147-x=89.6
-147 -147
-x=-57.4
(sin x)/(1 + cos x) + (1+ cos x)/(sin x) = 2 csc x
The first thing that always strikes me here, Shades, is to get a common denominator on the left, and then see if something "falls out."
[ (sinx)(sinx) + (1 + cosx)(1 + cosx)] / [ sinx (1 + cosx)] =
[sin^2x + 1 + 2cosx + cos^2x] / [ sinx (1 + cosx)] =
[ (sin^2x + cos^2x) + 1 + 2cosx] / [ sinx (1 + cosx)] =
[ 1 + 1 + 2cosx ] / [ sinx ( 1 + cosx) ] =
[ 2 + 2cosx] / [ sinx ( 1 + cosx) ] =
[ 2 ( 1 + cos x)] / [ sinx (1 + cosx) ] =
2 / sinx =
2 (1/sinx) =
2 (csc x)
Thanks, heureka!!!!!....BTW .....I meant to type "you're" instead of "your"......doh !!!!!!
m = [k w^2] / [√x ]
m = [ 2k (3w)^2 ] / √[8x]
m = [2k*9w^2] / (2 √[2x] )
m = [ 18kw^2 ] / (2 √[2x] )
m = [9kw^2]/ √[2x]
m = [9/√2] [ kw^2] / √x
So.....m is increased by a factor of 9/√2
Shane....it affects all three
Look at the graphs of -2t^2 + 6t + 2 and -2t^2 + 6t + 4 here : https://www.desmos.com/calculator/wwptrmff6z
The second graph has a greater starting and max height.....the change in the constant c also shifts the t intercept to the right, in this case
So K is correct
7 / 0.14 = x x = 50
You are describing: m ~ kw^2 / sqrtx
now add the changes you described: 2 (3)^2 / sqrt 8 the value of m will change by this amount.
simplifies to 18/sqrt8 = 18/2sqrt2 = 9 /sqrt2 or 9 (sqrt2/2)
If AT is an angle bisector of BAC, then BAT = 30° and ATB = 180 - 30 - 45 = 105°
We can find AB as follows
AT/sin45 = AB/sinATB
24/sin45 = AB/sin105
AB = 24sin105/sin45
And angle ATC is supplementary to angle ATB = 180 - 105 = 75°
Likewise, angle ACT = 180 - 60 - 45 = 75° = ATC
Then...in triangle ATC.......because ACT = ATC....then AT = AC = 24
Then....the area of ABC = (1/2)(AB)(AC)sin60 =
(1/2)(24sin105/sin45)(24)sin(60) =
(288)sin(105)sqrt(2)(sqrt(3)/ 2=
(144) sin(105)(sqrt(6) = about 340.7 units^2
[ The exact result is (216 + 72√3) units^6 ]
9.647x10^7
557
forty billion
TECHNICALY IT WOULD TAKE 26 jumps to get out of the well because when it jumps it goes up 3 meters then goes back down 2 meters.3-2=1. Multiply (25 times 1)+1= 26. The last one gets it completely out of the well...
How many triplets (x,y,z) are there if xyz = 2012 and x ≤ y ≤ z?
\(\begin{array}{|c|c|c|c|c|} \hline & x & y & z & x \le y \le z\\ \hline 1 & 1 & 1 & 2012 & \surd \\ 2 & 1 & 2 & 1006 & \surd \\ 3 & 1 & 4 & 503 & \surd \\ 4 & 1 & 503 & 4 & \\ 5 & 1 & 1006 & 2 & \\ 6 & 1 & 2012 & 1 & \\ 7 & 2 & 1 & 1006 & \\ 8 & 2 & 2 & 503 & \surd \\ 9 & 2 & 503 & 2 & \\ 10 & 2 & 1006 & 1 & \\ 11 & 4 & 1 & 503 & \\ 12 & 4 & 503 & 1 & \\ 13 & 503 & 1 & 4 & \\ 14 & 503 & 2 & 2 & \\ 15 & 503 & 4 & 1 & \\ 16 & 1006 & 1 & 2 & \\ 17 & 1006 & 2 & 1 & \\ 18 & 2012 & 1 & 1 & \\ \hline \end{array}\)
It's okay CPhill !
turn 800 into a percent out of 17,986.99?
800/17,986.99 =.044766 x 100 =4.4766%
17986.99/800 = 22.4837375
Move the decimal to the right twice.
Approximately 22%
0, 1, 1, 2, 3, 5, 8, 13, 21, 42, 76, 139, 257, 472, 868, 1,597, 2,937, 5402.......etc.
After the 9th term, or 21, each subsequent term is the SUM of the previous 3 terms.
Solve for y when x = 29.5.
y=472/29.5=16
a positive times a positive is positive. A negative times a postitibe or vise versa is negative. negative times a negative is a positive
Why is 0.5 ! = (√π )/2 ?
\(\boxed{~ \begin{array}{rcll} n! &=& \Gamma(n+1) \end{array} ~}\)
\(\begin{array}{rcll} 0.5! &=& \Gamma(0.5+1) \\ \end{array}\)
\(\boxed{~ \begin{array}{rcll} \Gamma(x+1) &=& x\cdot \Gamma(x) \end{array} ~}\)
\(\begin{array}{rcll} \Gamma(0.5+1) &=& 0.5\cdot \Gamma(0.5) \end{array}\)
\(\boxed{~ \begin{array}{rcll} \Gamma(0.5) &=& \sqrt{\pi} \end{array} ~}\)
\(\begin{array}{rcll} 0.5\cdot \Gamma(0.5) &=& 0.5\cdot \sqrt{\pi}\\ &=& \dfrac{\sqrt{\pi}} {2} \\\\ \mathbf{0.5!} & \mathbf{=} & \mathbf{ \dfrac{\sqrt{\pi}} {2} } \end{array}\)
The basis of calculus began in this guy's head and this guy's head.
9.647 x 107
The minimum number of pens that she would have to draw to get 16 of one color would be 16 - she either selects 16 of the red ones on the first 16 draws or 16 of the blue ones on the first 16 draws......
The maximum number of pens that she would have to draw is given by this scenario :
She draws all of the black and white ones on the first 20 draws
She then selects 15 of one color - either the red or blue - on the next 15 draws......
Then......on the next 15 draws she selects the opposite color to the previous 15 draws .......this is 20 + 15 + 15 = 50 draws to this point
Finally.....on the next draw.....she must select either a red or a blue.......so.....51 draws....just as Alan said.....!!!!
9 sheep lived and by the average weight of a 5ft 10in male, he is 173 lbs.
