Answer:
24000 pieces.
Step-by-step explanation:
Given:
Side lengths of cube = ![\frac{1}{4} \ foot](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B4%7D%20%5C%20foot)
The part of the truck that is being filled is in the shape of a rectangular prism with dimensions of 8 ft x 6 1/4 ft x 7 1/2 ft.
Question asked:
What is the greatest number of packages that can fit in the truck?
Solution:
First of all we will find volume of cube, then volume of rectangular prism and then simply divide the volume of prism by volume of cube to find the greatest number of packages that can fit in the truck.
![Volume\ of\ cube =a^{3}](https://tex.z-dn.net/?f=Volume%5C%20of%5C%20cube%20%3Da%5E%7B3%7D)
![=\frac{1}{4} \times\frac{1}{4}\times \frac{1}{4} =\frac{1}{64} \ cubic \ foot](https://tex.z-dn.net/?f=%3D%5Cfrac%7B1%7D%7B4%7D%20%5Ctimes%5Cfrac%7B1%7D%7B4%7D%5Ctimes%20%5Cfrac%7B1%7D%7B4%7D%20%3D%5Cfrac%7B1%7D%7B64%7D%20%5C%20cubic%20%5C%20foot)
Length = 8 foot, Breadth =
, Height =![7\frac{1}{2} =\frac{15}{2} \ foot](https://tex.z-dn.net/?f=7%5Cfrac%7B1%7D%7B2%7D%20%3D%5Cfrac%7B15%7D%7B2%7D%20%5C%20foot)
![Volume\ of\ rectangular\ prism =length\times breadth\times height](https://tex.z-dn.net/?f=Volume%5C%20of%5C%20rectangular%5C%20prism%20%3Dlength%5Ctimes%20breadth%5Ctimes%20height)
![=8\times\frac{25}{4} \times\frac{15}{2} \\=\frac{3000}{8} =375\ cubic\ foot](https://tex.z-dn.net/?f=%3D8%5Ctimes%5Cfrac%7B25%7D%7B4%7D%20%5Ctimes%5Cfrac%7B15%7D%7B2%7D%20%5C%5C%3D%5Cfrac%7B3000%7D%7B8%7D%20%3D375%5C%20cubic%5C%20foot)
The greatest number of packages that can fit in the truck = Volume of prism divided by volume of cube
The greatest number of packages that can fit in the truck = ![\frac{375}{\frac{1}{64} } =375\times64=24000\ pieces\ of\ cube](https://tex.z-dn.net/?f=%5Cfrac%7B375%7D%7B%5Cfrac%7B1%7D%7B64%7D%20%7D%20%3D375%5Ctimes64%3D24000%5C%20pieces%5C%20of%5C%20cube)
Thus, the greatest number of packages that can fit in the truck is 24000 pieces.
Given:
Height of man = 6 ft
Height of man's shadow = 11 feet
Height of building's shadow = 139 feet
To find:
The height of the building.
Solution:
We know that the heights of the objects and there shadows are always proportional.
![\dfrac{\text{Height of man}}{\text{Height of man's shadow}}=\dfrac{\text{Height of the building}}{\text{Height of building's shadow}}](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Ctext%7BHeight%20of%20man%7D%7D%7B%5Ctext%7BHeight%20of%20man%27s%20shadow%7D%7D%3D%5Cdfrac%7B%5Ctext%7BHeight%20of%20the%20building%7D%7D%7B%5Ctext%7BHeight%20of%20building%27s%20shadow%7D%7D)
Let x be the height of the building.
![\dfrac{6}{11}=\dfrac{x}{139}](https://tex.z-dn.net/?f=%5Cdfrac%7B6%7D%7B11%7D%3D%5Cdfrac%7Bx%7D%7B139%7D)
Multiply both sides by 139.
![\dfrac{6}{11}\times 139=x](https://tex.z-dn.net/?f=%5Cdfrac%7B6%7D%7B11%7D%5Ctimes%20139%3Dx)
![\dfrac{834}{11}=x](https://tex.z-dn.net/?f=%5Cdfrac%7B834%7D%7B11%7D%3Dx)
![75.8181...=x](https://tex.z-dn.net/?f=75.8181...%3Dx)
![x\approx 75.8](https://tex.z-dn.net/?f=x%5Capprox%2075.8)
Therefore, the building is 75.8 feet long.
Answer:(5,11)
Step-by-step explanation:
Step-by-step explanation: The slope of the line is 3/2, which means the X coordinate goes over by 2, and the Y goes over by 3.
Answer: Statement 1 is the same as statement 2
All 90 degrees are right angles and all right angles are 90 degrees
Step-by-step explanation:
1. If the measure of an angle is 90 degrees, then it is a right angle.
2. If an angle is a right angle, then it will measure 90 degrees.
Statement 1 is the same as statement 2
All 90 degrees are right angles and all right angles are 90 degrees
An ' equal to ' can be introduced such that
If 90 degrees = right Angle
Then right angle = 90 degrees