Part (a)
Use the slope formula to compute the slope from x = 4 to x = 6
So effectively we're finding the slope of the line through (4,70) and (6,68)
We get the following
m = (y2-y1)/(x2-x1)
m = (68-70)/(6-4)
m = -2/2
m = -1
Repeat for the points that correspond to x = 6 and x = 8
m = (y2-y1)/(x2-x1)
m = (73-68)/(8-6)
m = 5/2
m = 2.5
Now average the two slope values
We'll add up the results and divide by 2
(-1+2.5)/2 = 1.5/2 = 0.75
The estimate of T'(6) is 0.75
This works because T'(x) measures the slope of the tangent line on the T(x) curve. Averaging the secant slopes near x = 6 will help give us an estimate of T'(6), which is the slope of the tangent at x = 6 on T(x).
<h3>Answer: 0.75</h3>
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Part (b)
The value T'(6) = 0.75 represents the instantaneous rate of change of the temperature per hour.
More specifically, T'(6) = 0.75 means the temperature is increasing by an estimated 0.75 degrees per hour at the exact instant of x = 6 hours. This instantaneous rate of change is like a snapshot at this very moment in time; in contrast, the slope formula results we computed above measure the average rate of change between the endpoints mentioned.
Answer:
[-8, 7]
Step-by-step explanation:
The range is the set of values used for the y-coordinates of the all the points of the function.
The highest value of the function is at point (8, 7), so the greatest value y has is 7.
The lowest point of the function is at point (-3, -8), so the least value of y is -8.
Range: [-8, 7]
Answer:
270 remainder of four or 270.166666667.
Step-by-step explanation:
It is one of those
Answer:
Option A.
Step-by-step explanation:
Note: Let as consider, we have to find the total amount after 9 years.
It is given that,
Principal amount = $1000
Rate of compound (yearly) interest = 15% = 0.15
Time = 9 year
The formula for total amount is
where, P is principal, i is rate of interest and n is number of years.
Substituting P=1000, i=0.15 and n=9, we get
So, the total amount after 9 years is $3517.88.
Therefore, the correct option is A.
Answer:
my big brother had the same question so ill ask him to help u
Step-by-step explanation:
