So, the distance between two points (x1,y1) and (x2,y2) is:
d = sqrt( (x2-x1)^2 + (y2-y)^2 )
Some times is better the square of the distance:
d^2 = (x2-x1)^2 + (y2-y)^2
Now, in your case:
5^2 = (0-2)^2 + ( -6-k)^2 = (-2)^2 + (6+k)^2 = 4 + (6+k)^2
Notice the little thing about (-6-k)^2 = (6+k)^2 (less '-') Finally:
25 = 4 + (6+k)^2 ===> (6+k)^2 = 21,
6+k = sqrt(21)
Notice we did not expand (6+k)^2! No need this time. But now, the tricky part!
6+k=+sqrt(21) and 6+k=-sqrt(21), because both work (never forget that sqrt come with +/- when looking for solutions!)
k = -6 + sqrt(21) and k=-6-sqrt(21).
Both are valid answers. Some times one is not good because you need the solution be positive (for instance), but here, both are good.
Answer:
B= 32.11
A= 52.82
C= 95.07
Step-by-step explanation:
To find these angles, since you have all sides, you will need to use the law of cosines.
28 minutes late. 15 minutes until 9 from the start of his shift. 13 minutes after 9 add those two numbers = 28 minutes
Answer:
The curve is a circle of radius 9 centered at the point (0,9) and the equation is
Step-by-step explanation:
Proceed as follows:
Take . Then
Multiply both side by . Then
Use the following substitution . Then
By cancelling out x on both sides we get the following equation
or
Recall that given a expression of the form we can complete the square by adding an substracting the amount . So, we get . In our case, we will complete the square for y, then
. Then
or
.
Recall that the equation of a circle is given by where (h,k) is the center of the circle and r is the radius. In our case we have h=0, k = 9 and r = 9. So it is a circle of radius 9 centered at the point (0,9)