The minute hand of a clock is 4 inches long. how far does the tipof the minute hand move in 20 minnutes?
1 answer:
This is an arc length question, but it's a little hidden. The minute hand is the radius of the circle, so r=4. Next we need to know how much of the circle the tip of the minute hand will move through. Since there are 60 minutes in an hour, the minute hand will pass through 20/60=1/3 of the clock. Then we just use the circumference formula scaled by the amount of the clock we have:
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Answer:
i) 28 - 30i
ii) 36 + 28i
Step-by-step explanation:
i) x = 6 + i ⇒2x = 2(6 + i) = 12 + 2i
z = 4 - 8i ⇒ 4z = 4(4 - 8i) = 16 - 32i
2x + 4z = (12 + 2i) + (16 - 32i) = 28 - 30i
ii) w = -1 + 5i and z = 4 - 8i
w × z = (-1 + 5i)(4 - 8i) = -4 + 8i + 20i - 40⇒collect like terms
w × z = -4 + 28i - 40
∵
∴w × z = -4 + 28i - 40(-1) = -4 + 28i + 40 = 36 + 28i