This is correct. Nice job!
Perhaps, you notice in your answer that 2115=462−1? This is no coincidence.
Instead of letting f(0)=0, we let f(0)=1
And it follows that ∑99i=0f(i)=(1+1+2+3+⋯+9)2=462
Subtracting f(0), we have
462−f(0)=462−1=2116−1=2115
XZ = sqrt(28^2 - 24^2) = 4 sqrt 13
tan y = 4 sqrt 13 / 24 = sqrt 13 / 6
62 + ... + 162
2(31 + ... + 81)
2((1 + ... + 51) + 51 * 30)
2(1 + ... + 51) + 3060
51*52 + 3060
5712
x*xsqrt3*1/2 = 2x*3*1/2
x^2 sqrt3 = 6x
xsqrt3=6
x=2sqrt3
(1) we have the altitude = 20 so 20*30*1/2 = 300
(2) 13/2 = 6.5
note 1/a + 1/b = (a+b)/ab
a+b = 11/5
ab = 4/5
(11/5)/(4/5) = 11/4
Note that Vieta's can be generalized for degree $n.$ Try finding a formula.
ax2+bx+c=a(x−r1)(x−r2)ax2+bx+c=a(x2+x(−r1−r2)+r1r2)ax2+bx+c=a⋅x2+a⋅x(−r1−r2)+a⋅r1r2a(−r1−r2)=b(−1)(a)(r1+r2)=br1+r2=−baa⋅r1r2=cr1r2=ca
Hi Mobius,
You are correct. There is a second answer to the question, but does it fit in the range?
Best,
MPS
$\sec(x) = \frac{1}{\cos(x)}$
tan2(x)=(sinxcosx)2=sin2xcos2x=sin2xcos2x+cos2xcos2x−1=sin2x+cos2xcos2x−1=1cos2x−1
$\frac{5}{\cos(x)} = \frac{3}{\cos^2 x} - 2$
$5 \cos(x) = 3 - 2 \cos^2 x$
$2 \cos^2 x + 5 \cos x - 3 = 0$
$(\cos x + 3) (2 \cos x - 1) = 0$
$\cos x = -3$
$\cos x = \frac{1}{2}$
I think you can take it from here.