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#1 2005-09-23 06:32:25

Person
Guest

Solving Equations

I am stuck on two questions, please can you help me?

1.

If the radius of a circle is increased by 3cm the area is increased by 99*pi cm. Find the radius of the original circle.

2.

An approximate formula for the stopping distances when travelling in a car is given by

d = (v(v+20))/60

d=distance in metres
v=speed in m.p.h.

If a driver increases his speed by 10 m.p.h. it takes him 15 metres extra to stop. What is his initial speed.

Thanks in advance for helping! smile

#2 2005-09-23 07:44:00

MathsIsFun
Administrator

Offline

Re: Solving Equations

1. Note: Area of a circle = pir

Let's write it down as a formula, with "r" standing for the original radius:

pi(r+3) - pir = pi99

Now, let's solve it!
We can eliminate pi because it is in every term: (r+3) - r = 99
Expanding (r+3): (r+3)(r+3) - r = 99
Becomes: r + 2r3 + 3 - r = 99

Simplifying: 2r3 + 3  = 99
More: 6r + 9  = 99
More: 6r  = 90
More: r  = 90/6
Finally: r = 15

Let's Check:
Original Area = pi 15 = pi 225
Larger Area = pi 18 = pi 324
Yay!!


"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

#3 2005-09-23 15:58:41

Person
Guest

Re: Solving Equations

Yay! I got the same answer as well! But I used a different formula!

But I'm still stuck on number 2. sad

#4 2005-09-23 16:17:32

Person
Guest

Re: Solving Equations

I found out that the answer to number two to be.

v=30

But I only used Trial and Error, I need to find an equation.

Anyone able to think of one?

#5 2005-09-23 16:43:15

Person
Guest

Re: Solving Equations

Yay! I found the equation but I don't know how to solve it!

(v(v+20))       (v+10)(v+30)
________ =  _____________   - 15

     60                   60

Can you help me solve it?

#6 2005-09-23 17:30:09

MathsIsFun
Administrator

Offline

Re: Solving Equations

You could multiply every term by 60: (v(v+20))   =  (v+10)(v+30) - 15 x 60
Expand: v + 20v = v + 10v + 30v + 300 - 900
Subtract v: 20v = 40v - 600
divide by 20: v = 2v - 30
Subtract 2v: -v = -30
Therefore v = 30

Let's check:

At 45: d = (v(v+20))/60 = 30 x 50 / 60 = 25
At 55: d = (v(v+20))/60 = 40 x 60 / 60 = 40

Looks Good !


"The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  - Leon M. Lederman

#7 2005-09-24 00:40:15

Person
Guest

Re: Solving Equations

Thank you very much! That made it a lot less complicated

smile

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