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Lemur [1.5K]
3 years ago
15

Working together, Joe and Alberto can

Mathematics
1 answer:
Reika [66]3 years ago
6 0

10.014 hours will take Joe to do it alone, if Joe and Alberto can  pick forty bushels of apples in 4.74 hours,  had he done it alone it would have taken  Alberto nine hours.

Step-by-step explanation:

The given is,

               Joe and Alberto can  pick forty bushels of apples in 4.74 hours.

               Alberto done it alone it would have taken nine hours

Step:1

            For Joe and Alberto can working together,

                   1 hour work of Alberto and Joe = \frac{1}{4.74}

            For Alberto do it alone,

                    1 hour work of Alberto = \frac{1}{9}

            Relation for time and work,

           Alberto and Joe working together for 1 hr

                                    = Alberto 1 hr work +  Joe 1 hr work

           Above equation becomes,

           Joe 1 hr work =  Alberto and Joe working together for 1 hr -                    

                                                             Alberto 1 hr work

           From the given values above equation becomes,

                    Joe work 1 hr work = (\frac{1}{4.74}) -(\frac{1}{9}  )

                                                     = \frac{9-4.74}{42.66}

                              Joe 1 hr work = \frac{4.26}{42.66}

           Time taken for Joe work when he do it alone,

                                                     = \frac{42.66}{4.26}

            Time taken for Joe work = 10.014 hours

Result:

        10.014 hours will take Joe to do it alone, if Joe and Alberto can  pick forty bushels of apples in 4.74 hours,  had he done it alone it would have taken  Alberto nine hours.

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1) \sqrt{-48}=4\sqrt{3} \ i

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Step-by-step explanation:

We need to simply the following :

<u>Note: For all questions given we know that </u>\sqrt{-1}=i<u> using it in all the given questions.</u>

1) \sqrt{-48}

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\sqrt{-48}\\=\sqrt{48}\sqrt{-1}  \\=\sqrt{2\times2\times2\times2\times3}\ i\\=  \sqrt{2^2\times2^2\times3}\ i\\=2\times2\sqrt{3} \ i \\=4\sqrt{3} \ i

2) \sqrt{-63}

Factors of 63 are: 3x3x7

\sqrt{-63}\\=\sqrt{63}\sqrt{-1}  \\=\sqrt{3\times3\times7}\ i\\=  \sqrt{3^2\times7}\ i\\=3\sqrt{7} \ i

3) \sqrt{-72}

Factors of 72 are: 2x2x2x3x3

\sqrt{-72}\\=\sqrt{72}\sqrt{-1}  \\=\sqrt{2\times2\times2\times3\times3}\ i\\=  \sqrt{2^2\times3^2\times2}\ i\\=2\times3\sqrt{2} \ i \\=6\sqrt{2} \ i

4) \sqrt{-24}

Factors of 24 are: 2x2x2x3

\sqrt{-24}\\=\sqrt{24}\sqrt{-1}  \\=\sqrt{2\times2\times2\times3}\ i\\=  \sqrt{2^2\times2\times3}\ i\\=2\sqrt{2\times3} \ i \\=2\sqrt{6} \ i

5) \sqrt{-84}

Factors of 84 are: 2x2x3x7

\sqrt{-84}\\=\sqrt{84}\sqrt{-1}  \\=\sqrt{2\times2\times3\times7}\ i\\=  \sqrt{2^2\times3\times7}\ i\\=2\sqrt{21} \ i

6) \sqrt{-99}\\

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\sqrt{-99}\\=\sqrt{99}\sqrt{-1}  \\=\sqrt{3\times3\times11}\ i\\=  \sqrt{3^2\times11}\ i\\=3\sqrt{11} \ i \\=3\sqrt{11} \ i

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