Answer:
Volume of the pyramid is 448 cubic meters.
Step-by-step explanation:
Volume of the given pyramid = ![\frac{1}{3}(\text{Area of the rectangular base})(\text{Height of the pyramid})](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B3%7D%28%5Ctext%7BArea%20of%20the%20rectangular%20base%7D%29%28%5Ctext%7BHeight%20of%20the%20pyramid%7D%29)
Area of the rectangular base = Length × Width
= 12 × 16
= 192 m²
Volume of the pyramid = ![\frac{1}{3}(192)(7)](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B3%7D%28192%29%287%29)
= 448 m³
Therefore, the volume is 448 cubic meters.
32/4 is 8, so we know that the lengths of the sides are 8 feet.
Because of this
<u>I can safely say that the diagonal of the square is 8√2 feet long</u>.
Here's my proof:
Answer:
(a)
![\sqrt{105} => Irrational](https://tex.z-dn.net/?f=%5Csqrt%7B105%7D%20%3D%3E%20Irrational)
![-4 => Integer](https://tex.z-dn.net/?f=-4%20%3D%3E%20Integer)
![\frac{4}{3} => Rational](https://tex.z-dn.net/?f=%5Cfrac%7B4%7D%7B3%7D%20%3D%3E%20Rational)
(b)
![\sqrt{105}](https://tex.z-dn.net/?f=%5Csqrt%7B105%7D)
Step-by-step explanation:
Given
![\sqrt{105}](https://tex.z-dn.net/?f=%5Csqrt%7B105%7D)
![-4](https://tex.z-dn.net/?f=-4)
![\frac{4}{3}](https://tex.z-dn.net/?f=%5Cfrac%7B4%7D%7B3%7D)
Solving (a): The category of number the belong to
![\sqrt{105}](https://tex.z-dn.net/?f=%5Csqrt%7B105%7D)
Solve the square root
![\sqrt{105} = 10.246950766](https://tex.z-dn.net/?f=%5Csqrt%7B105%7D%20%3D%2010.246950766)
The result is irrational;
So:
![\sqrt{105} => Irrational](https://tex.z-dn.net/?f=%5Csqrt%7B105%7D%20%3D%3E%20Irrational)
![-4 => Integer](https://tex.z-dn.net/?f=-4%20%3D%3E%20Integer)
![\frac{4}{3}](https://tex.z-dn.net/?f=%5Cfrac%7B4%7D%7B3%7D)
This has an integer numerator and denominator;
So:
![\frac{4}{3} => Rational](https://tex.z-dn.net/?f=%5Cfrac%7B4%7D%7B3%7D%20%3D%3E%20Rational)
Solving (b): Order from least to greatest
i. ![\sqrt{105} = 10.246950766](https://tex.z-dn.net/?f=%5Csqrt%7B105%7D%20%3D%2010.246950766)
ii. ![-4](https://tex.z-dn.net/?f=-4)
iii. ![\frac{4}{3} = 1.33333](https://tex.z-dn.net/?f=%5Cfrac%7B4%7D%7B3%7D%20%3D%201.33333)
List out the corresponding numbers:
10.246950766; -4 and 1.333333
Reorder: from least to greatest:
-4; -1.3333333 and 10.246950766
<em>Hence; The correct order is:</em>
![\sqrt{105}](https://tex.z-dn.net/?f=%5Csqrt%7B105%7D)
Answer:
or 210°
Step-by-step explanation: