Alona has some wood cutouts of two different shapes - square and triangle. Each square cutout is 6 mm thick and each triangular
1 answer:
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The length of train is 120 meters
The speed of train is 25 meter per second
<u><em>Solution:</em></u>
The speed is given by formula:
Given that,
It takes a train 60 seconds to completely drive through a bridge of 1260 m
And 90 seconds to completely drive through a tunnel of 2010 m
Let the length of the train be "x"
<em><u>The total distance travelled by the train across the bridge is given by:</u></em>
total distance = x + 1260 + x = 2x + 1260
[ here we use x + x to represent that train completely drives through bridge ]
The time taken is given as 60 seconds
<em><u>Therefore, the speed is given as:</u></em>
<em><u>The total distance travelled by the train through the tunnel is given by:</u></em>
total distance = x + 2010 + x = 2x + 2010
The time taken is given as 90 seconds
<em><u>Therefore, the speed is given as:</u></em>
The speed of the train was the same in both cases.
Equate both speeds
Thus length of train is 120 meters
<em><u>Find the speed of train:</u></em>
Thus speed of train is 25 meter per second
<h3>Answer: 12</h3>
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Explanation:
The two integers multiply to 36, so,
ab = 36
which solves to
a = 36/b
Then we want to add the numbers such that we get the smallest possible result.
a+b = (36/b)+b
So we want (36/b)+b to be as small as possible.
Let's say we replace b with x and we consider this function
f(x) = (36/x) + x
The goal is to find when f(x) is smallest, ie, we want to minimize the function.
If we were to graph out the function, we get the curve shown below.
To make things easier, we'll only focus on positive values of x.
The lowest part of the curve is what we're after. Using the "minimum" function/feature on the graphing calculator, we would then find the lowest point occurs at (6,12). This point is considered a local minimum because it's the lowest point in that given neighborhood of x values.
So the input x = 6 leads to the smallest output f(x) = 12.
This in turn means b = 6 is going to pair with a = 36/b = 36/6 = 6.
In short, a = 6 and b = 6.
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As a check,
a*b = 6*6 = 36
a+b = 6+6 = 12
We can make a table of various values to help confirm that 12 is the smallest sum.
Side note: If you're not allowed to use a graphing calculator, then you'll need to use calculus.