need help with a few problems

jigbobber · 2008-08-26 21:11:47

1.The height of a child t years after birth is given by the formula

a) Find an expression for the rate at which the child grows.
b)show that

and state the significance of the result.

2.solve

3.

a)show that

b)Show that the total area of the can be expressed by the formula
c)Find the value of when the area is a maximum

thanks if you can help

Last edited by jigbobber (2008-08-27 01:50:43)

jigbobber · 2008-08-27 12:30:39

can anyone help?

gnitsuk · 2008-08-27 22:40:17

1)

a)

We have:

therefore the rate at which the child grows is given by:

b)

(t+8)^2 is always positive (it matters not if t+8 is +'ve or -'ve because we square it)

and so H'(t) will always be +'ve.

So the rate of growth of a child is always +'ve - i.e. the child never looses height, they always get taller.

Futher we can see the as t -> infinity so the rate of growth -> zero so as we get older we grow less rapidly.

gnitsuk · 2008-08-28 02:50:12

2)

Solve

Lets gather all terms on the LHS be subtracting RHS from both sides to give:

Call this equation (1) and let the LHS be called f(x)

Solving this is most easily done by factorising this expression. We can see simply by tring it that x = 1 is a root of the LHS so (x-1) must be a factor, so let's do the long division:

so (1) is equivilent to:

Again, it is easy to see that x = 1 is a root of the cubic and so (x-1) is yet again a factor:

So now we have reduced the problem to:

Again we easily spot a root of the quadratic, x = -2, and so (x+2) is a factor:

And we can see easily that:

so, we have reduced are problem to:

So, f(x) is zero at x = -2, x = 1 and x = 3

To check which way the curve is bending we check its value anywhere but at the zeros, so at x = 0 f(x) = -6, so now we can easily see that:

You can see the correctness of the result here:
Plot of x^4+11x vs 3*(x^3+x^2+2)

Last edited by gnitsuk (2008-08-28 02:53:58)

jigbobber · 2008-08-29 04:58:59

thanks for the help and also explaining clearly, really has helped.

anyone know how to do question 3?

jigbobber · 2008-08-30 02:11:16

anyone know how to do question 3 ,really need some help on it

G_Einstein · 2008-08-31 00:13:34

Here is the solution about the BC=x/2^(1/2)

From B make a line down from b to the segment CF,and the point that touch CF name it A.
CF=DE=x so CA=1/2*x

From C make a vertical line,and from B a horizontal line,and the point that begins to both of segments name it H,and you 'll have a square (HBCA).
Now:
CA=BA=x/2
BC^2=CA^2+BA^2
BC^2=x^2/4+x^2/4
BC^2=2x^2/4
BC^2=x^2/2
BC=squarerrot(x^2/2)
BC=x/squareroot(2)

G_Einstein · 2008-08-31 00:27:36

Here is the solution for the Area:

First let us split the "figure"into to figures.
The first (A1) is the triangle and the second(A2) the rectangle.

Now we'll work first with A1(A=area)

We had that BC=x/squareroot(2)
CF=x
From Pithgora's theorem we have:

BF^2=x^2-(x/squareroot(2))^2
BF^2=x^2-x^2/2
BF^2=x^2/2

BF=x/squareroot(2)

The area of the triangle FBC is A1=(BF*BC)/2
A1=(x/squareroot(2)*x/squareroot(2))/2
A1=(x^2/2)/2

A1=x^2/4

Now the area of the rectAngle is :
A2=FE*DE
A2=(10-x)x

A2=10x-x^2

Now the total area is:
A=A2+A1
A=10x-x^2+x^2/4
A=10x-(x^2-x^2/4)
A=10x-((4x^2-x^2)/4)

A=10x-(3x^2/4)
And this is the solution

G_Einstein · 2008-08-31 04:33:25

Last edited by G_Einstein (2008-08-31 04:44:02)

G_Einstein · 2008-08-31 04:34:35

G_Einstein · 2008-08-31 04:36:02

Last edited by G_Einstein (2008-08-31 04:36:42)

G_Einstein · 2008-08-31 04:44:27

Last edited by G_Einstein (2008-08-31 04:44:46)

jigbobber · 2008-08-31 14:14:43

thank you very much einstein

G_Einstein · 2008-08-31 21:25:07

I think that x must be

because x msut be postive,and the side of the rectangle can't be 0 or negative so

Last edited by G_Einstein (2008-08-31 21:34:12)

G_Einstein · 2008-08-31 21:33:27

But you can try values from 0.000000001 to 9.99999,or to do this:

and the result of this limit is 25.
So x->10,or x=9.9999999999999999999...
I'm not sure if this is the correct solution because I didn't learn yet this kind of examples,but you can ask also someone else if you want.
Did you understand how to procede to get the result of the question 3??????
:D

Last edited by G_Einstein (2008-08-31 21:41:16)

Math Is Fun Forum

#1 2008-08-26 21:11:47

need help with a few problems

#2 2008-08-27 12:30:39

Re: need help with a few problems

#3 2008-08-27 22:40:17

Re: need help with a few problems

#4 2008-08-28 02:50:12

Re: need help with a few problems

#5 2008-08-29 04:58:59

Re: need help with a few problems

#6 2008-08-30 02:11:16

Re: need help with a few problems

#7 2008-08-31 00:13:34

Re: need help with a few problems

#8 2008-08-31 00:27:36

Re: need help with a few problems

#9 2008-08-31 04:33:25

Re: need help with a few problems

#10 2008-08-31 04:34:35

Re: need help with a few problems

#11 2008-08-31 04:36:02

Re: need help with a few problems

#12 2008-08-31 04:44:27

Re: need help with a few problems

#13 2008-08-31 14:14:43

Re: need help with a few problems

#14 2008-08-31 21:25:07

Re: need help with a few problems

#15 2008-08-31 21:33:27

Re: need help with a few problems

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