Answer:
Step-by-step explanation:
Use the half angle identity for cosine:
cos(x/2)=+ or - sqrt(1+cos(x))/sqrt(2)
I'm going to figure out the sign part first for cos(x/2)...
so x is in third quadrant which puts x between 180 and 270
if we half x, x/2 this puts us between 90 and 135 (that's the second quadrant)
cosine is negative in the second quadrant
so we know that
cos(x/2)=-sqrt(1+cos(x))/sqrt(2)
Now we need cos(x)... since we are in the third quadrant cos(x) is negative...
If you draw a reference triangle sin(x)=3/5 you should see that cos(x)=4/5 ... but again cos(x)=-4/5 since we are in the third quadrant.
So let's plug it in:
cos(x/2)=-sqrt(1+4/5)/sqrt(2)
No one likes compound fractions (mini-fractions inside bigger fractions)
Multiply top and bottom inside the square roots by 5.
cos(x/2)=-sqrt(5+4)/sqrt(10)
cos(x/2)=-sqrt(9)/sqrt(10)
cos(x/2)=-3/sqrt(10)
Rationalize the denominator
cos(x/2)=-3sqrt(10)/10
Answer:
222 = score in 2nd game
Step-by-step explanation:
Let x = score in 1st game
3/4(x) + 30 = score in 2nd game
x + 3/4(x) + 30 = 478 Multiply thru by 4 to eliminate the fraction
4x + 3x + 120 = 1912
7x + 120 = 1912
7x = 1792
x = 256
3/4(x) + 30 = 3/4(256) + 30
= 192 + 30
222 = score in 2nd game
Check: 222 + 256 = 478
Answer:
5832 ways
Step-by-step explanation:
Since the circle has 8 sectors and there is 4 colour,
Assuming the sectors are numbered 1 to 8,
Sector 1 : can be coloured with any of the 4 colour in 4 ways
Sector 2 can be coloured with any of the remaining 3 colours in 3 ways
Sector 3 in 3 ways without using the colour in sector 2
Sector 4 in 3 ways without using the colour in sector 3
Sector 5 in 3 ways without using the colour in sector 4
Sector 6 in 3 ways without using the colour in sector 5
Sector 7 in 3 ways without using the colour in sector 6
Sector 8 in 2 ways without using the colours in sector 1 and 7
Number of ways of colouring = 4*3*3*3*3*3*3*2 = 5832 ways
Answer:
APC is 90 degrees
Step-by-step explanation:
When lines intersect and are perpendicular. that means the angle of intersection is 90 degrees.
APC is 90 degrees
