Suppose a railroad rail is 3 kilometers and it expands on a hot day by 12 centimeters in length. Approximately how many meters w
ould the center of the rail rise above the ground
1 answer:
For small angles, x, in radians,
tan(x) ≈ sin(x) = x
Use this to create an approximate diagram for the problem as shown in the figure below.
The actual deflected shape is parabolic, but it is approximated by an isosceles triangle with small equal angles.
The extend length is 3 km + 12 cm, which is
3000 + 0.12 = 3000.12 m
Half of the extended length is 1500.06 m
Let h+ the rise of the center of the rail above ground.
From the Pythagorean theorem, obtain
h² + 1500² = 1500.6²
h² = 1500.06² - 1500² = 180.004
h = 13.4 m, which is about 0.9% of the original length.
Answer: 13.4 m
tan(x) ≈ sin(x) = x
Use this to create an approximate diagram for the problem as shown in the figure below.
The actual deflected shape is parabolic, but it is approximated by an isosceles triangle with small equal angles.
The extend length is 3 km + 12 cm, which is
3000 + 0.12 = 3000.12 m
Half of the extended length is 1500.06 m
Let h+ the rise of the center of the rail above ground.
From the Pythagorean theorem, obtain
h² + 1500² = 1500.6²
h² = 1500.06² - 1500² = 180.004
h = 13.4 m, which is about 0.9% of the original length.
Answer: 13.4 m
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Answer:
The equation of the line in form where
are integers with no factor common to all three, and greater than or equal 0 is:
Step-by-step explanation:
Given:
x-intercept = 12
y-intercept = 4
To find the equation of line in the form where
are integers with no factor common to all three, and greater than or equal 0.
Solution:
The x-intercept is the point at which the line cuts the x-axis. The point of x-intercept is given as
Thus, on point of the line is (12,0)
The y-intercept is the point at which the line cuts the y-axis. The point of y-intercept is given as .
Thus, on point of the line is (0,4)
Using the two points we can find the slope of the line using the slope formula.
So, slope of the line can b given as:
The slope intercept form of the equation of he line is given as:
where represents slope of the line and
represents the y-intercept.
So, the equation of the line can be given as:
Multiplying each term by 3 to remove fraction.
Adding both sides.
Thus, the equation of the line in form where
are integers with no factor common to all three, and greater than or equal 0 is: