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**Person****Guest**

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: 7,552

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!!

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

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**Person****Guest**

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

But I'm still stuck on number 2.

**Person****Guest**

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**

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: 7,552

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 !

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

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**Person****Guest**

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

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