Step-by-step explanation:
answer is in the picture above
9514 1404 393
Answer:
see attached
Step-by-step explanation:
One way to approximate the derivative at a point is by finding the slope of the secant line between points on either side. That is what is done in the attached spreadsheet.
f'(0.1) ≈ (f(0.2) -f(0.0))/(0.2 -0.0) = -5 . . . for example
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Another way to approximate the derivative is to write a polynomial function that goes through the points (all, or some subset around the point of interest), and use the derivative of that polynomial function.
These points are reasonably approximated by a cubic polynomial. The derivative of that polynomial at the points of interest is given in the table in the second attachment. (f1 is a rounding of the derivative function f')
Answer:
A) 0.106
Step-by-step explanation:
8e^3x + 4 = 15
Subtract 4 from each side
8e^3x + 4-4 = 15-4
8e^3x = 11
Divide each side by 8
8/8e^3x = 11/8
e^(3x) = 11/8
Take the natural log of each side
ln(e^(3x)) = ln(11/8)
3x = ln(11/8)
Divide by 3
3x/3 = 1/3 ln(11/8)
x = 1/3 ln(11/8)
x =.106151244
To the nearest thousandth
x = .106
Answer:
16 ft³
Step-by-step explanation:
Volume of 1 cube = 1/3 x 1/3 x 1/3 = 1/27 ft³
Volume of 432 cubes = 432 x 1/27 = 16 ft³
Answer:
There are 60840 unique PINS if letters can be repeated but digits cannot be repeated
Step-by-step explanation:
In total, there are 26 letters and 10 digits.
The PIN has the following format:
L - L - N - N
The letters can be repeated, so for both letters, there are 26 options.
The digits cannot be repeated. So for the first digits there are 10 options. For the second there are 9, since the first digit used cannot be repeated.
In total:
26 - 26 - 10 - 9
26*26*10*9 = 60840
There are 60840 unique PINS if letters can be repeated but digits cannot be repeated
