Answer:
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Answer:
The answer would have came out of 3.84615384615
Then round up the answer to 3.85. So the unit price is $3.85
Yes it is possible for a geometric sequence to not outgrow an arithmetic one, but only if the common ratio r is restricted by this inequality: 0 < r < 1
Consider the arithmetic sequence an = 9 + 2(n-1). We start at 9 and increment (or increase) by 2 each time. This goes on forever to generate the successive terms.
In the geometric sequence an = 4*(0.5)^(n-1), we start at 4 and multiply each term by 0.5, so the next term would be 2, then after that would be 1, etc. This sequence steadily gets closer to 0 but never actually gets there. We can say that this is a strictly decreasing sequence.
If your teacher insists that the geometric sequence must be strictly increasing, then at some point the geometric sequence will overtake the arithmetic one. This is due to the nature that exponential growth functions grow faster compared to linear functions with positive slope.
Looking at this problem in the book, I'm guessing that you've been
introduced to a little bit of trigonometry. Or at least you've seen the
definitions of the trig functions of angles.
Do you remember the definition of either the sine or the cosine of an angle ?
In a right triangle, the sine of an acute angle is (opposite side) / (hypotenuse),
and the cosine of an acute angle is (adjacent side) / (hypotenuse).
Maybe you could use one of these to solve this problem, but first you'd need to
make sure that this is a right triangle.
Let's see . . . all three angles in any triangle always add up to 180 degrees.
We know two of the angles in this triangle ... 39 and 51 degrees.
How many degrees are left over for the third angle ?
180 - (39 + 51) = 180 - (90) = 90 degrees for the third angle.
It's a right triangle ! yay ! We can use sine or cosine if we want to.
Let's use the 51° angle.
The cosine of any angle is (adjacent side) / (hypotenuse) .
'BC' is the side adjacent to the 51° angle in the picture,
and the hypotenuse is 27 .
cosine(51°) = (side BC) / 27
Multiply each side of that equation by 27 :
Side-BC = (27) times cosine(51°)
Look up the cosine of 51° in a book or on your calculator.
Cosine(51°) = 0.62932 (rounded)
<u>Side BC</u> = (27) x (0.62932) = <u>16.992</u> (rounded)
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You could just as easily have used the sine of 39° .
That would be (opposite side) / (hypotenuse) ... also (side-BC) / 27 .
