In the pully system shown in this figure, MQ = 10 in, NP = 3in and QP=24in. Find MN
1 answer:
Answer:
The correct option is a. The length of MN is 25.
Step-by-step explanation:
Given information: MQ = 10 in, NP = 3 in and QP=24 in.
If the centers of two circles of radius r₁ and r₂ are d units apart, then the length of the direct common tangent between them is
Square both sides.
Take square root both sides.
Therefore length of MN is 25 and option a is correct.
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positive leading coefient so both ends point up
factor it to see wheere the roots are
the roots are r1,r2,r3,r4 in P(x)=(x-r1)(x-r2)(x-r3)(x-r4)
factor
P(x)=(x-3)(x-2)(x+1)(x+3)
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disregard negative roots becasue you can't have negative time or something
3 or 2
see my rough graph
here is rough scetch
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now, the perpendicular distance from the center of the hexagon to a side, namely the apothem, is 6√3, and each side is 12 units long, since there are 6 of them that'd be 72 for all, namely the perimeter.
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![\bf \stackrel{\textit{area of the hexagon}}{\left[\cfrac{1}{2}(6\sqrt{3})(72) \right]}~~~~+~~~~\stackrel{\textit{area of the 6 triangles}}{6\left[\cfrac{1}{2}(12)(11) \right]}](https://tex.z-dn.net/?f=%5Cbf%20%5Cstackrel%7B%5Ctextit%7Barea%20of%20the%20hexagon%7D%7D%7B%5Cleft%5B%5Ccfrac%7B1%7D%7B2%7D%286%5Csqrt%7B3%7D%29%2872%29%20%20%5Cright%5D%7D~~~~%2B~~~~%5Cstackrel%7B%5Ctextit%7Barea%20of%20the%206%20triangles%7D%7D%7B6%5Cleft%5B%5Ccfrac%7B1%7D%7B2%7D%2812%29%2811%29%20%20%5Cright%5D%7D)
now, the perpendicular distance from the center of the hexagon to a side, namely the apothem, is 6√3, and each side is 12 units long, since there are 6 of them that'd be 72 for all, namely the perimeter.
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