Error
<span>6 x = - 2 (5)
should be
</span><span>2 x = - 18 (5)
answer
</span><span>D.
Line 5</span>
Multiply the first 3 prime numbers that are 2 3 and 5 so the answer would be 30
Answer:
hope this helps you
have a great day God bless you
Answer: sqrt(2)/2 which is choice D
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Explanation
(3pi/4) radians converts to 135 degrees after multiplying by the conversion factor (180/pi).
The angle 135 degrees is in quadrant 2. We subtract the angle 135 from 180 to find the reference angle
180-135 = 45
Then you can use a 45-45-90 triangle to determine that the ratio of opposite over hypotenuse is sqrt(2)/2
sine is positive in quadrant 2
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Alternatively, you can use a unit circle. Refer to the diagram below. In red, I've circled the angle 3pi/4 radians. The terminal point for this angle has a y coordinate of sqrt(2)/2
Recall that y = sin(theta).
You can see how this works by thinking through what's going on.
In the first year the population declines by 3%. So the population at the end of the first year is the starting population (1200) minus the decline: 1200 minus 3% of 1200. 3% of 1200 is the same as .03 * 1200. So the population at the end of the first year is 1200 - .03 * 1200. That can be written as 1200 * (1 - .03), or 1200 * 0.97
What about the second year? The population starts at 1200 * 0.97. It declines by 3% again. But 3% of what??? The decline is based on the population at the beginning of the year, NOT based no the original population. So the decline in the second year is 0.03 * (1200 * 0.97). And just as in the first year, the population at the end of the second year is the population at the beginning of the second year minus the decline in the second year. So that's 1200 * 0.97 - 0.03 * (1200 * 0.97), which is equal to 1200 * 0.97 (1 - 0.03) = 1200 * 0.97 * 0.97 = 1200 * 0.972.
So there's a pattern. If you worked out the third year, you'd see that the population ends up as 1200 * 0.973, and it would keep going like that.
So the population after x years is 1200 * 0.97x
