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Fudgin [204]
3 years ago
5

A man walking on a railroad bridge is 2/5 of the way along the bridge when he notices a train at a distance approaching at the c

onstant rate of 45 mph . The man can run at a constant rate in either direction to get off the bridge just in time before the train hits him. How fast can the man run?
Mathematics
2 answers:
shusha [124]3 years ago
5 0

Answer: 9 mph

Step-by-step explanation:

Given that a man walking on a railroad bridge is 2/5 of the way along the bridge when he notices a train at a distance approaching at the constant rate of 45 mph .

If the man tend to run in the forward direction, he will cover another 2/5 before the train reaches his initial position. The distance covered by the man will be 2/5 + 2/5 = 4/5

The remaining distance = 1 - 4/5 = 1/5

If the man can run at a constant rate in either direction to get off the bridge just in time before the train hits him, the time it will take the man will be

Speed = distance/time

Time = 1/5d ÷ speed

The time it will take the train to cover the entire distance d will be

Time = d ÷ 45

Equate the two time

1/5d ÷ speed = d ÷ 45

Speed = d/5 × 45/d

Speed = 9 mph

makkiz [27]3 years ago
3 0

Answer:

The Man needs to run at 9 mph

Step-by-step explanation:

Let M stand for the man's speed in mph.  When the man  

runs toward point A, the relative speed of the train with respect  

to the man is the train's speed plus the man's speed (45 + M).  

When he runs toward point B, the relative speed of the train is the  

train's speed minus the man's speed (45 - M).

When he runs toward the train the distance he covers is 2 units.  

When he runs in the direction of the train the distance he covers  

is 3 units. We can now write that the ratio of the relative speed  

of the train when he is running toward point A to the relative speed  

of the train when he is running toward point B, is equal to the  

inverse ratio of the two distance units or

              (45 + M)          3

              -----------  =      ---

              (45 - M)          2

          90+2 M=135-3 M

⇒5 M = 45

⇒ M = 9 mph

The Man needs to run at 9 mph

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A bridge is built in the shape of a parabolic arch. The bridge arch has a span of 166 feet and a maximum height of 40 feet. Find
scoray [572]

Answer:

38.27775 feet

Step-by-step explanation:

The bridge has been shown in the figure.

Let the highest point of the parabolic bridge (i.e. vertex of the parabola) be at the origin, O(0,0) in the cartesian coordinate system.

As the bridge have the shape of an inverted parabola, so the standard equation, which describes the shape of the bridge is

x^2=4ay\;\cdots(i)

where a is an arbitrary constant (distance between focus and vertex of the parabola).

The span of the bridge = 166 feet and

Maximum height of the bridge= 40 feet.

The coordinate where the bridge meets the base is A(83, -40) and B(-83, -40).

There is only one constant in the equation of the parabola, so, use either of one point to find the value of a.

Putting A(83,-40) in the equation (i) we have

83^2=4a(-40)

\Rightarrow a=-43.05625

So, on putting the value of a in the equation (i), the equation of bridge is

x^2=-172.225y

From the figure, the distance from the center is measured along the x-axis, x coordinate at the distance of 10 feet is, x=\pm 10 feet, put this value in equation (i) to get the value of y.

(\pm10)^2=-172.225y

\Rightarrow y=-1.72225 feet.

The point P_1(10,-1.72225) and P_2(-10,-1.72225) represent the point on the bridge at a distance of 10 feet from its center.

The distance of these points from the x-axis is d=1.72225 feet and the distance of the base of the bridge from the x-axis is h=40 feet.

Hence, height from the base of the bridge at 10 feet from its center

= h-d

=40-1.72225=38.27775 feet.

8 0
3 years ago
PLEASE, I NEED THIS NOW!!!!
11111nata11111 [884]

Answer:

For the first one

x= About 32.02

y= About 27.58

z= About 55.16

For the second one

x= 6

y= 12

z= about 16.97

Step-by-step explanation:

Their all really simple

These are special right triangles, a 45, 45, 90 and a 30, 60, 90 triangle. The formla for these triangles are shown in the picture below.

Now for the first one ]

Lets find Z first

Now this is a 45 special right triangle so we know the other side s 39 but the hypotenuse is n\sqrt{2} (I’m using N becuase x and y is taken) So n is basically 39 (look at the image below) and just solve that. Now for x and y. We know its a 30, special right triangle. We know that 39 here is already the answer for  N\sqrt{3} so make an equation to find the n and you’ll get 27.58 for y. Now For x, its just doubled the y.

For the second one this is easier

We know that the x is (6) becuase its already in the radical number, now to find the hypotnuse, we double that and get 12. Now we know what y is becuase since the 2nd triangle is a 45/45/90, we know that 12 is y, the hypotnuse is just N\sqrt{2} and we just plug in the n with 12 and solve it!

6 0
3 years ago
A
kykrilka [37]

Answer:

One possible answer would be they sold 80 student tickets and 30 adult tickets

Step-by-step explanation:

set up two inequalities, one to show number of tickets that can be sold, and the other is how much money they need to make

5x+10y G than or =  700

x+y L than or = 110

The first inequality shows that each student (x) ticket sells for $5, and each adult (y) ticket sells for $10, and the amound has to be greater or equal to 700.

The second inequality shows that both student and adult tickets sold have to be less than or equal to 110.

First find either x or y, in this case finding y was easier

y is g than or = to 30

This means that they sold at least 30 adult tickets= $300

With y, plug into the inequality x+y L than or = to 110 to find x

x is less than or = to 80

This means that they sold at most 80 student tickets = $400

Hope this helps!

8 0
2 years ago
A backpack costs $18 and has a 7 percent tax. How much will Sheila have to pay for the backpack after tax? $1.26 $12.60 $19.26 $
elixir [45]
If you add 18 to 7% your number comes out as 19.26
7 0
3 years ago
Read 2 more answers
Can a triangle with the side lengths of 8, 4, and 12cm
leva [86]
This is a pathagorean triple is this triangle is a right triangle
6 0
3 years ago
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