You're an investigator for the National Transportation Safety Board, examining a subway accident in which a train going at 90 km/h collided with a slower train traveling in the same direction at 25 km/h . Your job is to determine the relative speed of the collision, to help establish new crash standards. The faster train's "black box" shows that it began negatively accelerating at 2.1 m/s2 when it was 48 m from the slower train, while the slower train continued at constant speed. whats the relative speed
Answers
The negative value shows that the quicker train is slowing down and was travelling at a speed approaching \(2.76 m/s\) when it collided with the slower train.
What is speed, for instance?You can determine an object's speed if you know how far it moves in a given length of time. For instance, an automobile is moving at a pace of 70 miles per hour if it covers 70 miles in a day (miles per hour).
Who established speed?Galileo Galilei, an Italian physicist, is credited as being the initial to calculate speed by dividing it by the distance travelled and the time required. Newton defined velocity as the amount of distance travelled in a given amount of time.
We can use the equation:
\(d = vi * t + 1/2 * a * t^2\)
where
\(d =\) distance between the two trains (\(48\) m)
\(vi =\) initial velocity of the faster train (\(90\) km/h \(= 25\) m/s)
\(a =\) acceleration of the faster train (\((-2.1 m/s^2)\))
Rearranging the equation to solve for t, we get:
t = (sqrt(vi^2 + 2ad) - vi) / a
Substituting the values, we get:
\(t = (\sqrt{(25^2 + 2*(-2.1)*48) - 25)} / (-2.1)\)
\(t = 6.02\) seconds
Now that we know the time, we can find the distance the faster train traveled before the collision:
distance \(= vi * t + 1/2 * a * t^2\)
distance \(= 25 * 6.02 + 1/2 * (-2.1) * (6.02)^2\)
distance \(= 124.11 m\) (rounded to two decimal places)
Finally, we can find the speed of the faster train at the moment of impact:
\(vf = \sqrt{(vi^2 + 2ad)}\)
\(vf = \sqrt{(25^2 + 2*(-2.1)*124.11)}\)
\(vf = 4.18 m/s\) (rounded to two decimal places)
Therefore, the relative speed of the collision is:
relative speed\(= (vf - vs) = (4.18 - 6.94) m/s = -2.76 m/s\)
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Related Questions
Aileen worked 35.5 hours last week. She earns $7.75 per hour. How much money did she make last week.
Answers
Answer:
275.125
Step-by-step explanation:
just multiply 35.5 with 7.75 and theres your answer
If you horizontally stretch the quadratic parent function, f(x) = x^2, by a factor
of 5, what is the equation of the new function?
Answers
Answer:
New functinon is g(x) = (1/32)x^5
Step-by-step explanation:
If you horizontally stretch the quadratic parent function, f(x) = x^2, by a factor
of 5, the equation of the new function will be g(x) = (x/5)^2, or g(x) = (1/32)x^5
Mr. Wilson has 30 students in his class. This is 12 more
students than Mr. Star has
How many students does Mr Star have
O A. ++30= 12
x=42 students
O B. **12=30
x= 72 students
O C. X+12=30
x=42 students
O D. x+12=30
x=18 students
Answers
Answer:
students of mr.wilson :30
students of Mr.star : 12 less than Mr.wilson
then, 30-12=18
A zip wire runs between two posts, 25m apart. The zip wire is at an angle of 10∘ to the horizontal. Calculate the length of the zip wire.
Answers
The length of the zip wire is approximately 25.42 meters.
To calculate the length of the zip wire, we can use trigonometry and the given information about the angle and the distance between the two posts.
Given:
Distance between the two posts: 25m
Angle of the zip wire to the horizontal: 10°
We can use the trigonometric function cosine (cos) to find the length of the zip wire. Cosine relates the adjacent side to the hypotenuse of a right triangle.
In this case, the adjacent side is the distance between the two posts (25m) and the hypotenuse is the length of the zip wire that we want to calculate.
Using the cosine function:
cos(angle) = adjacent/hypotenuse
cos(10°) = 25m/hypotenuse
To find the hypotenuse (length of the zip wire), we can rearrange the equation:
hypotenuse = 25m / cos(10°)
Using a calculator or trigonometric tables, we can find the value of cos(10°) to be approximately 0.9848.
Therefore, the length of the zip wire is:
hypotenuse = 25m / 0.9848 ≈ 25.42m
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the 7th grade fundraiser gives away a large container of gumballs to the student who is closest to guessing the correct number of gumballs in the container noticing that the container is a cube. Sally decides to count the number of gumballs along the length of one side if Sally get 729 gumballs how many gumballs did she count along one side of the container
Answers
If the container is a cube, every side is a square, so the length and the width are the same.
To get the number of gumballs based on the number of gumballs in one side, we can use the following equation
\(TotalGumballs=x^3\)Where x is the number of gumballs along one side. So, replacing the total by 729 and solving for x, we get:
\(\begin{gathered} 729=x^3 \\ \sqrt[3]{729}=x \\ 9=x \end{gathered}\)Answer: She counts 9 gumballs along one side of the container
-10 degrees Celsius is what Fahrenheit
Answers
Answer:
Step-by-step explanation:
i think if its -10 degrees i think the fahrenheit would be 50 degrees
PLEASE HELP!! 30 POINT!
What is the length of side s of the square shown below?
1450
6
s
90°
O A. 2
B. 6
O C. 16
Answers
Answer:
(E) 3(sq rt 2)
Step-by-step explanation:
the figure is a square so all four sides are equal and has 90 degree corners.
the diagonal has the value of 6 so:
6^2=s^2+s^2
36=2s^2
s^2=18 or sq rt 18 which would be 3(sq rt 2)
Round 765.2 to nearest hundreds
Answers
Help me please!!!! I really need this answer quickly
Answers
Answer:
X = 22
Step-by-step explanation:
This is a right triangle which means the angles add up to 90° total. So if 1 side is 15 and another side is 53 then 15 + 53 = 68 and 90 - 68 = 22 so X = 22 which is the missing side.
What is the circumference of this circle? Use π ≈ 3.14. Round your answer to the nearest tenth of a centimeter.
the diameter is 13
Answers
The circumference of the given circle is 41 cm
What is a circle?A circle is a round-shaped figure that has no corners or edges. In geometry, a circle can be defined as a closed, two-dimensional curved shape.
The circumference of a circle is the boundary length of the circle, it is basically the perimeter of the circle, in degree measure it can not exceed by 360°
Given that, a circle, with diameter, 13 cm, we need to find it circumference.
We know that, the circumference of a circle is given by,
Circumference of the circle = π × diameter
= 3.14 × 13
= 40.82
≈ 41 cm
Hence, the circumference of the given circle is 41 cm
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The tickets for the field trip were purchased yesterday for both students and instructors. Children tickets cost $9, adult tickets cost $11. The number of children tickets purchased was three more than ten times the number of adults tickets purchased. How many of each were purchased if all of the tickets cost a total of $936 dollars?
Answers
The 9 adult tickets and 93 children tickets were purchased.Let's assume the number of adult tickets purchased is "a" and the number of children tickets purchased is "c."
According to the given information, children tickets cost $9 and adult tickets cost $11. So, the total cost of children tickets is 9c, and the total cost of adult tickets is 11a.
The problem also states that the total cost of all the tickets is $936. Therefore, we can write the following equation:
9c + 11a = 936
Additionally, it is mentioned that the number of children tickets purchased was three more than ten times the number of adult tickets purchased:
c = 10a + 3
We can now solve this system of equations to find the values of "a" and "c." By substituting the value of "c" from the second equation into the first equation, we have:
9(10a + 3) + 11a = 936
90a + 27 + 11a = 936
101a = 936 - 27
101a = 909
a = 909 / 101
a = 9
Substituting this value back into the second equation, we find:
c = 10(9) + 3
c = 90 + 3
c = 93.
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About 217,000 high school students took the AP Statistics exam in 2017. The free-response section of the exam consisted of five open-ended problems and an investigative task. Each free-response question is scored on a 0 to 4 scale (with 4 being the best). For one of the problems, a random sample of 30 student papers yielded a mean score of x =1.267 and a standard deviation of 1.230. a. Find and interpret the standard error of the mean. b. Construct and interpret a 90% confidence interval to estimate the true mean score on this question.
Answers
The standard error is of 0.2246, which means that the mean scores for samples of 30 vary around 0.2246 from the mean.
What is a confidence interval?The confidence interval is the range of values that you expect your estimate to fall between a certain percentage of the time if you run your experiment again or re-sample the population in the same way.
The confidence interval formula is \(\bar x\pm t\frac{s}{\sqrt{n}}\).
Where, \(\bar x\) is the sample mean, t is the critical value, n is the sample size and s is the standard deviation for the sample.
Here,
\(\bar x\) =1.267, s=1.23, n=30
The standard error is Se= 1.23/√30
= 0.2246
Item a:
The standard error is of 0.2246, which means that the mean scores for samples of 30 vary around 0.2246 from the mean.
Item b:
Using a t-distribution calculator, considering a confidence level of 0.99 with 30 - 1 = 29 df, the critical value is t = 2.7564.
\(\bar x\pm tS_c\)
\(\bar x+ tS_c\) =1.267-2.7564(0.2246) =0.6479
\(\bar x- tS_c\) =1.267+2.7564(0.2246) =1.8861
Therefore, the 99% confidence interval to estimate the true mean score on this question is (0.6479, 1.8861). It means that we are 99% that the true mean score of all students in this question is between 0.6479 and 1.8861.
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Please help find length
Answers
Answer:
180
Step-by-step explanation:
to find the side of the smaller triangle you do \(5^{2}\) x \(12^{2}\) and get 3600. Then do\(\sqrt{} 3600\) and get 60. Since the larger triangle is 3 times that size you do 3 x 60 and get 180.
select the correct anwser from each drop down menu
in this graph the y intercept of the line is
the equation of the line is y=
Answers
Answer: -2=y
Step-by-step explanation:
Answer:
2-y
Step-by-step explanation:
The nutritional chart on the side of a box of a cereal states that there are 87 calories in a 3/4 cup serving. How many calories are in 8 cups of the cereal?
Answers
Answer:
Total calories in 8 cup = 928 calories
Step-by-step explanation:
Given:
Calories in 3/4 cup of cereal = 87 calories
Find:
Total calories in 8 cup
Computation:
Total calories in 8 cup = 8 x 87 x [4/3]
Total calories in 8 cup = 928 calories
Which answers describe the shape below? Check all that apply.
A. Parallelogram
B. Rectangle
C. Square
D. Rhombus
E. Trapezoid
F. Quadrilateral
Answers
Answer:
Parallelogram.
Step-by-step explanation:
Because parallelogram has its opposite sites equal.
Which of these coordinate pairs are on the same vertical line?
A
(0, 3) and (16, 3)
B
(3, 2) and (-3, -2)
C
(4, 1) and (-4, 6)
D
(3, 1) and (3, -12)
Answers
Answer:
D
Step-by-step explanation:
Answer:
D is ur answer
Step-by-step explanation:
a pile of coins, consisting of quarters and half dollars is worth $11.75. If there are 2 more quarters than half dollars, how many of each are there?
Answers
Answer:
Hope it helps ..and ☆HAPPY New year MY DEAR ☆
Step-by-step explanation:
Let the number of half dollars be x,
number of quarters = x + 2
amount of half dollars = 0.5x
amount of quarters = 0.25(x + 2)
= 0.25x + 0.5
total amount = 0.5x + 0.25x + 0.5
= 0.75x + 0.5
0.75x + 0.5 = 11.75
0.75x = 11.25
x = 15
number of quarters = x + 2
= 15 + 2
= 17
There are 17 quarters and 15 half dolla
17 quarters, 15 half dollars
Step-by-step explanation:
Find the inverse for the relation.{ (-5,7), (-6, -8), (1, -2), (10, 3) }
Answers
Answer:
{(7, -5), (-8, -6), (-2, 1), (3, 10)}Step-by-step explanation:
The inverse for the relation (a, b) is (b, a).
Therefore the inverse for the relation
{(-5, 7), (-6, -8), (1, -2), (10, 3)}is
{(7, -5), (-8, -6), (-2, 1), (3, 10)}{(7, -5), (-8, -6), (-2, 1), (3, 10)} is the inverse for the relation { (-5,7), (-6, -8), (1, -2), (10, 3) }.
What are coordinates?A pair of numbers called coordinates are used to locate a point or a form in a two-dimensional plane. The x-coordinate and the y-coordinate are two numbers that define a point's location on a 2D plane.
Given, few coordinates { (-5,7), (-6, -8), (1, -2), (10, 3) }
We need to find inverse relation of these coordinates.
Since, The inverse of a relation is a relation obtained by interchanging or swapping the elements or coordinates of each ordered pair in the relation.
Inverse relation in sets can be defined using the ordered pairs. The domain and range of an inverse relation can be written by swapping the domain and range of that relation. That means the domain of relation will be the range of its inverse, and the range of relation will be the domain of its inverse.
The inverse for the relation (a, b) is (b, a).
Therefore, the inverse for the relation { (-5,7), (-6, -8), (1, -2), (10, 3) } is:
{(7, -5), (-8, -6), (-2, 1), (3, 10)}
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which expression have a value of 2/3
A: 8+(24 divided by 12) X 4
B:8+24 divided by (12X4)
C: 8+24 divided 12X4
D: (8+24) divided (12X4)
Answers
32 / 48 =2/3
32% of 120 is 38.4. pls help
Answers
Answer:
Step-by-step explanation:
pls finish question first
A negative number on the x-axis (-a, b) would move in what direction?
A positive number on the x-axis (+a, b) would move in what direction?
A negative number on the y-axis (a, -b) would move in what direction?
A positive number on the y-axis (a, +b) would move in what direction?
Please answer for points and brainliest!
Answers
a) A negative number on the x-axis (-a, b) would move in the left direction by one unit.
To find out why, check point (0, b) on the y-axis and point (-a, b) on the x-axis.
The distance between these two points is a unit, meaning that the point (-a, b) is one unit to the left of the point (0, b).
b) A positive number on the x-axis (+a, b) would move in the right direction by a unit.
Again, let's look at the point (0, b) on the y-axis and the point (+a, b) on the x-axis.
The distance between the two points is also one unit, which means the point (+a, b) is one unit to the right of the point (0, b).
c) A negative number on the y-axis (a, -b) would move in the downward direction by b units.
Assume that point (a, 0) is on the x-axis and point (a, -b) is on the y-axis. The distance between them is b units, which means that the point (a, -b) is b units below the point (a, 0).
d) A positive number on the y-axis (a, +b) would move in the upward direction by b units.
Also, check the point (a, 0) on the x-axis and point (a, +b) on the y-axis. The distance between these two points is b units, which means that the point (a, +b) is b units above the point (a, 0).
What is a number?A number is a mathematical term used to show the quantity or value of a thing. It can be depicted using numerals, symbols, or words.
Examples include 30, hundred, -8, 6x, "5", 0.67, etc.
Numbers can be Positive - numbers greater than zero, or negative - numbers less than zero.
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Question 12(Multiple Choice Worth 2 points)
(Writing Two-Step Equations MC)
A new gaming chair costs $455.95. You have already saved $136.45 and earn $35.50 each week babysitting. Write and solve an equation to determine how many weeks, w, you must babysit to earn enough money to buy the new gaming chair.
35.5 + 136.45w = 455.95; w = 9
35.5w + 136.45 = 455.95; w = 9
35.5w − 136.45 = 455.95; w = 17
35.5w − 455.95 = 136.45; w = 17
Answers
The equation that represents the number of weeks that is needed to baby sit to buy gaming chair is 35.5w + 136.45 = 455.95; w = 9 , the correct option is (b) .
In the question ,
it is given that
the cost of the gaming chair = $455.95
amount of money already saved for the gaming chair = $136.45
amount of money earned by baby sitting each week = $35.50 .
let the number of weeks required to baby sit is " w " .
the equation can be represented by
cost of chair = money saved + money earned in w weeks
Substituting the values from above ,
we get
455.95 = 136.45 + 35.5w
On solving further ,
136.45 + 35.5w = 455.95
35.52w = 455.95 - 136.45
35.52w = 319.5
w = 319.5 / 35.52
w = 8.99
w ≈ 9
the number of weeks = 9
Therefore , The equation that represents the number of weeks that is needed to baby sit to buy gaming chair is 35.5w + 136.45 = 455.95; w = 9 .
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(a) Write an equation in terms of x that represents the problem.
(b) Solve the problem.
The difference of a number and 16 is the same as the product of the number and 3. Find the number.
Answers
Answer:
-8
Step-by-step explanation:
x - 16 = 3x
Solve for x
-2x = 16
x = -8
Determine which set of side measurements could be used to form a right triangle.
4, 11, 20
16, 21, 25
5, 13, 25
3, 4, 5
Answers
The set of side measurements that could be used to form a right triangle is 3, 4 and 5 option (D) is correct.
What is a right-angle triangle?
It is a triangle in which one of the angles is 90 degrees and the other two are sharp angles. The sides of a right-angled triangle are known as the hypotenuse, perpendicular, and base.
It is given that:
The side length of the triangle is shown in the option:
As we know,
Pythagoras' theorem is the square of the hypotenuse in a right-angled triangle is equal to the sum of the squares of the other two sides.
Using Pythagoras' theorem:
From option(D):
3, 4 and 5
(3)² + (4)² = 5²
9 + 16 = 25 (True)
Thus, the set of side measurements that could be used to form a right triangle is 3, 4 and 5 option (D) is correct.
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Line k has a slope of 2/3. Find the slope of a line parallel to line k.
Answers
Answer:
We have to remember
slope = m
if the slope of line is parellel so it will be the same with other slope
m1= m2
2/3= 2/3
so the answer is 2/3
hope it helps ^°^
Answer:
2/3
Step-by-step explanation:
Parallel lines have the same slopes. Therefore,
\(m_{k} =m_{p}\)
The slope of line k (\(m_{k}\)) will be equal to the slope of the line parallel to k (\(m_{p}\)).
We know that the slope of line k is 2/3.
\(m_{k}=\frac{2}{3}\)
Therefore, the slope of the line parallel to line k is also 2/3.
\(\frac{2}{3}=m_{p}\)
The slope of a line parallel to line k is 2/3.
Translate this sentence into an equation.
Answers
Answer:
24 + c = 40
C= Chau’s height
If x, y, and z are positive integers and 3x=4y=7z, then the least possible value of x+y+z is?
A. 33
B. 40
C. 49
D. 61
E. 84
Answers
Answer:
D
Step-by-step explanation:
3x, 4y, and 7z must be equal to the LCM of 3, 4, and 7 in order to be the smallest value. The LCM is 84 which means x = 28, y = 21 and z = 12. 28 + 21 + 12 = 61.
Answer:
61
Step-by-step explanation:
3x=4y=7z
x =4/3 y
x = 7/3 z
Since they have to be integers
y and z must be multiples of 3
y = 7/4 z
Since they have to be integers
z must be multiple of 4
Z must be a multiple of 12
Let z = 12
Then
y = 7/4 *12
y = 21
x = 7/3 *12
x = 28
x+y+z
28+ 21+12
61
Lmk.................
Answers
Answer:
A) 8t
Step-by-step explanation:
I hope this helps :)
My dog, Crash, can run 2/3 of a mile in 7 minutes. How many minutes does it take him to run one mile.
Answers
Answer:
10 1/2 minutes
Step-by-step explanation:
Becuase 7/2=3.5 then 7+3.5=10.5