f (x) = -x^2 -6x + 3
f (x) = - [ x^2 + 6x - 3 ] take 1/2 of 6 = 3...square it = 9....add it and subtract it
f(x) = - [ x^2 + 6x + 9 - 3 - 9 ] factor the first three terms.....simplify the last two
f(x) = - [ (x + 3)^2 - 12 ] apply the negative across the terms
f(x) = -(x +3)^2 + 12 ....this is vertex form......and the vertex is (-3, 12)
The rest of the problem is the same as before....the negative out front indicates that the parabola is inverted [upside down ]
Thanks @CPhill.....can you please solve it again using the method of completing the square?
(3, -3) forms a 45 degree angle in the 4th quadrant = [315° ]
It has a length of sqrt [ 3^2 + (-3)^2 ] = sqrt (18) = 3sqrt (2)
\(\frac{\csc x\cos x}{\tan x + \cot x} \\~\\ =\frac{\frac{1}{\sin x}*\cos x}{\frac{\sin x}{\cos x} + \frac{\cos x}{\sin x}} \\~\\ =\frac{\cos x}{\sin x}*\frac{1}{\frac{\sin x}{\cos x} + \frac{\cos x}{\sin x}} \\~\\ =\frac{\cos x}{\sin x*\frac{\sin x}{\cos x} + \sin x* \frac{\cos x}{\sin x}} \\~\\ =\frac{\cos x}{\frac{\sin^2 x}{\cos x} + \cos x} \\~\\ =\frac{\cos x}{\frac{\sin^2 x}{\cos x} + \frac{\cos^2 x}{\cos x}} \\~\\ =\frac{\cos x}{\frac{\sin^2 x+\cos^2 x}{\cos x}} \\~\\ =\frac{\cos x}{\frac{1}{\cos x}} \\~\\ = \cos^2 x\)
:))
(csc(x)*cos(x)) divided by tan(x)+cot(x) =
[1/sinx) *cos(x)] / [ sinx/cosx + cosx/sinx] =
[ cot x ] / [ (sin^2 x + cos^2 x ) / sinx cosx ] =
[ cot x ] / [ 1 / sinx cosx ] =
[ cot x] [ sin x cos x ] =
[cosx / sin x ] [sin x cos x ] =
cos^2 (x)
It would be going at an angle down and right to the origin.
Hey I want to answer!
perimeter = side + side + side + side
All the sides are congruent, so
perimeter = 4(side)
The diagonals bisect each other, so the legs of the little triangles are 16/2 and 30/2.
Use pythagorean theorem to find length of one side.
82 + 152 = side2
√(289) = side
17 = side
Substitute.
perimeter = 4(17)
perimeter = 68
1L = 1000cm^3
So....150L = 150,000 cm ^3
Volume of cylinder = pi * (diameter/2)^2 *h =
150,000 = pi * (48/2)^2 * h
150,000 = pi * 24^2 * h =
150,000 = 576pi * h divide both sides by 576pi
[150,000] / [ 576pi ] = h = about 82.89 cm
3/4 min = 45 seconds......so
1/45 of this = 1 second ....so....
1/45 * 5.85 = 0.13 cm per second
Images not displaying for me....(sometimes).....
Sometimes the image shows....sometimes I get "Waiting for Moderation".......huh????
That is great :)
Learn about Pascal's triangle here :))
http://www.mathsisfun.com/pascals-triangle.html
Thanks i understand it now
oh nm
Note, Rebirth....adding the angles 4n + 7 and 4n + 5....we want to combine like terms.....so
4n + 4n + 5 + 7 =
8n + 12
Your area is correct but I do not think that your perimeter is.
You need to use pythagoras and I think that you will bet an answer wit a part of it under a square root sign.
If you round this off to the nearest whole numer it is 21 but I think you should leave it as a surd (with the square root sign)
75*.08=6 6
first where did you get 8n and 12 from?
Volume = side^3
Surface area = 6*side^2
So......take the cube root of the volume.....this will equal the side
Then......square that value and multiply by 6.......this will be the surface area......
5+5=5+5
Note that the two angles designated as 4n + 7 and 4n + 5 are straight angles.....they sum to 180
So...let's solve for n....and we have
4n + 7 + 4n + 5 = 180 simplify
8n + 12 = 180 subtract 12 from both sides
8n = 168 divide by 8 on both sides
n = 21
Now....by the Exterior Angle Theorem....m equals the sum of [ 4n + 5] + [26]
And n = 21......so....m = 4(21) + 5 + 26 = 84 + 5 + 26 = 89 + 26 = 115
So am i suppose to mutiply 21 or 89 to n to see if they equal 180 degrees?
The answer is 8. When you say the power of ___, you just need to multiply your number by that many times.
So in your example, you can solve it as
2 x 2 x 2
2 multiplied by 2 is 4
4 multiplied by 2 is 8
~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Another example can be 3 to the power of 4
3 x 3 x 3 x 3
3 multiplied by 3 is 9
9 multiplied by 3 is 27
27 multiplied by 3 is 81
im still not getting it
College?! l'm a junior in high school...
