......................................3 yards?
Answer:
the first equation
Step-by-step explanation:
22.5/(x-6) + 22.5/(x+6) = 9
multiply by x-6
=> (x-6)22.5/(x-6) + (x-6)22.5/(x+6) = 9(x-6)
=> 22.5 + (x-6)22.5/(x+6) = 9(x-6)
multiply by x+6
=> (x+6)22.5 + (x+6)(x-6)22.5/(x+6) = 9(x-6)(x+6)
=> (x+6)22.5 + (x-6)22.5 = 9(x-6)(x+6)
distribute
=> 22.5x+6(22.5) + 22.5x - 6(22.5) = 9(x^2 - 36)
=> 45x = 9x^2 - 9(36)
=> 0 = 9x^2 - 45x - 9(36)
divide by 9
=> 0 = x^2 - 5x - 36
=> 0 = x^2 - 5x - 36
=> 0 = (x - 9)(x + 4)
x=9 and -4
Answer:
Step-by-step explanation:
Given the expression cosec (x) = 4 and tan(x)< 0
since cosec x = 1/sinx
1/sinx = 4
sinx = 1/4
From SOH, CAH TOA
sinθ = opposite/hypotenuse
from sinx = 1/4
opposite = 1 and hypotenuse = 4
to get the adjacent, we will use the Pythagoras theorem
adj² = 4²-1²
adj² = 16-1
adj ²= 15
adj = √15
cosx = adj/hyp = √15/4
tanx = opposite/adjacent = 1/√15
since tan < 0, then tanx = -1/√15
From double angle formula;
sin2x = 2sinxcosx
sin2x = 2(1/4)(√15/4)
sin2x = 2√15/16
sin2x = √15/8
for cos2x;
cos2x = 1-2sin²x
cos2x = 1-2(1/4)²
cos2x = 1-2(1/16)
cos2x= 1-1/8
cos2x = 7/8
for tan2x;
tan2x = tanx + tanx/1-tan²x
tan2x = 2tanx/1-tan²x
tan2x = 2(-1/√15)/1-(-1/√15)²
tan2x = (-2/√15)/(1-1/15)
tan2x = (-2/√15)/(14/15)
tan2x = -2/√15 * 15/14
tan2x = -30/14√15
tan2x = -30/7√15
rationalize
tan2x = -30/7√15 * √15/√15
tan2x = -30√15/7*15
tan2x = -2√15/7
Answer:
2! Thank it if it was helpful :D
Step-by-step explanation:
7x-4x=3+3
3x=6
x=2
