Answer:
1) 270 degrees
2) pi/4 rad
Step-by-step explanation:
1.) For which value of theta is sine theta = negative 1?
Given
sintheta = -1
theta = arcsin(-1)
theta = -90degrees
Since sin is negative in the third and 4th quadrant
In the third quadrant, theta = 180 + 90 = 270degrees
In the fourth quadrant, theta = 360 - 90 = 270 degrees
Hence the required value of theta is 270degrees
2) Given the radius of the circle to be 1, the y axis value will also be 1 units
Opposite = 1
adjacent = 1
hyp = √1²+1²
hyp = √2
sin theta = opp/hyp
sin theta = 1/√2
theta = arccsin(1/√2)
theta = 45 degrees
Express in radians
45 degrees = pi/4 radians
Hence the required angle in the first quadrant is pi/4 rad
This is the concept of applications of linear equations; suppose you need x number of type A and y number of type be to make the profits required;
Total number of printers will be:
x+y=120....i
Total amount made will be:
24x+18y=2340....ii
thus solving equations i and ii by substitution we shall have:
x+y=120
x=120-y
thus substituting the above in equation ii we get:
24(120-y)+18y=2340
2880-24y+18y=2340
putting like terms together we get
-24y+18y=2340-2880
540=6y
thus
y=540/2
y=90
hence;
x=120-90=30
Therefore to make the profit of $2340 you must sale 90 type A printers and 30 type B printers
9514 1404 393
Answer:
see attached for the drawing
slope = -1/2
Step-by-step explanation:
For the rise of -1 and the run of 2, the slope is ...
m = rise/run = -1/2 . . . . slope in simplest form
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<em>Additional comments</em>
It usually works best if you can identify points on the graph where the line crosses grid intersections. Then the number of squares in each direction can be counted easily. If you work with two grid intersections that are closest together, then the ratio of rise to run will already be in reduced form.
On this graph, there are other grid crossing points that are 4, 6, 8 units to the right or left of the one where we started. You need to remember that "run" is positive in the "right" direction, and "rise" is positive in the "up" direction.
We have shown the "rise" and "run" lines above the graphed line. They can also be shown below the graphed line.
Here, the grid squares are 1 unit in each direction. You need to pay attention to the scale, because some graphs have different numbering vertically than horizontally. The values for "rise" and "run" need to be figured using the appropriate scale.
To solve the equation, we can first take 17.1 to the right hand side, changing the minus to addition :
1/6x -17.1 = 18
1/6x = -18+17.1
1/6x = -0.9
To take away the fraction, we multiply both sides by 6 so that 1/6 can be taken away to solve the equation:
1/6x = -0.9
1/6x x 6 = -0.9 x 6
6/6x = -3.6
x = -3.6
We can also turn the decimal number into fraction to solve the equation in fraction:
-0.9
= -0.9 x 1/10
= -9/10
To solve the equation:
1/6x = -9/10
x = -9/10 x 6
x = -36/10
x = -18/5
x= -3 3/5
Therefore, x = -3.6 or -3 3/5.
Hope it helps!
