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Answer:
- airplane: 225 mph
- wind: 45 mph
Step-by-step explanation:
The average speed with the wind is (540 mi)/(2 h) = 270 mi/h.
The average speed against the wind is (540 mi)/(3 h) = 180 mi/h.
Let a and w represent the speeds of the airplane and wind, respectively.
a + w = 270 . . . . speed with the wind
a - w = 180 . . . . speed against the wind
2a = 450 . . . . . . sum of the two equations
a = 225 . . . . . . divide by 2
w = a -180 = 45
The speed of the airplane is 225 miles per hour; the speed of the wind is 45 miles per hour.
Answer:
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Step-by-step explanation:
Answer:
at first we put the numbers in order from least to greatest
2 , 6 , 6 , 7 , 8 , 9
1st quartile = 6
median = (6+7)/2 = 6.5
3rd quartile = 8
Find the roots
solve
we use hmm, completing the suare
2(x²-1.5x)=4
divide both sides by 2
x²-1.5x=2
take 1/2 of linear coeiftn and square it
-1.5/2=-0.75, (-0.75)²=0.5625
add that to both sides
x²-1.5x+0.5625=2+0.5625
factor perfect squaer trinomial
(x-0.75)²=2.5625
square root both sides, remember to take positive and negative square roots
x-0.75=+/-√2.5625
add 0.75 to both sides
x=0.75+/-√2.5625
the roots are x=0.75+√2.5625 and x=0.75-√2.5625
1/a and 1/b
1/(0.75+√2.5625) and 1/(0.75-√2.5625)
if the roots of a quadratic equation are r1 and r2 then it factors to
(x-r1)(x-r2)
so then we can factor our equation to be

if we were to try and expand it, we would get
x²+0.75x-0.5
that's the simpliest equation with roots 1/a and 1/b where a and b are he roots of 2x²-3x=4
x²+0.75x-0.5 is answer
Answer:
tan2θ = 4√2/7
Step-by-step explanation:
Given sin theta=1/3 and 0 < theta< π/+
Required
tan 2 theta
tan2 theta = 2tanθ/1-tan²θ
Get tan θ
sinθ = opp/hyp
adj = √3²-1²²
adj = √9-1
adj = √8
tanθ = opp/adj = 1/2√2
tan2 theta = 2(1/2√2/1-(1/2√2)²
tan2θ = 1/√2/1-1/8
tan2θ = 1/√2/7/8
tan2θ = 8/7√2
Rationalize
tan2θ = 8√2/14
tan2θ = 4√2/7