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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 cm². 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!

MathsIsFun

Administrator

Registered: 2005-01-21

Posts: 7,711

Re: Solving Equations

1. Note: Area of a circle = pi×r²

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

pi×(r+3)² - pi×r² = pi×99

Now, let's solve it!
We can eliminate pi because it is in every term: (r+3)² - r² = 99
Expanding (r+3)²: (r+3)(r+3) - r² = 99
Becomes: r² + 2×r×3 + 3² - r² = 99

Simplifying: 2×r×3 + 3²  = 99
More: 6×r + 9  = 99
More: 6×r  = 90
More: r  = 90/6
Finally: r = 15

Let's Check:
Original Area = pi × 15² = pi × 225
Larger Area = pi × 18² = pi × 324
Yay!!

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

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.

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?

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?

MathsIsFun

Administrator

Registered: 2005-01-21

Posts: 7,711

Re: Solving Equations

You could multiply every term by 60: (v(v+20))   =  (v+10)(v+30) - 15 x 60
Expand: v² + 20v = v² + 10v + 30v + 300 - 900
Subtract v²: 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 !

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

Person

Guest

Re: Solving Equations

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