Answer:
A
Step-by-step explanation:
Answer:
Rosaria purchased 50 bracelets and 70 necklaces
Step-by-step explanation:
Let the number of bracelets be b and the number of necklaces be n
b + n = 120 •••••(i)
Secondly;
10b + 11n = 1270 ••••(ii)
Total cost of b bracelets at 10 per 1 is 10b
Total cost of n bracelets at 11 per 1 is 11n
Adding both gives 1270
From i, b = 120-n
Substitute this into ii
10(120-n) + 11n = 1270
1200 - 10n + 11n = 1270
n = 1270-1200
n = 70
b = 120-n
b = 120-70
b = 50
The maximum speed of a boat at 30 feet length of water is 0.093 nautical miles/hour or knots.
<u>Step-by-step explanation:</u>
- The equation for the maximum speed, s is given by s²= (16/9)x
- where, x is the length of the water line in feet.
It is given that, the modeled equation s²= (16/9)x is used to find the maximum speed in knots or nautical miles per hour.
The question is asked to find the maximum speed when the length of the water is 30 feet.
Therefore, to find the maximum speed in 30 feet water, the given modeled equation is used. So, substitute the 30 feet in place of x.
<u>Now, calculating the maximum speed :</u>
s² = (16/9)(30)
s² = 480 / 9
s² = 53.3
Taking square root on both sides,
s = √53.3
s = 7.3
The maximum speed of a boat at 30 feet length of water is 7.3 nautical miles/hour or knots.
Answer:
the rate of change of the water depth when the water depth is 10 ft is; ![\mathbf{\dfrac{dh}{dt} = \dfrac{-25}{100 \pi} \ \ ft/s}](https://tex.z-dn.net/?f=%5Cmathbf%7B%5Cdfrac%7Bdh%7D%7Bdt%7D%20%20%3D%20%5Cdfrac%7B-25%7D%7B100%20%20%5Cpi%7D%20%5C%20%20%5C%20ft%2Fs%7D)
Step-by-step explanation:
Given that:
the inverted conical water tank with a height of 20 ft and a radius of 8 ft is drained through a hole in the vertex (bottom) at a rate of 4 ft^3/sec.
We are meant to find the rate of change of the water depth when the water depth is 10 ft.
The diagrammatic expression below clearly interprets the question.
From the image below, assuming h = the depth of the tank at a time t and r = radius of the cone shaped at a time t
Then the similar triangles ΔOCD and ΔOAB is as follows:
( similar triangle property)
![\dfrac{h}{r}= \dfrac{5}{2}](https://tex.z-dn.net/?f=%5Cdfrac%7Bh%7D%7Br%7D%3D%20%5Cdfrac%7B5%7D%7B2%7D)
![\dfrac{h}{r}= 2.5](https://tex.z-dn.net/?f=%5Cdfrac%7Bh%7D%7Br%7D%3D%202.5)
h = 2.5r
![r = \dfrac{h}{2.5}](https://tex.z-dn.net/?f=r%20%3D%20%5Cdfrac%7Bh%7D%7B2.5%7D)
The volume of the water in the tank is represented by the equation:
![V = \dfrac{1}{3} \pi r^2 h](https://tex.z-dn.net/?f=V%20%3D%20%5Cdfrac%7B1%7D%7B3%7D%20%5Cpi%20r%5E2%20h)
![V = \dfrac{1}{3} \pi (\dfrac{h^2}{6.25}) h](https://tex.z-dn.net/?f=V%20%3D%20%5Cdfrac%7B1%7D%7B3%7D%20%5Cpi%20%28%5Cdfrac%7Bh%5E2%7D%7B6.25%7D%29%20h)
![V = \dfrac{1}{18.75} \pi \ h^3](https://tex.z-dn.net/?f=V%20%3D%20%5Cdfrac%7B1%7D%7B18.75%7D%20%5Cpi%20%5C%20h%5E3)
The rate of change of the water depth is :
![\dfrac{dv}{dt}= \dfrac{\pi r^2}{6.25}\ \dfrac{dh}{dt}](https://tex.z-dn.net/?f=%5Cdfrac%7Bdv%7D%7Bdt%7D%3D%20%5Cdfrac%7B%5Cpi%20r%5E2%7D%7B6.25%7D%5C%20%20%5Cdfrac%7Bdh%7D%7Bdt%7D)
Since the water is drained through a hole in the vertex (bottom) at a rate of 4 ft^3/sec
Then,
![\dfrac{dv}{dt}= - 4 \ ft^3/sec](https://tex.z-dn.net/?f=%5Cdfrac%7Bdv%7D%7Bdt%7D%3D%20-%204%20%20%5C%20ft%5E3%2Fsec)
Therefore,
![-4 = \dfrac{\pi r^2}{6.25}\ \dfrac{dh}{dt}](https://tex.z-dn.net/?f=-4%20%3D%20%5Cdfrac%7B%5Cpi%20r%5E2%7D%7B6.25%7D%5C%20%20%5Cdfrac%7Bdh%7D%7Bdt%7D)
the rate of change of the water at depth h = 10 ft is:
![-4 = \dfrac{ 100 \ \pi }{6.25}\ \dfrac{dh}{dt}](https://tex.z-dn.net/?f=-4%20%3D%20%5Cdfrac%7B%20100%20%5C%20%5Cpi%20%7D%7B6.25%7D%5C%20%20%5Cdfrac%7Bdh%7D%7Bdt%7D)
![100 \pi \dfrac{dh}{dt} = -4 \times 6.25](https://tex.z-dn.net/?f=100%20%5Cpi%20%5Cdfrac%7Bdh%7D%7Bdt%7D%20%20%3D%20-4%20%5Ctimes%206.25)
![100 \pi \dfrac{dh}{dt} = -25](https://tex.z-dn.net/?f=100%20%20%5Cpi%20%5Cdfrac%7Bdh%7D%7Bdt%7D%20%20%3D%20-25)
![\dfrac{dh}{dt} = \dfrac{-25}{100 \pi}](https://tex.z-dn.net/?f=%5Cdfrac%7Bdh%7D%7Bdt%7D%20%20%3D%20%5Cdfrac%7B-25%7D%7B100%20%20%5Cpi%7D)
Thus, the rate of change of the water depth when the water depth is 10 ft is; ![\mathtt{\dfrac{dh}{dt} = \dfrac{-25}{100 \pi} \ \ ft/s}](https://tex.z-dn.net/?f=%5Cmathtt%7B%5Cdfrac%7Bdh%7D%7Bdt%7D%20%20%3D%20%5Cdfrac%7B-25%7D%7B100%20%20%5Cpi%7D%20%5C%20%20%5C%20ft%2Fs%7D)
Answer:
Each t-shirt costs about $9.46
Step-by-step explanation:
We can represent as the function
![f(x)=28x+30](https://tex.z-dn.net/?f=f%28x%29%3D28x%2B30)
![295=28x+30](https://tex.z-dn.net/?f=295%3D28x%2B30)
![265=28x](https://tex.z-dn.net/?f=265%3D28x)
![x=9.46](https://tex.z-dn.net/?f=x%3D9.46)