If a gardener make $60 a day working and has to pay $15 for each day that he does not show up and he only works a total of 20 da
1 answer:
Answer:
14 days
Step-by-step explanation:
Amount earned by gardener for each day worked = $60
Amount paid by gardener for each day when absent = $15
Total number of days = 20
Let the total number of days when the gardener was working = x
Then he was absent for (20 - x) days.
Total amount earned during this period = $750
Then,
=>
=> \[75x = 1050\]
=> x = 14
So the gardener worked for 14 days out of 20.
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Answer:
Step-by-step explanation:
This is a related rates problem from calculus using implicit differentiation. The main equation is Pythagorean's Theorem. Basically, what we are looking for is when y = 6 and
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The equation for Pythagorean's Theorem is
where x and y are the legs and c is the hypotenuse. The length of the hypotenuse is 10, so when we find the derivative of this function with respect to time, and using implicit differentiation, we get:
and divide everything by 2 to simplify:
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Since we are looking for , that can be our only unknown and everything else has to have a value. So what do we know?
If we construct a right triangle with 10 as the hypotenuse and use 6 for y, we can solve for x (which is the only unknown we have, actually). Using Pythagorean's Theorem to solve for x:
and
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x = 8.
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Remember the derivative is
so
and
and
so