What is the measure of the angle in standard position?

Step-by-step explanation:

What's inside the set of parenthesis is a description of the angle in terms of cos and sin.  This says that the angle has a cos of square root of 3 over 2, and a sin of negative 1 over 2.  

The cos of this angle is the line directly horizontal ON the x axis, since cos is the same as x.

The sin of this angle is the line that would be there if you dropped an altitude from the arrow on the x line to the arrow on the other line.

The tangent ratio, being side opposite over side adjacent will give us the angle we need.  Use the inverse tangent and enter in those values and you'll get that the angle is -30.  

OR

even easier than that, look at your unit circle to see where there is a cos, sin combination of those values.  It will be located at -30 degrees, which is also 330 degrees.

linearly: 8560 bacteria

exponentially: approximately 75233 bacteria

step-by-step explanation:

assuming it is not exponential (we would have some really complicated logarithms), let's say it is linear. then, after 5 hours, it increased by 1200 bacteria, so every hour it increases by 240 bacteria. this means that after 19 hours, we get 19 * 240 + 4000 bacteria or 3800 + 760 + 4000 = 7800 + 760 = 8560 bacteria.

because it says round your answer, i will do this exponentially (with a calculator, of course). first, we need to find how much it multiplies by every hour, by taking the 5th root of 52/40 or 13/10. this is approximately 0.167. we still need to add 1 to this, because we are multiplying by that number, not adding that amount of the number. now, we just calculate 4000 * (1.167)^19. use a calculator to get approximately 75232.6, or 75233.

step-by-step explanation: