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Gre4nikov [31]
3 years ago
11

At noon, ship A is 130 km west of ship B. Ship A is sailing east at 25 km/h and ship B is sailing north at 20 km/h. How fast is

the distance between the ships changing at 4:00 PM?
Mathematics
1 answer:
Hitman42 [59]3 years ago
8 0

Answer:

answer = 12.87 km/h

Step-by-step explanation:

Given

Ship A is sailing east at 25 km/h = \frac{dx}{dt}

ship B is sailing north at 20 km/h =\frac{dy}{dt}

here x and y are the  sailing at t = 4 : 00 pm for ship A and B respectively

so we get x = 4 ×25 =100 km/h

                 y = 4× 20 = 80 km/h

let z is the distance between the ships, we need to find \frac{dz}{dt} at t = 4 hr

At noon, ship A is 130 km west of ship B (12:00 pm)

so equation will be

z^2 = (130-x)^2 + y^2......................(i)\\put x = 100 and y = 80 \\\\we |  | get \\

z^2 = 30^2 + 80^2\\z =\sqrt{7300} km/h

derivative first equation w . r. to t we get

2z\frac{dz}{dt} =-2(130-x)\frac{dx}{dt}+2y\frac{dy}{dt}

\frac{dz}{dt} =\frac{1}{z}[(x -130)\frac{dx}{dt} +y\frac{dy}{dt}]

\frac{dz}{dt} = \frac{( -20\times25 + 80\times20)}{\sqrt{7300} }

     = \frac{1100}{85.44}\\  = 12.87km/h

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\sqrt{64}=8

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Runner A crosses the starting line of a marathon and runs at an average pace of 5.6 miles per hour. Half an hour later, Runner B
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5 0
3 years ago
Find the value of x. X=?<br>Volume = 1500 ​
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6 0
2 years ago
*Please I need help quickly* Approximate the mean of the frequency distribution for the ages of the residents of a town.
Cerrena [4.2K]

Answer:

The mean age of the frequency distribution for the ages of the residents of a town is 43 years.

Step-by-step explanation:

We are given with the following frequency distribution below;

 

     Age                      Frequency (f)               X                    X \times f

     0 - 9                            30                         4.5                   135

    10 - 19                           32                        14.5                  464

    20 - 29                         12                         24.5                 294

    30 - 39                         20                        34.5                 690

    40 - 49                         25                        44.5                1112.5

    50 - 59                         53                        54.5                2888.5

    60 - 69                         49                        64.5                3160.5

    70 - 79                          13                         74.5                968.5

    80 - 89                  <u>        8        </u>                  84.5         <u>        676        </u>

    Total                      <u>      242      </u>                                  <u>      10389      </u>

Now, the mean of the frequency distribution is given by the following formula;

                          Mean =  \frac{\sum X \times f}{\sum f}

                                     =  \frac{10389}{242}  = 42.9 ≈ 43 approx.

Hence, the mean age of the frequency distribution for the ages of the residents of a town is 43 years.

5 0
3 years ago
Read 2 more answers
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