Answer: (2,30), (5,66)
Step-by-step explanation: I truly don’t know if this is correct, but at the beginning, the crystal was already 6 mm. She then realized it increased 12 mm every hour, so if one hour passed, it would be 12+6= 18. Okay, so now that we know that, we multiple the hours by 12 and then add the 6.
12x2= 24
24+ 6= 30,
12x5= 60
60+6= 66
2(n-9) = 3(n + 5)
2n - 18 = 3n + 15
2n - 3n = 15 + 18
-n = 33
n = -33
Answer:
1/2 + 5/2 i
Step-by-step explanation:
(-5+i) i
---------* --------
2i i
cannot have i in the denominator so we multiply by i
(-5+i) i -5i + i^2
---------* -------- = ----------------
2i i +2i^2
remember i^2 = -1
-5i + -1 -1 -5i
= ---------------- = ------------------
+2(-1) -2
get rid of the negative in the denominator by multiplying the top and bottom by -1
(-1 -5i) * -1
= ------------------
-2*(-1)
(1 +5i)
= ------------------ = 1/2 + 5/2 i
2
Answer:
the second one
Step-by-step explanation:
Answer:
-16/65
Step-by-step explanation:
Given sinα = 3/5 in quadrant 1;
Since sinα = opp/hyp
opp = 3
hyp = 5
adj^2 = hyp^2 - opp^2
adj^2 = 5^2 = 3^2
adj^2 = 25-9
adj^2 = 16
adj = 4
Since all the trig identity are positive in Quadrant 1, hence;
cosα = adj/hyp = 4/5
Similarly, if tanβ = 5/12 in Quadrant III,
According to trig identity
tan theta = opp/adj
opp = 5
adj = 12
hyp^2 = opp^2+adj^2
hyp^2 = 5^2+12^2
hyp^2 = 25+144
hyp^2 = 169
hyp = 13
Since only tan is positive in Quadrant III, then;
sinβ = -5/13
cosβ = -12/13
Get the required expression;
sin(α - β) = sinαcosβ - cosαsinβ
Substitute the given values
sin(α - β) = 3/5(-12/13) - 4/5(-5/13)
sin(α - β)= -36/65 + 20/65
sin(α - β) = -16/65
Hence the value of sin(α - β) is -16/65
