Density = Mass of Liquid / Volume of tank
The problem here is that the liquid isn't identified.....so.....determining its mass is impossible
However...assuming that we have water.....its mass is almost exactly 1kg per L
So 8314.5 L ≈ 8314.5 kg
So.....the density is
8314.5 kg / [ 5 * 2 * 23 ] dm^3 ≈ 8314.5 kg / 230 dm^3 ≈ 36.15 kg / dm^3
The tank can hold 55692 cm^3 (1)
The volume of the log plus the volume of the water in the tank =
pi ( 5)^2 * 44 + 55692 (.95) ≈ 56363.2 cm^3 (2)
So the approximate volume that spills out = (2) - (1) ≈ 671.152 cm^3
Our answers differ probably due to rounding......but.....close enough !!!!
Population / Density = Area ....so....
186,440 / 1678 ≈ 111.1 square miles
3x-4x+7y-2 = 45 simplify
-1x + 7y - 2 = 45 add 2 to both sides
-1x + 7y = 47
This is the equation of a line.....see the graph, here :
https://www.desmos.com/calculator/awwi8jf2ej
(-5/8) / (-3/4) invert the second fraction and multiply
(-5/8) * (-4/3) =
20 / 24 =
5 / 6
The height ,H, is given by :
H = 3000*sin (15°) ≈ 776.5 m
sec (3x) = 2
This happens where cos (3x) = 1/2
So 3x = pi/3 + 2 pi *n and 3x = 5pi / 3 + 2pi*n where n is an integer
Dividing both sides by 3, we have that
x = pi/9 + (2/3)pi*n and x = 5pi/ 9 + (2/3)pi*n where n is an integer
sin (7x) = -sqrt (3) / 2
Note
sin (7x ) = -sqrt (3) / 2 when either
7x = 4 pi / 3 + 2pi*n or 7x = 5 pi/ 3 + 2pi *n where n is an integer
Dividing both by 7, then
x = 4 pi / 21 + (2pi/7)n or x = 5 pi/ 21 + (2p/7)n where n is an integer
3 cot^2(x) − 1 = 0 add 1 to both sides
3 cot^2 (x) = 1 divide both sides by 3
cot^2( x) = 1/3 take the square root of both sides
cot (x) = ±√ (1/3) =
So
cot (x) = √ (1/3) and this happens at pi/ 3 + pi* n where n is an integer
And
cot (x) = - √1/3) and this happens at -pi/3 + pi*n where n is an integer
3.5 + 2.7 + 1.9.......
The common difference is - .8
The 30th term, a30, is given by :
a30 = 3.5 - .8(29) = -19.7
And the sum is given by
[a1 + a30] * n / 2 where a1 = 3.5, a30 = -19.7 and n = 30
[ 3.5 + -19.7] * 30 / 2 = -243
