Answer:
120°; 240°
Step-by-step explanation:
Let's first solve for
:
At this point it's just a matter of drawing a circle, and mark where the angle is(please excuse my paint skills, but free hand drawing would be even worse). Red line, is
on the cosines, and both the green and blue lines are valid solutions. The green line is a quarter of a circle, plus 30°, or 120°. The blue one is 3/4 of a circle, minus 30 degrees, or 240°.
y>3x+6
y>4/3x-5 <- (The sign is greater than or equal to btw)
Let x = the amount of time that the third person needs to work on the job to add up to one
1 = 1/2 + 1/3 + x
1 - 1/2 - 1/3 = x
To subtract the fractions we need to put them all over a common denominator. Let's use 3*2 = 6 as the denominator; so 1 = 6/6, 1/2 = 3/6, 1/3 = 2/6:
6/6 - 3/6 - 2/6 = x
1/6 = x
The third person must work 1/6 time on the project.
We will use demonstration of recurrences<span>1) for n=1, 10= 5*1(1+1)=5*2=10, it is just
2) assume that the equation </span>10 + 30 + 60 + ... + 10n = 5n(n + 1) is true, <span>for all positive integers n>=1
</span>3) let's show that the equation<span> is also true for n+1, n>=1
</span><span>10 + 30 + 60 + ... + 10(n+1) = 5(n+1)(n + 2)
</span>let be N=n+1, N is integer because of n+1, so we have
<span>10 + 30 + 60 + ... + 10N = 5N(N+1), it is true according 2)
</span>so the equation<span> is also true for n+1,
</span>finally, 10 + 30 + 60 + ... + 10n = 5n(n + 1) is always true for all positive integers n.
<span>
</span>