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nydimaria [60]
3 years ago
9

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?
Mathematics
1 answer:
aivan3 [116]3 years ago
3 0

Answer:  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

2013-x\times 3=0\\\\\Rightarrow 3x=2013\\\\\Rightarrow x=\dfrac{2013}{3}=671.

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.


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If f(x)= 3x squares +1 and g(x) =1-x what is the value of (f-g)(2)
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Step-by-step explanation:

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Method 1

f(2)=3(2)²+1                                [exponent]

f(2)=3(4)+1                                  [multiply]

f(2)=12+1                                     [add]

f(2)=13

g(2)=1-(2)                                    [subtract]

g(2)=-1                  

(f-g)(2)=13-(-1)                            [subtract f(2) and g(2)]

(f-g)(2)=14

--------------------------------------------------------------------------------------------------------

Method 2

(f-g)(x)=3x²+1-(1-x)                     [distribute -1]

(f-g)(x)=3x²+1-1+x                      [combine like terms]

(f-g)(x)=3x²+x

(f-g)(2)=3(2)²+2                         [plug in x=2, exponent]

(f-g)(2)=3(4)+2                           [multiply]

(f-g)(2)=12+2                             [add]

(f-g)(2)=14

--------------------------------------------------------------------------------------------------------

Now, we know that (f-g)(2)=14. We confirmed this with both methods.

8 0
3 years ago
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