The first thing we must do in this case is find the derivatives:
y = a sin (x) + b cos (x)
y '= a cos (x) - b sin (x)
y '' = -a sin (x) - b cos (x)
Substituting the values:
(-a sin (x) - b cos (x)) + (a cos (x) - b sin (x)) - 7 (a sin (x) + b cos (x)) = sin (x)
We rewrite:
(-a sin (x) - b cos (x)) + (a cos (x) - b sin (x)) - 7 (a sin (x) + b cos (x)) = sin (x)
sin (x) * (- a-b-7a) + cos (x) * (- b + a-7b) = sin (x)
sin (x) * (- b-8a) + cos (x) * (a-8b) = sin (x)
From here we get the system:
-b-8a = 1
a-8b = 0
Whose solution is:
a = -8 / 65
b = -1 / 65
Answer:
constants a and b are:
a = -8 / 65
b = -1 / 65
Independent variable = number of cars with domain 30 to 100 cars
Dependent variable = money raised with range $600 to $2000
The line would be called the median. The definition of '<span>A line connecting a vertex of a scalene triangle with the midpoint of the opposite side' pertains to the median. There are three medians that connect the scalene triangle. </span>
<h3>Answer: Choice D</h3>
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Explanation:
The long way to do this is to multiply all the fractions out by hand, or use a calculator to make shorter work of this.
The shortest way is to simply count how many negative signs each expression has.
The rule is: if there are an even number of negative signs, then the product will be positive. Otherwise, the product is negative.
For choice A, we have 3 negative signs. The result (whatever number it is) is negative. Choice B is a similar story. Choice C is also negative because we have 1 negative sign. Choices A through C have an odd number of negative signs.
Only choice D has an even number of negative signs. The two negatives multiply to cancel to a positive. The negative is like undoing the positive. So two negatives just undo each other. This is why the multiplied version of choice D will be some positive number.
Or you can think of it as opposites. If you are looking up (positive direction) and say "do the opposite" then you must look down (negative direction). Then if you say "do the opposite", then you must look back up in the positive direction.