5. Suppose a railroad is 2 km long, and it expands on a hot day by 50 cm in length. Approximately how high would the center of the rail rise above the ground? (Hint: Convert all measurements to meters BEFORE calculating any values)
Answers
L₁ = 2 km = 2000 km
The extended length after expansion is
L₂ = L₁ + 50 cm
= 2000 + 0.5
= 2000.5 m
Assume that the deflected shape is a circle with radius = r, as shown in the figure below.
The central angle of the deflected shape is 2θ.
The deflected length is calculated as
2rθ = L₂.
That is
rθ = 2000.5/2 = 1000.25
r = 1000.25/θ (1)
By definition (from the figure)
sinθ = 1000/r (2)
Substitute (1) into (2).
sin θ = (1000 θ)/1000.25 = 0.99975 θ
To find θ, define the function
f(θ) = 0.99975 θ - sin θ
A graphical solution from the calculator yields
θ = 0.0038 rad.
Therefore from (1), obtain
r = 263223.7 m
The height of the center of the rail above ground is
h = r - r cos θ = r(1 - cos θ)
= 263223.7(1 - cos(0.0038))
= 1.9 m
Answer: 1.9 m
To find the height at which the center of a railroad rail would rise due to expansion, convert all measurements to meters and use the formula h ≈ ΔL / 8. For expansion of 50 cm, the rail would rise approximately 6.25 cm.
The student has asked how high the center of a 2 km long railroad rail would rise when it expands by 50 cm on a hot day. First, we need to convert all measurements to meters: the railroad is 2000 m long, and it expands by 0.50 m. To find the height that the rail would rise, we can consider the rail as forming an arc of a circle after expansion.
We have the original length of the rail as the diameter of the circle and the expanded length as a slightly longer arc of the same circle. As the increase in length due to expansion is very small compared to the original length, we can use the approximation that the height of the rise is equal to the arc's excess length divided by 8 (h ≈ ΔL / 8).
Applying this formula: h ≈ 0.50 m / 8 = 0.0625 m or 6.25 cm. This approximation works under the assumption that the bend in the rail is mild, as it would be in reality due to the small degree of expansion.
Related Questions
In order to avoid heavy traffic, Antonio can drive home after working less than 7 hours (h < 7) or after working more than 9 hours (h >9). How can these inequalities be written as one statement?
7 < h < 9
7 > h > 9
h < 7 or h > 9
h > 7 or h < 9
Answers
Answer:
Option C is correct.
The inequalities can be written as one statement as : h<7 or h>9
Step-by-step explanation:
Let h be the working hours
Antonio can drive home after working less than 7 hours.
Less than symbol represented by ('<')
then, we have h<7
Antonio after working more than 9 hours.
More than symbol represented by ('>').
then, we have h>9
Since, we use inequalities when there is a range of possible answers for a given situation
Now, as per the given statement,
the inequalities can be written as one statement as; h<7 or h>9
True or false, the product of two rational numbers is never equal to 1.
Answers
The product of two rational numbers can indeed be equal to 1. For example, 2/3 (two-thirds) and 3/2 (three-halves) are both rational numbers, and their product is 1.
Explanation:The product of two rational numbers can indeed equal to 1. This is a False statement. For example, if we take 2/3 (two-thirds) and 3/2 (three-halves), both are rational numbers because they can be expressed as fractions, i.e., ratios of two integers. In this case, if we multiply these two numbers together, i.e., (2/3)*(3/2), we get 6/6, which equals 1. Therefore, it's possible that the product of two rational numbers can equal 1, hence proving the provided statement to be false.
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Sarah received $55 for her birthday. She used some of that money to buy 3 shirts priced at m dollars each.
How much money does Sarah have left?
Write your answer as an expression.
Answers
You could figure out the equation if the 3 were M and M had a number but this is unsolvable. SORRY
m=11
each shirt is $11
please help! I have a deadline tonight!!!!
Answers
y = 3/2x - 2
or
y = 1.5x - 2
To graph it, make a point at (0, -2) (the y-intercept).
Each unit to the right, increase the y axis by 1.5
Each unit to the left, decrease the y axis by 1.5
A sphere has a radius of 3 and a hemisphere has a radius of 6. Compare the ratio of the volume of the sphere to the volume of the hemisphere.
Answers
S/H=2rs^3/rh^3
S/H=(2*3^3)/6^3
S/H=54/216
S/H=1/4
So the volume of the hemisphere is 4 time the volume of the sphere.
V=4/3 π r³
V=4/3 π 3³ = 113.097335529
Volume of a Hemisphere:
V=½(4/3 π r³)
V=½(4/3 π 6³) = 452.389342117
113.097335529 to 452.389342117
Pretty much 1/4 right on the nuts (0.24999999999944737866981989309472)
I WILL GIVE BRAINLIEST
Julian compared numbers with similar digits. Using mathematical language, explain how each set of numbers is different
SET A: 13.542 and 35.42
SET B: 781 and 78.1
SET C: 1.2 and 01.20
Answers
Set B: Is the second number divided by 10
Set C: Is the same number
Zayed is helping his classmates get ready for their math test by making them identical packages of pencils and calculators. He has 72 pencils and 24 calculators and he must use all of the pencils and calculators. If Zayed creates the greatest number of identical packages possible, how many pencils will be in each package?
Answers
Answer:
3 pencils
Step-by-step explanation:
We are given Zayed is helping his classmates get ready for their math test by making them identical packages of pencils and calculators.
Number of pencils=72
Number of calculators=24
If Zayed creates the greatest number of identical packages
Then , we find GCF of 72 and 24
[tex]72=2\times 2\times 2\times 3\times 3[/tex]
[tex]24=2\times 2\times 2\times 3[/tex]
GCF=[tex]2\times 2\times 2\times 3[/tex]
Hence, Zayed creates 24 packages.
Number of pencils in each package=[tex]\frac{72}{24}=3[/tex]
Hence, 3 pencils and one calculator will be in each package .
Answer:
3 pencils
Step-by-step explanation:
What is the value of x/3y , when x = 18 and y = 3?
3/18
2
3
6
Answers
x = 18
y = 3
x/3y becomes 18/3(3) = 18/9 = 2
A quadrilateral has vertices A(3, 5), B(2, 0), C(7, 0), and D(8, 5). Which statement about the quadrilateral is true?
Answers
Daniel and Sofia both solve this system of equations: y = -1.5x + 5.7 y = 0.5x + 0.3 Daniel's solution is (1.1, 2.4). Sofia's solution is (2.7, 1.65). They graph the equations to check their work. Based on the graph, whose solution is more likely to be correct?Daniel is more likely to be correct. The x-coordinate of the intersection is between 1 and 2 and the y-coordinate of the intersection is between 2 and 3. Sofia is more likely to be correct. The x-coordinate of the intersection is between 2 and 3 and the y-coordinate of the intersection is between 1 and 2. or niether
Answers
y = 0.5x + 0.3
-1.5x + 5.7 = 0.5x + 0.3
-1.5x - 0.5x = 0.3 - 5.7
-2x = - 5.4
x = -5.4/-2
x = 2.7
y = 0.5x + 0.3
y = 0.5(2.7) + 0.3
y = 1.35 + 0.3
y = 1.65
solution is (2.7, 1.65)
Sophia is more likely to be correct because the x coordinate is between 2 and 3 and the y coordinate is in between 1 and 2
Answer:
Sofia is more likely to be correct
=)
Step-by-step explanation:
Point D represents a negative number. Which point represents the opposite of that number?
Answers
The negative number - 7 and its opposite number 7 are represented on the number line.
What is a number line?A number line refers to a straight line in mathematics that has numbers arranged at regular intervals or portions along its width. A number line is often shown horizontally and can be postponed in any direction.
Point D represents a negative number which is -7.
We know that if the number is 'a', then the opposite number of the number 'a' will be '-a'.
Then the point representing the opposite of that number will be given as,
⇒ -(-7)
⇒ 7
The negative number - 7 and its opposite number 7 are represented on the number line.
The diagram is given below.
More about the number line link is given below.
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The complete question is given below.
Point D represents a negative number which is - 7. Which point represents the opposite of that number?
Which is the general form of the equation of the circle shown? x2 + y2 + 4x – 2y – 4 = 0 x2 + y2 + 4x – 2y + 2 = 0 x2 + y² – 4x + 2y – 4 = 0 x2 + y² – 4x + 2y + 2 = 0
Answers
For the second picture, the center is (-2,1) and the radius is square root of 3.
For the third picture, the center is (2,-1) and the radius is 3.
For the last picture, the center is (2,-1) and the radius is square root of 3.
Answer:
THE ANSWER IS A
Step-by-step explanation:
517.21 km what is the nearest 10km?
Answers
Final answer: 520 km
Part A: Explain why the x-coordinates of the points where the graphs of the equations y = 4−x and y = 8−x−1 intersect are the solutions of the equation 4−x = 8−x−1. (4 points)
Part B: Make tables to find the solution to 4−x = 8−x−1. Take the integer values of x between −3 and 3. (4 points)
Part C: How can you solve the equation 4−x = 8−x−1 graphically? (2 points)
Answers
Part B: Just plug in number between -3-(3) for x
Part C: Solve the equation by drawing the slope of both equations and find where both lines intersect
Solve the system of equations.
11x+4y=-46
7x-4y=10
Answers
7x-4y=10
---------------add
18x = -36
x = -2
7x-4y=10
7(-2)-4y=10
-4x = 24
y = - 6
answer
(-2,-6)
The solution is x = -2 and y = -6.
What are linear equations?First-order equations are linear equations. The coordinate system defines the linear equations for lines. A linear equation in one variable is one in which there is only one variable and the equation has a homogeneous variable of degree 1. There can be more than one variable in a linear equation. When there are two variables in a linear equation, it is referred to as a "linear equation with two variables" and so on.
Given equations 11x + 4y = -46
and 7x - 4y = 10
add both equations
11x + 4y + 7x - 4y = -46 + 10
18x = -36
x = -36/18
x = -2
substitute the value of x in equation
11x + 4y = -46
11(-2) + 4y = -46
4y = -46 + 22
4y = -24
y = -6
Hence the solution for given equations is x = -2 and y = -6.
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Which are correct representations of the inequality 6x ≥ 3 + 4(2x – 1)? Check all that apply.
A=1 ≥ 2x
B=6x ≥ 3 + 8x – 4
and on a graph
.5 shaded to the left
- .5 shaded to the right
.5 shaded to the right
Answers
checking all that apply the correct answers would be A B and C
The correct answers are:
A) 1 ≥ 2x ; B) 6x ≥ 3 + 8x – 4 ; and .5 shaded to the left
Explanation:
Our inequality given is 6x ≥ 3 + 4(2x - 1). First we use the distributive property:
6x ≥ 3 + 4(2x) + 4(-1)
6x ≥ 3 + 8x - 4
This means A is correct.
Next we can subtract 8x from each side:
6x-8x ≥ 3+8x-4-8x
-2x ≥ 3-4
-2x ≥ -1
Divide both sides by -1 (remember to flip the inequality symbol):
-2x/-1 ≥ -1/-1
2x ≤ 1
This can also be written as 1 ≥ 2x, so B is correct.
To finish solving this, divide both sides by 2:
2x/2 ≤ 1/2
x ≤ 0.5
To graph this, we circle 0.5 and fill it in (since it is less than or equal to), and shade to the left (since it is less than).
Please help!! I attached an image, will give most brainliest
Answers
The stem is the value in the left and the leaf is the values listed on the right side of the table. In this case, it represents the tens and ones place.
The smallest of those values are 2 which is answer choice F.
Write 2 expressions that represent the areas of 4 triangles
Answers
Solve 2a 2 - 3a - 2 = 0
{-1/2, 2}
{1/2, -2}
{}
Answers
a^2-3a-4
(a-4)(a+1)
(a-2)(2a+1)
Find zeros
a-2=0
a=2
2a+1=0
2a=-1
a=-1/2
Final answer: {-1/2, 2}
What type of stock receives an equal part of the profits on each share to be distributed after all other obligations of a company have been satisfied?
Answers
how do you reduce the fraction of 28/49
Answers
reduce by 7
28/7 4
---- = ----
49/7 7
your answer will be: 4/7
hope this helps :D
28/7 4
---- = ----
49/7 7
your answer will be: 4/7
PLease Answer!
The Mali Empire of West Africa was known far and wide for the great wealth of its rulers. The empire fell in the year 1610.
Let x represent any year. Write an inequality in terms of x and 1610 that is true only for values of x that represent years after the year the Mali Empire fell.
Answers
The year 1610 is not inclusive as this is the year when the Empire fell
the answer is x>1610
how do you slove this problem
Answers
(a)=a
6x-4-(2x-8)
-(2x+8)=-2x-8
6x-4-2x-8
4x-12
I hope this is more clear
Pls solve 7x-4(6-x)+12 and show steps pls.
Answers
7× - 24 + 4x + 12
Combine like terms
7x + 4x -24 + 12
11x - 12
Connor is asked to find the probability of rolling a prime number on a die. He states that this is a simple event. True or false? A. True B. False
Answers
A triangle can have sides whose lengths are 9cm, 16cm, and
Answers
assuming that the lengths are not the hypotenuse, then we can square the two numbers.
81 + 256 = c^2
337 = c^2
√337 = c
to go into decimals, the answer would be: c = 18.358
____________________________
This would refer to a right triangle;
a² + b² = c² ;
In which : 3² + 4² = 5² ;
or: 9 + 16 = 25 .
_____________________________________
A cross section of a cone taken perpendicular to the base and intersecting the apex of the cone is what shape?
Answers
Answer:
The answer is a triangle.
Step-by-step explanation:
A cross section of a cone taken perpendicular to the base and intersecting the apex of the cone - The shape will be a triangle.
A cone has one circular base with two slant heights that are attached at the vertex. When it is cut in such a way that the cross-section is perpendicular to the base and it passes through the vertex or apex, then a triangle is formed.
For better visualization, you can also see the attached image.
A cross section of a cone taken perpendicular to the base and intersecting the apex of the cone - The shape will be a triangle.
The answer is a triangle.
A cross-section of a cone taken perpendicular to the base and intersecting the apex of the cone is a triangle.
When you cut a cone perpendicular to its base and through its apex, the resulting cross-section will be a triangle. The shape of the cross-section depends on the angle at which you make the cut. If the cut is parallel to one of the sides of the cone, the cross-section will be a right-angled triangle.
If the cut is made at an angle to the sides of the cone, the cross-section will be an isosceles or scalene triangle.
In any case, the cross-section will always be a triangular shape with its vertices at the apex of the cone and the points where the cut intersects the base of the cone.
A cone has one circular base with two slant heights that are attached at the vertex. When it is cut in such a way that the cross-section is perpendicular to the base and it passes through the vertex or apex, then a triangle is formed.
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A dance competition on television had five elimination rounds. After each elimination, only one-fourth of the contestants were sent to the next round. The table below shows the number of contestants in each round of the competition: x 1 2 3 4 5 f(x) 512 128 32 8 2 Compute the average rate of change of f(x) from x = 2 to x = 4 and describe what it represents.
−60 contestants per round, and it represents the average rate at which the number of contestants changed from the second round to the fourth round
−120 contestants per round, and it represents the average rate at which the number of contestants changed from the second round to the fourth round
−60 contestants per round, and it represents the number of contestants who will reach the final round
−120 contestants per round, and it represents the number of contestants who will reach the final round
Answers
When x = 4, f(x) = 8
The changing rate is [tex] \frac{8-128}{4-2}= \frac{-120}{2}=-60 [/tex]
This changing rate represents the decrease of the number of contestants as the competition approaches the final.
Correct option is the first option
−60 contestants per round and it represents the average rate at which the number of contestants changed from the second round to the fourth round
Answer:
A
Step-by-step explanation:
Simplify six to the -3rd power over six to the fifth power
Answers
In a casino, the chance of winning a certain game is 14.5%. If you play the game 20 times, what’s your best estimate for the number of times you would win? Round off your answer to the nearest whole number.
Answers
w=20(14.5/100)
w=20(0.145)
w=2.9
w≈3
So you would expect to win 3 times out of 20 attempts (rounded to the nearest whole number of wins)