The magic dragon has 2013 heads. leo the brave is cutting off the dragon's heads at a speed of 5 heads per minute. the dragon's heads are growing back at a speed of 2 heads per minute. how many heads will the dragon have in an hour? how long will the "fight" last?

 The answer is 1833 heads  and 11 hours, 11 minutes.

Step-by-step explanation:  Given that the Magic Dragon has 2013 heads. The brave Leo is cutting off the Dragon's heads at a speed of 5 heads per minute. But, the Dragon's heads are growing back at a speed of 2 heads per minute.

So, the number of heads of Dragon that are decreasing per minute = 3.

Therefore, after 1 hour, i.e., 60 minutes, The number of heads of the Dragon

= 2013 - 60 × 3 = 2013 - 180 = 1833 heads.

Now, the fight will last until all the heads of the Dragon are cut. Let the fight lasts for 'x' minutes, then

Hence the fight lasts for 671 minutes, i.e., 11 hours and 11 minutes.

Thus, the Dragon will have 1833 heads after 1 hour and the fight will last for 11 hour and 11 minutes.

hello from mrbilldoesmath!

answer:

(7 x + 6 y) (49 x^2 - 42 x y + 36 y^2)

discussion:

the trick is to recognize that 343 = 7^3 and 216 = 6^3 and, in general,

a^3 + b^3 =   (a + b) (a^2 - a b + b^2).

in our case

343x^3+216y^3   =   (7x)^3 + (6y)^3

so take a = 7x and b = 6y in the above equation to get the answer.

you,

mrb

you estimate that the angle of elevation to the top of the 86th floor (the observatory) is 82 .the total height of the building is another 123 meters above the 86th floor.

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