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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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6 0
3 years ago
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two glasses of milk and 3 snack bars have a total of 78 carbohydrates​ (carbs), and 4 glasses of milk and 3 snack bars have a to
padilas [110]

Answer:

Each glass of milk is 9 carbs.

Each snack bar is 19.7 carbs.

Step-by-step explanation:

1. I know that 2 glasses of milk with 3 snack bars is 78 carbs.

The next part of the sentence has two times the amount of milk with the same amount of snack bars for 96 carbs.

Now, I will find the difference in the amount of carbs.

96 - 78 = 18 carbs.

So two glasses of milk = 18 carbs.

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So, each glass of milk is 9 carbs.

2. Since we know this, we can subtract the amount of carbs from the glasses of milk from the total amount of carbs.

78 - 19 = 59

In the first scenario, there are 59 carbs per 3 snack bars.

To find the amount of each snack bar, divide 59 by 3.

59 ÷ 3 = 19.7 when rounded to the nearest tenth.

Therefore, each snack bar is 19.7 carbs.

3 0
2 years ago
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What is the radian measure of the smallest angle formed by the hands of a clock at 7 o'clock?
netineya [11]
See the picture attached to better understand the problem
we know that
a full circle is a 360 degrees
divided in 12 equals parts-------> 360/12-------> 30 degrees each part

<span>the smallest angle formed by the hands of a clock at 7 o'clock has 5 parts
so
5*30</span>°------> 150°

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5 0
3 years ago
Which sequence of similar transformations could map △ABC onto △A'B'C'?
nadya68 [22]

Answer:  A sequence of similar transformations of dilation and translation could map △ABC onto △A'B'C'.


Step-by-step explanation:

Similar transformations:  If one figure can be mapped onto the other figure using a dilation and a congruent rigid transformation or a rigid transformation followed by dilation then the two figures are said to be similar.

In the attachment △ABC mapped onto △A'B'C' by a sequence of dilation from origin and scalar factor k followed by translation.

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Answer:

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Step-by-step explanation:

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So, let The increase  in price from 2008 to 2009 = $ 7.70 - $ 7.36

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Or, Percentage increase = \frac{$ 0.34}{$ 7.36} × 100

∴  Percentage increase = 4.619 %

Hence The increase price of movie ticket is $ 0.34   or 4.619 %  Answer

8 0
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