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Guest:
Ball falls down from 20 m height. It's height differences are h=-4,9t^2+20 I need to build a graph. From where do I start?

H is height and T is time
so should I do this?
t 1 2 3 4
h -4,9*1^2+20 to build a graph?

GuestOct 20, 2013

+118725

Firstly my last entry had an omission in it that added to your confusion.
I have now added it in red. I have also changed +-2pi*k to just +2pi*k because since k can be a positive or a negative integer the - was not necessary.
Sorry about the confusion.

You had
theta = +-pi/6 + pi*n
I had
theta = +-pi/6 + 2pi*k OR (pi+-pi/6) + 2pi*k

These are both the same. I just seperated them because they would give different answers for cos.

Your logic is fine. You simply didn't think about cos(5pi/6)=cos(-5pi/6)= -1/root3
Hence you missed the second solution.

Now for some English terms
Even numbers are 2,4,6,...
Odd numbers are 1,3,5,.....

An even function is a function which is symmetrical about the y axis. (The axis of symmetry is x=0)
Hence f(-x) = f(x)
For example y=cos x OR y=x ²

An odd function is a function where f(-x) = - f(x)
For example y=sin x OR y=x ³
Odd functions are said to have point symmetry because if you rotate the the function 180 degrees about the origin (0,0) then it sits back over itself. I hope that makes sense to you.

You taught me a new word too. I had to look up what homogeneous equations were. I don't know where the word homogeneous comes from, I guess it refers to the fact that they all end up the same ratio, that is tan.

MelodyOct 20, 2013

+118725

http://www.mymathforum.com/

I'm sorry but I don't know the answer to this question.
I would like to suggest that you post this question in a more advanced forum.
the link above is one such forum.
It has high school questions but it also has uni questions.
The questions are divided up into different sections
Try to find the most appropriate section in order to maximize your chances of a good answer.

If you get an answer I would be interested in seeing it.

MelodyOct 20, 2013

+118725

What is the fifth root of .00032?

The 5th root is a power of one fifth
0.00032 ^ (1/5) =

MelodyOct 20, 2013

+118725

f(x) = sin ² (x)* cos(x)

Are you familiar with the product rule?
the product rule says that if
y = uv
then y' = uv' + vu'

let
u = sin ² (x) = (sin x) ²
u' = 2* sin x * cos x (I have used composite function rule or chain rule to get this derivative)

v = cos x
v' = -sin x

so
y' = [ (sin x) ²]*[-sin x] + [cos x ] * [2* sin x * cos x]

y' = -(sin x) ³ + 2 *sin x * (cos x) ²

y' = 2 *sin x * (cos x) ² -(sin x) ³

y' = 2*sin x*cos ²x - sin ³x

Do you understand what I have done?

MelodyOct 20, 2013

+118725

If it was a rectangular prism the volume would be
V=l*b*h
V= 48*8 = 384 cm ³

But this is a pyramid not a prism.
The volume of a pyramid is 1/3 the volume of the corresponding prism
so

V = 1/3 * 384 cm ³

V = 128 cm ³

MelodyOct 20, 2013

+118725

Google translation (original was in Indonesian)

area bounded by the following curves rotated around the X axis rotating objects specified volume occurs.
y = x ²-4x +4, X axis and Y axis

My translation
Find the volume of revolution when the area bounded by y = x ²-4x +4, the x axis and the y axis is rotated about the x axis.

This is a concave up parabola, the vertex is at (2,0)
I think now it would be easier to do it in an attachment.

Ini adalah cekung up parabola, verteks di (2,0)
Saya pikir sekarang akan lebih mudah untuk melakukannya dalam lampiran.

I hope this helps Florin
Saya harap ini membantu Florin

Volume of revolution.jpg

MelodyOct 20, 2013

+118725

e is just an irrational number with special properies, a bit like pi.

to get an approximate value for e on my calculator (casio) I would press

shift e ^x 1 =

It is approx equal to 2.718281828

This is an approximation because e is irrational and therefore cannot be written exactly.

I hope this helps.

MelodyOct 20, 2013

+118725

-(1/3)(-6y)(3x)(-3)(-1)=

Well, if you are multiplying 2 numbers together
If both numbers have the same sign, both positive, or both negative, then the sign of the answer will be positive
If one of the numbers is positive and the other is negative, then the sign of the answer will be negative.

From this you should be able to work out if the answer is positive or negative

now it is just
(sign that you have worked out) 1/3 *6 * 3 * 3 * 1

1/3 of 6 is 2
Can you do the rest?

MelodyOct 20, 2013

+118725

9x^2-16x-8
I assume you want this factorised.
To do this you need to find 2 numbers that add to -16 and multiply to (9*-8)
no such numbers exist

So it cannot be factorised with rational numbers.

MelodyOct 20, 2013

+118725

There is no solution to this problem

If you want to prove this, let the two numbers be x and y.

x + y = 3 so y=3-x
and
x*y=40
so
x(3-x)=40

Expand the left side, then take it all to one side and put = 0
When you use the quadratic formula to solve you will find that there are no solutions.

MelodyOct 20, 2013

+118725

hi Is 1 1/4% greater than 0.125

1 1/4 = 1.25

1.25% = 1.25 / 100 = 0.0125

Do you know which is bigger? 0.125 or 0.0125 ?

MelodyOct 20, 2013

+118725

Calculus is a clever way to deal with instantaneous rates of change. It doesn't matter what the rate is measuring the techniques are really the same.
I would expect you to gain a similar degree of understanding.

MelodyOct 20, 2013

+3146

[input]1/5 + 5x= 7x -18[/input]

1/5 + 5x= 7x -18
subtract (7x -18) on both sides
1/5 + 5x-(7x -18) = ( 7x -18)-( 7x -18)
1/5 + 5x-7x +18 = 0
1/5 -2x+18 = 0
1/5 +18-2x = 0
18.2-2x = 0
add 2x on both sides
18.2-2x+2x = 2x
18.2 = 2x
divide both sides by 2
2x/2 = 18.2/2
x = 9.1

adminOct 20, 2013

Oct 19, 2013

+259

m - 4 < -3 => m < -3 + 4 => m < 1

scrutinizerOct 19, 2013

It is a diamond to reply the answer to an oganized way...... right to left equal up and bottom...

GuestOct 19, 2013

+259

20 min = 1/3 hour, and the speed is 1/2 : 1/3 = 3/2 miles per hour

scrutinizerOct 19, 2013

+259

My regret, this might be really awkward to face a threat of the tasks like this one. Is it common practice of the modern education?

scrutinizerOct 19, 2013

+259

Absolutely. 5x^2+28x-12=0, D = 14^2 + 60 = 256, x = (-14 +-16)/5 => x1 = 2/5, x2 = -6. Factorizing gives us (x - 2/5)*(x + 6) = 0

scrutinizerOct 19, 2013

+259

0.2 I suppose

scrutinizerOct 19, 2013

+3146

[input]diff( sin(x)^2*cos(x), x)[/input]

adminOct 19, 2013

+259

Frankly, it mudded waters completely. L'Hopital rule is used when indeterminacy occurs in order to evaluate it. I guess that expression is a part of the task. Could you present the whole of it?

scrutinizerOct 19, 2013

+118725

Khadar's answer is good but I suspect that you need a surd answer.

4root3 * 6root6
=4*6*root3*root6
=24root18
=24root(9*2)
=24*root9*root2
=24*3*root2
=72root2 inches square

MelodyOct 19, 2013

+118725

Which bit is 3^x-3 ?

Do you still need help or is it all sorted now?

MelodyOct 19, 2013

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