Simplify the expression. Show your work.
1 answer:
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Answer:
(6, - 4 )
Step-by-step explanation:
Given the 2 equations
-
y = 3 → (1)
x -
= 12 → (2)
Multiply (1) by 8 and (2) by 6 to clear the fractions
2x - 3y = 24 → (3)
10x - 3y = 72 → (4)
Rearrange (3) expressing - 3y in terms of x by subtracting 2x from both sides
- 3y = 24 - 2x
Substitute 3y = 24 - 2x into (4)
10x + 24 - 2x = 72, that is
8x + 24 = 72 ( subtract 24 from both sides )
8x = 48 ( divide both sides by 8 )
x = 6
Substitute x = 6 in either (3) or (4) and solve for y
Substituting in (3)
2(6) - 3y = 24
12 - 3y = 24 ( subtract 12 from both sides )
- 3y = 12 ( divide both sides by - 3 )
y = - 4
Solution is (6, - 4 )
So the car is moving at 651 revolutions per minute, with wheels of a radius of 18inches
so, one revolution, is just one go-around a circle, and thus 2π, 651 revolutions is just 2π * 651, or 1302π, the wheels are moving at that "angular velocity"
now, what's the linear velocity, namely, the arc covered per minute
well
now, how much is that in miles/hrs? well
let's keep in mind that, there are 12inches in 1foot, and 5280ft in 1mile, whilst 60mins in 1hr
thus
notice, after all the units cancellations, you're only left with mi/hrs
so, one revolution, is just one go-around a circle, and thus 2π, 651 revolutions is just 2π * 651, or 1302π, the wheels are moving at that "angular velocity"
now, what's the linear velocity, namely, the arc covered per minute
well
now, how much is that in miles/hrs? well
let's keep in mind that, there are 12inches in 1foot, and 5280ft in 1mile, whilst 60mins in 1hr
thus
notice, after all the units cancellations, you're only left with mi/hrs