A man walks 5 feet, turns 20 degrees and then walks another 10 feet. How far is the man from where he started? Round your answer
1 answer:
Answer:
About 14.8 ft
Step-by-step explanation:
This is a triangle. A man walks one direction, turns, and walks another direction. The question asks for you to find the distance, which is the hypotenuse side. This makes our triangle (see attachment 1)
Since this is not a right triangle, we will use law of cosines.
We are given 2 sides and an angle. However, 20 degrees is the exterior angle. To find the interior angle (green theta), we have to do a calculation:
180-20=160 degrees. This is green theta.
Now, we have all we need to use law of cosines. (see attachment 2)
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Answer:
a
f'(t) is negative
b
The unit is degC/min
c
At <u>35</u> minutes after the coffee was put on the counter, its temperature is <u>68</u> and will <u>decrease</u> by about <u>0.75</u> in the next 30 seconds.
Step-by-step explanation:
From the question we are told we are told that
The equation for the temperature of a cup of coffee place on a counter is
Here t is the time in minutes the coffee was put on the counter
Generally f(t)' is the derivative of f(t) at it represents the change of the temperature of the cup of coffee with respect to time
Generally for the coffee placed on the counter after a couple of minutes the temperature will decrease hence f(t)' is negative
Generally the unit of the temperature is in degrees Celsius while that of time is in minutes
So the change in temperature with time f(35)' will be in degrees Celsius/minutes (i.e degC/min)
From the question we are told that
i.e the rate of change of temperature after 35 minutes is 1.5
and
i.e the temperature of the cup of coffee after 35 minutes is 67 degC
Now after another t= 30 seconds = the rate of change of the temperature of the cup of coffee is
=>
=>
So
At <u>35</u> minutes after the coffee was put on the counter, its temperature is <u>68</u> and will <u>decrease</u> by about <u>0.75</u> in the next 30 seconds.