Posts Tagged with ‘Math Answers’
Monday, September 6th, 2010
Solution:
These are the formulas used to solve triangles:
1. The sum of the internal angles equals 180o …A + B + C = 180o
2. The ‘sine rule’ …
3. The ‘cosine rule’ …
a² = b² + c² – 2bc cosA
or
b² = a² + c² – 2ac cosB
or
c² = b² + a² – 2ba cosC
In the problem that you gave us, we know the length of the three sides of the triangle:
a = 11.4
b = 13.7
c = 12.2
When no angles are known, the cosine rule is the only option, so 11.42 =13.72 +12.22 – 2*13.7*12.2*cosA….Therefore cosA = 0.617955.
You can now use a calculator or a table to find the value of A. You should get A = 0.9047 radians = 51.833 degrees = 51 degrees and 50 minutes.
Use the sine rule to find one of the remaining angles.
=
So sin(B) = = 0.944835
You can now use a calculator or a table to find the value of B. You should get B = 1.237 radians = 70.8801 degrees = 70 degrees and 53 minutes.
Finding the third angle is easy, since we know that A + B +C =180 degrees. C = 180 – 51.833 – 70.880 = 57.287 degrees = 57 degrees and 17 minutes.
Visual representation:
Monday, September 6th, 2010
Solution:
Monday, September 6th, 2010
Solution:
First let’s apply the reverse cosine function to both sides of the equation:
cos-1(cos(2x)) = cos-1 (0.32) = cos-1 ()
Now if you take the inverse cosine the cosine of 2x, you get 2x…so:
2x = cos-1 ()
2x 71.34°
x 35.67° (which is approximately the same as 0.622 radians)
This looks like it might be the final answer, but actually it’s only one of the many correct answers. One way to see this is by graphing y=cos(2x) and seeing where it intersects the line y=0.32. If you do this, you will see that the intersections occur at multiple points:
As you can see, the intersections occur at x 0.622 radians, 2.519 radians, 3.764 radians, 5.660 radians, etc. The general form of the solution set is as follows:
Saturday, September 4th, 2010
Solution:
- The formula for the volume of a sphere is
- r = 6
- =
Saturday, July 24th, 2010
Solution:
First, we can write
Then we can substitute this into the second equation you get
We can simplify this to
If multiply both sides by 25 and expand this out we get
This can be simplified to: Or
Thus the solutions for a are 6 and -4
The solutions for b can be found by the equation (b=4 when a=6, and b=-2 then a=-4)
- Another way to solve this is by looking at the equations graphically. When you plot the two equations, you can see there they intersect.
As you can see, they intersect at two places:
You can plug the answers into both equations to confirm that they are both true using these two values of a and b.
Saturday, July 24th, 2010
Solution:
1. 3x + 4y=25
2. 2x – 5y=9
We could rewrite these as follows by multiplying the first equation by 5 and the second by 4:
1. 15x + 20y = 125
2. 8x – 20y = 36
If we add the above two equations, we can eliminate y:
23x = 161
So x =3D 7, and plugging this into the first equation we can figure out
y: 21 + 4y =3D 25,
so y = 1
Saturday, July 24th, 2010
Solution:
- 2x – =y=61
- 2x + y= -7
If you subtract the second equation from the first, you can eliminate x and you are left with -4y = 68.
So y =3D -17, and plugging this into the first equation we can figure out
y: 2x = (-51)=61,
so x = 5
Friday, July 23rd, 2010
Solution:
- 2x – =y=61
- 2x + y= =7
If you subtract the second equation from the first, you can eliminate x and you are left with -4y = 68.
So y = 3D -17, and plugging this into the first equation we can figure out
y: 2x = (-51)=61,
so x = 5
Friday, July 23rd, 2010
Solution:
The expression “9/10 of 80” can be written as
This is equal to 72.