During Diwali, candles are lit all around the country in celebration. How many candles would need to be lit in a 40 x 40 meter s
quare area in order for an astronaut in the International Space Station (400 kilometers above ground) to see a spot of light which is as bright as a single candle at 100 meters?
Any answer within 10% of the correct answer is accepted. Ignore atmospheric effects for simplicity.
Any answer within 10% of the correct answer is accepted. Ignore atmospheric effects for simplicity.
1 answer:
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You can use the definition:
Then if
we have
Then the derivative is
I'm guessing the second part of the question asks you to find the tangent line to <em>f(x)</em> at the point <em>a</em> = 0. The slope of the tangent line to this point is
and when <em>a</em> = 0, we have <em>f(a)</em> = <em>f</em> (0) = -2, so the graph of <em>f(x)</em> passes through the point (0, -2).
Use the point-slope formula to get the equation of the tangent line:
<em>y</em> - (-2) = 3 (<em>x</em> - 0)
<em>y</em> + 2 = 3<em>x</em>
<em>y</em> = 3<em>x</em> - 2
Answer:
No you do not.
This is because we can use Pythagoras Theorem to show that our location sits outside the 15 mile radius of the cell tower.
To work is out you would write the equation
Then to work out the Hypotheses you would
Which proves that the location is outside of the 15 Mile radius of the cell tower.