A tank holds 3000 gallons of water, which drains from the bottom of the tank in half an hour. The values in the table show the v
1 answer:
Answer:
The slope of the secant line PQ is the following for each point:
Q Slope (a)
(5, 2097) -131.7 gal/min
(10, 1308) -105.6 gal/min
(20, 303) -95.4 gal/min
(25, 87) -69.3 gal/min
(30, 0) -52 gal/min
Step-by-step explanation:
The slope can be easily obtained by using a linear approximation for the 2 points P and Q. In this case, with the slope a:
(1)
(2)
if equations 1 and 2 are subtracted:
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Answer:
Step-by-step explanation:
The formula for the dot product of vectors is
u·v = |u||v|cosθ
where |u| and |v| are the magnitudes (lengths) of the vectors. The formula for that is the same as Pythagorean's Theorem.
which is
which is
I am assuming by looking at the above that you can determine where the numbers under the square root signs came from. It's pretty apparent.
We also need the angle, which of course has its own formula.
where uv has ITS own formula:
uv = (14 * 3) + (9 * 6) which is taking the numbers in the i positions in the first set of parenthesis and adding their product to the product of the numbers in the j positions.
uv = 96.
To get the denominator, multiply the lengths of the vectors together. Then take the inverse cosine of the whole mess:
which returns an angle measure of 30.7. Plugging that all into the dot product formula:
gives you a dot product of 96