Answer:
6.84 ≤ x ≤ 37.39
Step-by-step explanation:
we have
-----> equation A
we know that
The company wants to keep its profits at or above $225,000,
so
-----> inequality B
Remember that P(x) is in thousands of dollars
Solve the system by graphing
using a graphing tool
The solution is the interval [6.78,39.22]
see the attached figure
therefore
A reasonable constraint for the model is
6.84 ≤ x ≤ 37.39
We have been given that a company makes wax candles in the shape of a solid sphere. Each candle has a diameter of 15 cm. We are asked to find the number of candles that company can make from 70,650 cubic cm of wax.
To solve our given problem, we will divide total volume of wax by volume of one candle.
Volume of each candle will be equal to volume of sphere.
, where r represents radius of sphere.
We know that radius is half the diameter, so radius of each candle will be
cm.
![\text{Volume of one candle}=\frac{4}{3}\cdot 3.14\cdot (7.5\text{ cm})^3](https://tex.z-dn.net/?f=%5Ctext%7BVolume%20of%20one%20candle%7D%3D%5Cfrac%7B4%7D%7B3%7D%5Ccdot%203.14%5Ccdot%20%287.5%5Ctext%7B%20cm%7D%29%5E3)
![\text{Volume of one candle}=\frac{4}{3}\cdot 3.14\cdot 421.875\text{ cm}^3](https://tex.z-dn.net/?f=%5Ctext%7BVolume%20of%20one%20candle%7D%3D%5Cfrac%7B4%7D%7B3%7D%5Ccdot%203.14%5Ccdot%20421.875%5Ctext%7B%20cm%7D%5E3)
![\text{Volume of one candle}=1766.25\text{ cm}^3](https://tex.z-dn.net/?f=%5Ctext%7BVolume%20of%20one%20candle%7D%3D1766.25%5Ctext%7B%20cm%7D%5E3)
Now we will divide 70,650 cubic cm of wax by volume of one candle.
![\text{Number of candles}=\frac{70,650\text{ cm}^3}{1766.25\text{ cm}^3}](https://tex.z-dn.net/?f=%5Ctext%7BNumber%20of%20candles%7D%3D%5Cfrac%7B70%2C650%5Ctext%7B%20cm%7D%5E3%7D%7B1766.25%5Ctext%7B%20cm%7D%5E3%7D)
![\text{Number of candles}=\frac{70,650}{1766.25}](https://tex.z-dn.net/?f=%5Ctext%7BNumber%20of%20candles%7D%3D%5Cfrac%7B70%2C650%7D%7B1766.25%7D)
![\text{Number of candles}=40](https://tex.z-dn.net/?f=%5Ctext%7BNumber%20of%20candles%7D%3D40)
Therefore, 40 candles can be made from 70,650 cubic cm of wax.