I am stuck on two questions, please can you help me?
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.
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!
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
Original Area = pi × 15² = pi × 225
Larger Area = pi × 18² = pi × 324
Yay! I got the same answer as well! But I used a different formula!
But I'm still stuck on number 2.
I found out that the answer to number two to be.
But I only used Trial and Error, I need to find an equation.
Anyone able to think of one?
Yay! I found the equation but I don't know how to solve it!
________ = _____________ - 15
Can you help me solve it?
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
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 !
Thank you very much! That made it a lot less complicated