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NeX [460]
2 years ago
14

Train A arrives at central station on the hour and every 12 minutes. Train B arrives o the hour and every 15 minutes. When do bo

th trains arrive at the same time?
Mathematics
1 answer:
lana [24]2 years ago
7 0

Answer:

Every 30 hours

Step-by-step explanation:

Train A arrives at central station on the hour and every 12 minutes, you mean with that on every 72 minutes

Train B arrives at central station on the hour and every 15 minutes, you mean with that on every 75 minutes

In accordance with the given, the smallest number containing numbers 72 and 75 is  1800 minutes.

When we convert this number of minutes in hours we get:

1800 / 60 = 30 hours

God with you!!!

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Urgent, It is a Calculus question and I’ll appreciate your help. Thanks
BaLLatris [955]

Answer:

  4733

Step-by-step explanation:

Please refer to the attached diagram.

Point A can be assigned x-coordinate "p". Then its y-coordinate is 6p^2. The slope at that point is y'(p) = 12p.

Point B can be assigned x-coordinate "r". Then its y-coordinate is 6r^2. The slope at that point is y'(r) = 12r.

We want the slopes at those points to have a product of -1 (so the tangents are perpendicular). This means ...

  (12p)(12r) = -1

  r = -1/(144p)

The slope of line AB in the diagram is the ratio of the differences of y- and x-coordinates:

  slope AB = (ry -py)/(rx -px) = (6r^2 -6p^2)/(r -p) = 6(r+p) . . . . simplified

The slope of AB is also the tangent of the sum of these angles: the angle AC makes with the x-axis and angle CAB. The tangent of a sum of angles is given by ...

  tan(α+β) = (tan(α) +tan(β))/1 -tan(α)·tan(β))

__

Of course the slope of a line is equal to the tangent of the angle it makes with the x-axis. The tangent of angle CAB is 2 (because the aspect ratio of the rectangle is 2). This means we can write ...

  slope AB = ((slope AC) +2)/(1 -(slope AC)(2))

  6(p+r)=\dfrac{12p+2}{1-(12p)(2)}\\\\3(p+r)(1-24p)=6p+1\qquad\text{multiply by $1-24p$}\\\\3\left(p-\dfrac{1}{144p}\right)(1-24p)=6p+1\qquad\text{use the value for r}\\\\3(144p^2-1)(1-24p)=144p(6p+1)\qquad\text{multiply by 144p}\\\\ 3456 p^3+ 144 p^2+ 24 p+1 =0\qquad\text{put in standard form}\\\\144p^2(24p+1)+(24p+1)=0\qquad\text{factor by pairs}\\\\(144p^2+1)(24p+1)=0\qquad\text{finish factoring}\\\\p=-\dfrac{1}{24}\qquad\text{only real solution}\\\\r=\dfrac{-1}{144p}=\dfrac{1}{6}

So, now we can figure the coordinates of points A and B, and the distance between them. That distance is given by the Pythagorean theorem as ...

  d^2 = (6r^2 -6p^2)^2 +(r -p)^2

  d^2 = (6(1/6)^2 -6(-1/24)^2)^2 +(1/6 +1/24)^2 = 25/1024 +25/576 = 625/9216

Because of the aspect ratio of the rectangle, the area is 2/5 of this value, so we have ...

  Rectangle Area = (2/5)(625/9216) = 125/4608 = a/b

Then a+b = 125 +4608 = 4733.

_____

<em>Comment on the solution</em>

The point of intersection of the tangent lines is a fairly messy expression, and that propagates through any distance formulas used to find rectangle side lengths. This seemed much cleaner, though maybe not so obvious at first.

6 0
3 years ago
Can anyone help please
Liula [17]
The answer is yes. The triangles are congruent.

I measured them with a ruler and they are the same length.

Hope this helped! c:
8 0
3 years ago
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The box-and-whisker plots show data for the test scores of four groups of students in the same class. Which plot represents data
bixtya [17]

Answer:

The answer is B.

Step-by-step explanation:

7 0
3 years ago
Using the slope and the y-intercept, graph the line represented by the following equation. Then select the correct graph. 3y = 2
Over [174]
First, let's write the given equation in slope-intercept form: y = mx + b

In slope-intercept form, the slope of the line is m, and the y-intercept is b. The slope is a measure of how steep the graph is at any point and is found by doing rise over run. This means the change in y values divided by the change in x values. Next, y-intercept is just where the graph crosses the y axis.

All we need to do to get the equation in slope-intercept form is to divide each term by 3. This will isolate the y.

y= \frac{2}{3}x-2

As you can see, the slope of the line is 2/3, and the y-intercept is -2.

To graph the line, plot a point at (0,-2). This is the point where the graph crosses the y axis. Then from that point, count up two and right 3. Plot a point here as well. Lastly, connect the two points with a straight line.

See attached picture for the graph.

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3 years ago
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Write the expression 12 x 4^2 in words
lawyer [7]

Answer and Step-by-step explanation:

Twelve times four squared.

This is how you would write the expression in word format.

<em><u>#teamtrees #PAW (Plant And Water)</u></em>

7 0
2 years ago
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