In trigonometry, we start from the point (1,0), so this is the 0-degree point. Then, we start rotating counter clockwise along the unit circle.
Note that rotating 180 or -180 degrees is actually the same, because you travel half the circumference clockwise or counter clockwise. In both cases, you start from the rightmost point of the circle, (1,0), and arrive at the leftmost point, (-1,0).
Now, for every point (x,y) on the unit circle, given by a certain angle 
, we have
So, in this case, the angle of -180 is associated with the point (-1,0), and thus we have
Answer:
$200 : $150
Step-by-step explanation:
Sum the parts of the ratio, 4 + 3 = 7 parts
Divide the total by 7 to find the value of one part of the ratio.
$350 ÷ 7 = $50 ← value of 1 part of the ratio
4 parts = 4 × $50 = $200
3 parts = 3 × $50 = $150
Answer:
Step-by-step explanation:
Given: 
Initial value: y(1)=6
Let 
Variable separable
Integrate both sides
Initial condition, y(1)=6
Put C into equation
Solution:
or
Hence, The solution is or
The percent that is 33 is (33/88)*100 = 37.5%
Answer:
- <em>0.75</em><em> liters of 5% hydrochloric acid solution </em>
- <em>0.25</em><em> liters of 45% hydrochloric acid solution.</em>
Step-by-step explanation:
Let us assume that, x liters of the 5% hydrochloric acid and y liters of the 45% hydrochloric acid solutions are combined.
As Rajan need total of 1 liter of solution, so
i.e 
--------------------1
As Rajan needs 5% hydrochloric acid and 45% hydrochloric acid to make a 1 liter batch of 15% hydrochloric acid, hence acid content of the mixture of two acids will be same as of the final one, so
i.e 
-------------2
Putting value of x from equation 1 in equation 2,
Putting the value of y in equation 1,
Therefore, Rajan must use 0.75 liters of 5% hydrochloric acid solution and 0.25 liters of 45% hydrochloric acid solution.
