Answer: sqrt(2)/2 which is choice D
======================================================
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
------------
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).
Answer: The interest is $60
Step-by-step explanation:
500*112%=$560
560/18=$31.11
$60 in interest is paid, or an additional $3.33 a month (Bringing the monthly loan payment to a grand total of $31.11)
<h3>Answer:</h3>
- f(1) = 2
- No. The remainder was not 0.
<h3>Explanation:</h3>
Synthetic division is quick and not difficult to learn. The number in the upper left box is the value of x you're evaluating the function for (1). The remaining numbers across the top are the coefficients of the polynomial in decreasing order by power (the way they are written in standard form). The number at lower left is the same as the number immediately above it—the leading coefficient of the polynomial.
Each number in the middle row is the product of the x-value (the number at upper left) and the number in the bottom row just to its left. The number in the bottom row is the sum of the two numbers above it.
So, the number below -4 is the product of x (1) and 1 (the leading coefficient). That 1 is added to -4 to give -3 on the bottom row. Then that is multiplied by 1 (x, at upper left) and written in the next column of the middle row. This proceeds until you run out of numbers.
The last number, at lower right, is the "remainder", also the value of f(x). Here, it is 2 (not 0) for x=1, so f(1) = 2.
