Prime factor both numbers
9 = 3 x 3 = 3^2
15 = 3 x 5
We pick each unique factor along with its higest power.......
This gives us 3^2 and 5
Take the product of this
3^2 x 5 =
9 x 5 =
45 and this is the LCM
Let the distance betwen the two cities,in miles = D
And....Distance / Rate = Time
And let's convert the rate to miles per minute.....60 mph = 1 mile per minute......45 mph = 3/4 miles per minute
So....equating the times, we have that 11 minutes added to the faster train's time = the slower train's time.......algebraically, we have :
D / 1 + 11 = D / (3/4) simplify
D + 11 = (4/3)D subtract D from both sides
11 = (1/3)D multiply both sides by 3
33 = D
Thus....the cities are 33 miles apart
Proof....the faster train covers this distance in 33 min.......the slower train takes (4/3) as long = (4/3)*33 = 4 * 11 = 44 minutes......so......the slower train takes 11 minutes longer
If sin A = tan A ....then
sin A = sin A / cos A multiply both sides by cos A
sin A cos A = sin A divide both sides by sin A
cos A = sin A / sin A
cos A = 1
And A = 0°
I like the similar triangle approach, Omi....!!!!!
No......I'm a "mime"
1, 4, 8, 9, 75 and 100 ...... 273
4 (75) - 100 + 8*9 + 1 =
300 - 100 + 72 + 1 =
200 + 72 + 1 =
273
No....I didn't look at any of heureka's answers, either.....LOL!!!!!!
10^90 =
1,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000
Mmmmm....now....about that $10 ........!!!!!!!
Since we can orient these circles in any fashion that we would like.....let the first circle be centered at (0,3)....and the top of this circle will be at (0,7) [because its radius is 4]
Now....let the second circle also have its "top" at (x, 7), where x is the center of this circle....since the radius is 7, then this center will be on the x axis....[note that the tangent to both circles will just be a horizontal line passing through (0,3) and (x,7)
And since the center of the second circle is 13 units from the center of the first, we can solve this distance equation to find this center x coordinate
√ [ (x - 0)^2 + (3 -0)^2 ] = 13 → √ [x ^2 + 9 ] = 13 → x^2 + 9 = 169 → x^2 = 160 → x = 4√10
So.....the second circle will be centered at (4√10, 0 )
And the length of the common external tangent will just be "x" = 4√10
See the situation, here : https://www.desmos.com/calculator/kpz4qhtdgl
37,000 = 3.7 x 104
Math operations with "infinity" don't behave like "regualr" math....for instance : infinity - infinity = infinity
And a real number x infinity = infinity
