliliters%7D)
36 milliliters of rain accumulated in the bucket from time <em>t</em> = 0 to <em>t</em> = 3.
You can use a frequency table for steak tasting, where each numbers represents the steak that was the chosen as the best.
Answer: (x,y) = (1,6)
Step-by-step explanation: