Step-by-step explanation:
the speed is 130 miles / hour.
that means the train travels 130 miles in 1 hour.
so, the question is, how far is it traveling. when it is going with that speed for 6 hours ?
well, 130 × 6 = 780 miles.
formally, speed is "distance / time".
multiplying this by some time, we have then an expression of "(distance / time) × time", which is then simply "distance".
Red = r
Blue = b
Green = g
Step 1: Write as algebraic equations.
r = b + 6
g = b - 4
Step 2: Merge the two equations together to form one, by adding them together.
r + g = b + b + 6 - 4
Step 3: Simplify.
r + g = 2b + 2
Step 4: Make b the subject.
2b + 2 = r + g
2b = r + g - 2
b = 0.5(r + g - 2)
ANSWER
b = 0.5(r + g - 2)
Answer:
A=2
B=12
C=5
D=13
SA=411mm
Step-by-step explanation:
SA=bh+(s1+s2+s3)H
=12×5+(12+2+13)(13)
Answer:
The volume of the sphere is 14m³
Step-by-step explanation:
Given
Volume of the cylinder = ![21m^3](https://tex.z-dn.net/?f=21m%5E3)
Required
Volume of the sphere
Given that the volume of the cylinder is 21, the first step is to solve for the radius of the cylinder;
<em>Using the volume formula of a cylinder</em>
The formula goes thus
![V = \pi r^2h](https://tex.z-dn.net/?f=V%20%3D%20%5Cpi%20r%5E2h)
Substitute 21 for V; this gives
![21 = \pi r^2h](https://tex.z-dn.net/?f=21%20%3D%20%5Cpi%20r%5E2h)
Divide both sides by h
![\frac{21}{h} = \frac{\pi r^2h}{h}](https://tex.z-dn.net/?f=%5Cfrac%7B21%7D%7Bh%7D%20%3D%20%5Cfrac%7B%5Cpi%20r%5E2h%7D%7Bh%7D)
![\frac{21}{h} = \pi r^2](https://tex.z-dn.net/?f=%5Cfrac%7B21%7D%7Bh%7D%20%3D%20%5Cpi%20r%5E2)
The next step is to solve for the volume of the sphere using the following formula;
![V = \frac{4}{3}\pi r^3](https://tex.z-dn.net/?f=V%20%3D%20%5Cfrac%7B4%7D%7B3%7D%5Cpi%20r%5E3)
Divide both sides by r
![\frac{V}{r} = \frac{4}{3r}\pi r^3](https://tex.z-dn.net/?f=%5Cfrac%7BV%7D%7Br%7D%20%3D%20%5Cfrac%7B4%7D%7B3r%7D%5Cpi%20r%5E3)
Expand Expression
![\frac{V}{r} = \frac{4}{3}\pi r^2](https://tex.z-dn.net/?f=%5Cfrac%7BV%7D%7Br%7D%20%3D%20%5Cfrac%7B4%7D%7B3%7D%5Cpi%20r%5E2)
Substitute ![\frac{21}{h} = \pi r^2](https://tex.z-dn.net/?f=%5Cfrac%7B21%7D%7Bh%7D%20%3D%20%5Cpi%20r%5E2)
![\frac{V}{r} = \frac{4}{3} * \frac{21}{h}](https://tex.z-dn.net/?f=%5Cfrac%7BV%7D%7Br%7D%20%3D%20%5Cfrac%7B4%7D%7B3%7D%20%2A%20%5Cfrac%7B21%7D%7Bh%7D)
![\frac{V}{r} = \frac{84}{3h}](https://tex.z-dn.net/?f=%5Cfrac%7BV%7D%7Br%7D%20%3D%20%5Cfrac%7B84%7D%7B3h%7D)
![\frac{V}{r} = \frac{28}{h}](https://tex.z-dn.net/?f=%5Cfrac%7BV%7D%7Br%7D%20%3D%20%5Cfrac%7B28%7D%7Bh%7D)
Multiply both sided by r
![r * \frac{V}{r} = \frac{28}{h} * r](https://tex.z-dn.net/?f=r%20%2A%20%5Cfrac%7BV%7D%7Br%7D%20%3D%20%5Cfrac%7B28%7D%7Bh%7D%20%2A%20r)
------ equation 1
From the question, we were given that the height of the cylinder and the sphere have equal value;
This implies that the height of the cylinder equals the diameter of the sphere. In other words
, where D represents diameter of the sphere
Recall that ![D = 2r](https://tex.z-dn.net/?f=D%20%3D%202r)
So, ![h = D = 2r](https://tex.z-dn.net/?f=h%20%3D%20D%20%3D%202r)
![h = 2r](https://tex.z-dn.net/?f=h%20%3D%202r)
Substitute 2r for h in equation 1
![V = \frac{28r}{2r}](https://tex.z-dn.net/?f=V%20%3D%20%5Cfrac%7B28r%7D%7B2r%7D)
![V = \frac{28}{2}](https://tex.z-dn.net/?f=V%20%3D%20%5Cfrac%7B28%7D%7B2%7D)
![V = 14](https://tex.z-dn.net/?f=V%20%3D%2014)
Hence, the volume of the sphere is 14m³