Answer:
Part A) The volume of the entire cone is ![168\pi\ in^3](https://tex.z-dn.net/?f=168%5Cpi%5C%20in%5E3)
Part B) see the explanation
Step-by-step explanation:
Part A) we know that
The volume of a cone is equal to
![V=\frac{1}{3}\pi r^{2}h](https://tex.z-dn.net/?f=V%3D%5Cfrac%7B1%7D%7B3%7D%5Cpi%20r%5E%7B2%7Dh)
where
r is the radius of the base of the cone
h is the height of the cone
In this problem triangle ABD is similar to triangle ACE
Remember that If two figures are similar, then the ratio of its corresponding sides is proportional
so
![\frac{AB}{AC}=\frac{BD}{CE}](https://tex.z-dn.net/?f=%5Cfrac%7BAB%7D%7BAC%7D%3D%5Cfrac%7BBD%7D%7BCE%7D)
substitute the given values
![\frac{7}{14}=\frac{3}{x}](https://tex.z-dn.net/?f=%5Cfrac%7B7%7D%7B14%7D%3D%5Cfrac%7B3%7D%7Bx%7D)
solve for x
![x=14(3)/7\\x=6\ in](https://tex.z-dn.net/?f=x%3D14%283%29%2F7%5C%5Cx%3D6%5C%20in)
To find out the volume of the entire cone we have
![r=CE=x=6\ in](https://tex.z-dn.net/?f=r%3DCE%3Dx%3D6%5C%20in)
![h=AC=14\ in](https://tex.z-dn.net/?f=h%3DAC%3D14%5C%20in)
substitute in the formula
![V=\frac{1}{3}\pi (6)^{2}(14)](https://tex.z-dn.net/?f=V%3D%5Cfrac%7B1%7D%7B3%7D%5Cpi%20%286%29%5E%7B2%7D%2814%29)
![V=168\pi\ in^3](https://tex.z-dn.net/?f=V%3D168%5Cpi%5C%20in%5E3)
Part B) How did you determine the value for x in triangle ACE
In this problem triangle ABD is similar to triangle ACE
If two figures are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruent
so
![\frac{AB}{AC}=\frac{BD}{CE}](https://tex.z-dn.net/?f=%5Cfrac%7BAB%7D%7BAC%7D%3D%5Cfrac%7BBD%7D%7BCE%7D)
substitute the given values and solve for x
Answer:
n-16=29 doesn't belong
Step-by-step explanation:
When you solve all the equations, you get n=13, but n can't equal 13 when you plug it in the equation n-16=29. N would have to equal 45.
Answer:
You bought 5 erasers.
Step-by-step explanation:
You have the erasers sold for 4 dollars each and you have only 20 dollars left over to buy erasers so you divide 20 by 4 to get 5
The exponent 2 outside the brackets is distributed on 3 as well. 3 exponent 2 gives 9, not 6. answer would be 9x^4y^8