Answer:
3, in both a), b)
Step-by-step explanation:
a) The slope of the line tangent to the curve that passes through the point (2,-10) is equal to the derivative of p at x=2.
Using differentiation rules (power rule and sum rule), the derivative of p(x) for any x is 
. In particular, the value we are looking for is 
.
If you would like to compute the equation of the tangent line, we can use the point-slope equation to get 
b) The instantaneus rate of change is also equal to the derivative of P at the point x=2, that is, P'(2). This is equal to 
.
We will be using the formulas:
speed=distance/time
time=distance/speed
distance=speed×time
First let's find out Diane's rate of swimming. We can measure this by finding the slope (y/x) of a given coordinate on the graph. One point is (10,15), so you do 15/10=1.5m/s
Now for Rick's rate of swimming, just take a pair of values from the table. 12.5/10=1.25m/s
By the way m/s is metres per second for this
So at a constant speed of 1.5m/s, Diane swam 150m in 150/1.5= 100 seconds, or 1 minute 40 seconds
And at a constant speed of 1.25m/s, Rick swam 150m in 150/1.25= 120 seconds, or 2 minutes.
So the difference between their two times is 20 seconds
Answer:
114
Step-by-step explanation:
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