10.44yd
a^2 + b^2 = c^2
3^2 + 10^2 = c^2
109 = c^2
C (Hypotenuse) ≈ 10.44
Given that grain is falling from a chute onto the ground, forming a conical pile whose diameter is always three times its height.
So if D is the diameter and h is the height of the conical pile then we can write:
D=3h
We know that diameter = 2r, where r is the radius
2r=3h
![r=\frac{3h}{2}](https://tex.z-dn.net/?f=r%3D%5Cfrac%7B3h%7D%7B2%7D)
Volume of conical pile is given by formula
![V=\frac{1}{3}\pi r^2h](https://tex.z-dn.net/?f=%20V%3D%5Cfrac%7B1%7D%7B3%7D%5Cpi%20r%5E2h)
Given that volume is 1110 cubic feet.
Now plug the values of Volume and r into equation of volume
![1110=\frac{1}{3}\pi (\frac{3h}{2})^2h](https://tex.z-dn.net/?f=%201110%3D%5Cfrac%7B1%7D%7B3%7D%5Cpi%20%28%5Cfrac%7B3h%7D%7B2%7D%29%5E2h)
![1110=\frac{1}{3}\pi\cdot\frac{9h^2}{4}\cdot h](https://tex.z-dn.net/?f=%201110%3D%5Cfrac%7B1%7D%7B3%7D%5Cpi%5Ccdot%5Cfrac%7B9h%5E2%7D%7B4%7D%5Ccdot%20h)
![1110=\pi\cdot\frac{3h^3}{4}](https://tex.z-dn.net/?f=%201110%3D%5Cpi%5Ccdot%5Cfrac%7B3h%5E3%7D%7B4%7D)
![1110\cdot\frac{4}{3\pi}=h^3](https://tex.z-dn.net/?f=%201110%5Ccdot%5Cfrac%7B4%7D%7B3%5Cpi%7D%3Dh%5E3)
![471.098631552=h^3](https://tex.z-dn.net/?f=%20471.098631552%3Dh%5E3)
take cube root of both sides
7.78103342467=h
Hence height is approx 7.78 feet.
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➷ The range is the highest value minus the smallest value
Therefore, you just need to subtract the two values to find the values:
-2 - 4 = -6
The difference is just 6, so your answer is C. 6
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✽</u></h3>
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Answer:
= 184/5
Step-by-step explanation:
converting mixed numbers to fractions, our initial equation becomes,
44/5 × 2/11
Applying the fractions formula for multiplication you get,
= 924/5
Simplifying 924/5, the answer is
=184 4/5
![\huge \bf༆ Answer ༄](https://tex.z-dn.net/?f=%5Chuge%20%5Cbf%E0%BC%86%20Answer%20%E0%BC%84)
Sales tax on the item is ~
![{ \qquad{ \sf{ \dashrightarrow}}} \: \: \sf \$23.40](https://tex.z-dn.net/?f=%20%7B%20%5Cqquad%7B%20%5Csf%7B%20%5Cdashrightarrow%7D%7D%7D%20%20%5C%3A%20%20%5C%3A%20%5Csf%20%5C%2423.40)
Cost of the item is ~
![{ \qquad{ \sf{ \dashrightarrow}}} \: \: \sf \$390](https://tex.z-dn.net/?f=%7B%20%5Cqquad%7B%20%5Csf%7B%20%5Cdashrightarrow%7D%7D%7D%20%20%5C%3A%20%20%5C%3A%20%5Csf%20%5C%24390)
sale tax rate is ~
![{ \qquad{ \sf{ \dashrightarrow}}} \: \: \sf \: \dfrac{ \$23.40}{ \$390} \times 100](https://tex.z-dn.net/?f=%7B%20%5Cqquad%7B%20%5Csf%7B%20%5Cdashrightarrow%7D%7D%7D%20%20%5C%3A%20%20%5C%3A%20%5Csf%20%5C%3A%20%5Cdfrac%7B%20%5C%2423.40%7D%7B%20%5C%24390%7D%20%20%5Ctimes%20100)
![{ \qquad{ \sf{ \dashrightarrow}}} \: \: \sf \: 0.06 \times 100](https://tex.z-dn.net/?f=%7B%20%5Cqquad%7B%20%5Csf%7B%20%5Cdashrightarrow%7D%7D%7D%20%20%5C%3A%20%20%5C%3A%20%5Csf%20%5C%3A%200.06%20%5Ctimes%20100)
![{ \qquad{ \sf{ \dashrightarrow}}} \: \: \sf \: 6 \%](https://tex.z-dn.net/?f=%7B%20%5Cqquad%7B%20%5Csf%7B%20%5Cdashrightarrow%7D%7D%7D%20%20%5C%3A%20%20%5C%3A%20%5Csf%20%5C%3A%206%20%20%5C%25)
Therefore, the sales tax rate is 6 %