Answer:
a. The distance the train travelled in the first hour is approximately 28.3 miles
b. The location of the train at 5:00 p.m. is 53 miles east, and 46 miles west
c. The location of the train at any given time by the function, f(t) = (-8 + 24·t, -10 + 15·t)
d. The train does not collide with the cyclist when the bike goes over the train tracks
Step-by-step explanation:
a. The given information on the train's motion are;
The location south the train is spotted = 10 miles south and 8 miles west
The time the observer spotted the train = 2:00 pm
The location the train is spotted at 3:00 p.m. = 5 miles north and 16 miles east
Therefore, the difference between the two times the train was spotted, t = 3:00 p.m. - 2:00 p.m. = 1 hour
Making use of the coordinate plane for the two locations the train was spotted, we have;
The initial location of the train = (-10, -8)
The final location of the train = (5, 16)
Therefore the distance the train travelled in the first hour is given by the formula for finding the distance, 'd', between two points, (x₁, y₁) and (x₂, y₂) as follows;
[tex]d = \sqrt{\left (x_{2}-x_{1} \right )^{2}+\left (y_{2}-y_{1} \right )^{2}}[/tex]
Therefore;
[tex]d = \sqrt{\left (5-(-10) \right )^{2}+\left (16-(-8) \right )^{2}} = 3 \cdot\sqrt{89}[/tex]
The distance the train travelled in the first hour, d = 3·√89 ≈ 28.3 miles
b. The speed of the train, v = (Distance travelled by the train)/Time
∴ v ≈ 28.3 miles/(1 hour) = 28.3 miles per hour
The speed of the train in the first hour, v ≈ 28.3 mph
The direction of the train, θ, is given by the arctangent of the slope, 'm', of the path of the train;
[tex]\therefore The \ slope \ of \ the \ path \ of \ the \ train, \, m =tan(\theta) = \dfrac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
∴ m = tan(θ) = (5 - (-10))/(16 - (-8)) = 0.625
c. Distance = Velocity × Time
At 5:00 p.m., we have;
The time difference, Δt = 5:00 p.m. - 3:00 p.m. = 2 hours
The distance, d₁ = (28.3 mph × 2 hours = 56.6 miles
Using trigonometry, we have the horizonal distance travelled, 'Δx', in the 2 hours is given as follows;
Δx = d₁ × cos(θ)
∴ Δx = 56.6 × cos(arctan(0.625)) ≈ 48
The increase in the horizontal position of the train, relative to the point (5, 16), Δx ≈ 48 miles
The vertical distance increase in the two hours, Δy is given as follows;
Δy = 56.6 × sin(arctan(0.625)) ≈ 30
The increase in the vertical position of the train, relative to the point (5, 16), Δy ≈ 30 miles miles
Therefore; the location of the train at 5:00 p.m. = ((5 + 48), (16 + 30)) = (53, 46)
The location of the train at 5:00 p.m. = 53 miles east, and 46 miles west
c. The function, 'f', that would give the train's position at time-t is given as follows;
The P = f(28.3·t, θ)
Where;
28.3·t = √(x² + y²)
θ = arctan(y/x)
Parametric equations
y - 5 = 0.625·(x - 16)
∴ y = 0.625·x - 10 + 5
The equation of the train's track is therefore, presented as follows;
y = 0.625·x - 5
d = 28.3·t
The y-component of the velocity, [tex]v_y[/tex] = 3*√89 mph × sin(arctan(0.625)) = 15 mph
Therefore, we have;
y = -10 + 15·t
The x-component of the velocity, vₓ = 3*√89 mph × cos(arctan(0.625)) = 24 mph
Therefore, we have;
x = -8 + 24·t
The location of the train at any given time, 't', f(t) = (-8 + 24·t, -10 + 15·t)
d. The speed of the cyclist next to the observer at 2:00 p.m., v = 10 mph
The distance of the cyclist from the track = The x-intercept = 5/0.625 = 8
The distance of the cyclist from the track = 8 miles
The time it would take the cyclist to react the track, t = 8 miles/10 mph = 0.8 hours
The location of the train in 0.8 hours, is f(0.8) = (-8 + 24×0.8, -10 + 15×0.8)
∴ f(0.8) = (11.2, 2)
At the time the cyclist is at the track along the east-west axis, at the point (8, 0), the train is at the point (11.2, 2) therefore, the train does not collide with the cyclist when the bike goes over the train tracks.
If the cyclist is travelling at 10 mph the train does not collide with the cyclist when the bike goes over the train tracks.
The location south the train is spotted = 10 miles south and 8 miles west
The time the observer spotted the train = 2:00 pm
The location of the train is spotted at 3:00 p.m. = 5 miles north and 16 miles east
Thus, the difference between the two times the train was spotted,
t = 3:00 p.m. - 2:00 p.m. = 1 hour
What is the distance?The distance is the product of velocity and time.
Distance = Velocity × Time
The initial location of the train = (-10, -8)
The final location of the train = (5, 16)
Therefore the distance the train travelled in the first hour
[tex]d = \sqrt{(x_{2} -x_{1} )^{2} +(y_{2} -y_{1} )^{2} } \\d = \sqrt{(5 -(-10) )^{2} +(16-(-8) )^{2} }[/tex]
d = 3√89
The distance the train travelled in the first hour, d = 28.3 miles
b. The speed of the train, v = (Distance travelled by train)/Time
∴ v ≈ 28.3 miles/(1 hour) = 28.3 miles per hour
The speed of the train in the first hour, v ≈ 28.3 mph
The direction of the train, θ, is given by the arc tangent of the slope, 'm', of the path of the train;
∴ m = tan(θ) = (5 - (-10))/(16 - (-8))
m = 0.625
c. Distance = Velocity × Time
At 5:00 p.m., we have;
The time difference, Δt = 5:00 p.m. - 3:00 p.m. = 2 hours
The distance, d₁ = (28.3 mph × 2 hours = 56.6 miles
Using trigonometry, we have the horizontal distance travelled, 'Δx', in the 2 hours is given as follows;
Δx = d₁ × cos(θ)
∴ Δx = 56.6 × cos(arctan(0.625)) ≈ 48
The increase in the horizontal position of the train, relative to the point (5, 16), Δx ≈ 48 miles
The vertical distance increase in the two hours, Δy is given as follows;
Δy = 56.6 × sin(arctan(0.625)) ≈ 30
The increase in the vertical position of the train, relative to the point (5, 16), Δy ≈ 30 miles miles
Therefore; the location of the train at 5:00 p.m. = ((5 + 48), (16 + 30)) = (53, 46)
The location of the train at 5:00 p.m. = 53 miles east, and 46 miles west
c. The function, 'f', that would give the train's position at time-t is given as follows;
The P = f(28.3·t, θ)
28.3·t = √(x² + y²)
θ = arctan(y/x)
Parametric equations
y - 5 = 0.625·(x - 16)
∴ y = 0.625·x - 10 + 5
The equation of the train's track is, therefore, presented as follows;
y = 0.625·x - 5
d = 28.3·t
The y-component of the velocity,
= 3 × √89 mph × sin(arctan(0.625)) = 15 mph
Therefore, we have
y = -10 + 15·t
The x-component of the velocity,
vₓ = 3 × √89 mph × cos(arctan(0.625))
= 24 mph
Therefore, we have;
x = -8 + 24·t
The location of the train at any given time, 't',
f(t) = (-8 + 24·t, -10 + 15·t)
d. The speed of the cyclist next to the observer at 2:00 p.m., v = 10 mph
The distance of the cyclist from the track = The x-intercept
= 5/0.625 = 8
The distance of the cyclist from the track = 8 miles
The time it would take the cyclist to reach the track, t = 8 miles/10 mph = 0.8 hours
The location of the train in 0.8 hours, is f(0.8)
= (-8 + 24×0.8, -10 + 15×0.8)
∴ f(0.8) = (11.2, 2)
therefore, If the cyclist is travelling at 10 mph the train does not collide with the cyclist when the bike goes over the train tracks.
Learn more about distance;
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Help me with this problem ASAP
What is the MEAN of the data - (12, 8, 6, 12, 16, 12) *
helppp
Answer: the mean is 11
Step-by-step explanation:
Answer:
11
Step-by-step explanation:
Add them all together then divide by the nuber of variables
anyone know ??? i need help badly right now
Answer:
Answer is A 520mm²
I hope you like it
Answer:
9. C, II and III.
10. The correct answer is 944 cubic mm, as far as I can tell. I double checked my formulas and calculations. You can copy the formulas/calculations below and email your teacher. I have tried to figure out how they got the numbers they have. The best guess I can come up with is that they used 6 as the diameter of the cylinder, using 3 for the radius. That gets us closer, at 749 cubic mm, but not quite there.
Step-by-step explanation:
9. If the cylinder is standing upright, the horizontal cut would be a circle or oval, and the vertical cut could be a rectangle
10. First we'll get the volume of the base rectangle. Then we'll calculate the volume of a cylinder, then divide that part in half, because it's 1/2 a cylinder on top of a rectangular prism.
Volume of a rectangular prism:
V = (length)(width)(height)
= 11 x 9 x 6 = 594 cubic mm
Volume of a cylinder:
V = (pi)(radius)^2(height)
The radius = 1/2 the diameter of the circle...the diameter is 9, so the radius is 4.5
= (3.14)(4.5)(4.5)(11)
= 699.435
That would be for a full cylinder with radius 4.5 and height of 11. We have half of one, so 699.435/2 = 349.7175 cubic mm
Add the volume of the 1/2 cylinder to the volume of the rectangular prism:
349.7175 + 594 = 943.7175, rounded = 944...which is none of your answers :/
Sorry I couldn't give you an "A, B, C, D" answer, but I don't think any of those are correct.
how to do this question plz answer
A man travels 2 miles, turn left and travels 3 miles, turn left again and travel 6 miles. How far is he from the starting point?
Answer: 5 miles
Step-by-step explanation:
this creates a polygon which can be shortened to be a triangle with side lengths 3 and 4 and the hypotenuse unknown. to find the side length you use the formula a^2 + b^2 = c^2
3^2 + 4^2 = c^2
9 + 16 = c^2
25 = c^2
sqrt(25) = c
c = 5
Please answer! I will mark you Brsinliest! The pictures are together.
Answer:
V = 65.97π
Step-by-step explanation:
Answer:
g00gle is a really great source for these questions!
Just put in the information and they do they work!
Step-by-step explanation:
66 inches cubed since you round up .03 decimals!
or 65.97 if you aren't supposed to round
f(x) = -x^(4)
Identify the function as a translation, compression, stretch, or reflection
Answer: don't know the answer but I hope this helps.
Step-by-step explanation:
Devin is making a candle by pouring melted wax into a mold in the shape of a square pyramid. Each side of the base of the pyramid is 6 cm and the height of the pyramid is 9 cm. To get the wax for the candle, Devin melts cubes of wax that are each 4 cm by 4 cm by 4 cm. How many of the wax cubes will Devin need in order to make the candle? Show your work.
The volume of the square pyramid is 6 x 6 x 9/3 = 108 cubic cm.
Volume of the cube = 4 x 4 x 4 = 64 cubic cm
Number of cubes needed: 108/64 = 1 11/16 cubes (1.6875)
Answer:
Solution given:
square pyramid
each side of base[b]=6cm
height[h]=9cm
Volume of square pyramid[V]=[tex] \frac{1}{3 } {b}^{2} h \\ \frac{1}{3} {6}^{2} \times 9 = 108cm ^{3} [/tex]
now
length of cube [l]=4cm
volume of cube[v]=l³=4³=64cm³
now
no of wax needed=[tex] \frac{V}{v} [/tex]=[tex] \frac{108cm³}{64cm³} [/tex]=[tex] \frac{27}{16 } =1\frac{11}{16} [/tex]
is needed.
The equation of the scatter plot trend line is y = -1700x + 32000 where y is the value of the car in dollars and x is the age of cars in years. Use the trend line equation to predict the value of a car after 7 years.
Answer:
20100
Step-by-step explanation:
According to the scenario, computation of the given data are as follows,
Given equation
y = -1700x + 32000
Where x is the age of car and y is the value of the car.
Then value after 7 years can be calculated as follows,
y = -1700 (7) + 32000
y = -11900 + 32000
y = 20,100
So, the value of car after 7 years will be 20100.
What problems did Title IX address? Check all that apply.
lack of support for international students
limited opportunities for female athletes
limited resources in scientific courses of study
lack of scholarships and championships for women in sports
limited resources and facilities for women
Answer:
limited resources and facilities for women
lack of scholarships and championships for women
limited opportunities for female athletes
2,4,5
Statement two, four, and five are correct title IX law mandates institutions to obtain federal assistance to combat gender-based violence and harassment and respond to survivors' needs.
What is Title IX?Title IX is a potent instrument for fighting campus violence because it is a federal (national) legislation. To ensure that all students have equal access to education, the law mandates institutions to obtain federal assistance to combat gender-based violence and harassment and respond to survivors' needs.
As per the Title IX law:
Limited opportunities for female athletes.Lack of scholarships and championships for women in sports.Limited resources and facilities for women.Thus, statement two, four, and five are correct title IX law mandates institutions to obtain federal assistance to combat gender-based violence and harassment and respond to survivors' needs.
Learn more about the Titel IX law here:
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Find the 11th term of the geometric sequence 6, -18, 54, ...
Answer:
354294
Step-by-step explanation:
Use the formula
[tex]a_{n} = a_{1} r^{n - 1}[/tex]
In your problem [tex]a_{1}[/tex] = 6 r = -3 n = 11
11th term = [tex]a_{11}[/tex] = [tex]6(-3)^{11 - 1} = 6(-3)^{10}[/tex] = 6(59049)
= 354294
Pls help if you know the answer and explain, if you get it right I'll give you brainly
find the volume of the larger rectangular prism
Answer:
1/8 to the power of 3
Step-by-step explanation:
its 1/2 length x 1/2 width x 1/2 height
can you please help? no links please. I have to pass this
Answer:
Step-by-step explanation:
10 times 10 times 60 = 6000
6000 - (1600 + 2000) = 2,400
Answer:
7200 [tex]in^3[/tex]
Step-by-step explanation:
volume of the bottom + volume of the middle part + volume of the top part (I'm sorry this is so vague T-T)
[tex](8*60*10)+(2*40*10)+(8*20*10)= 4800+800+1600=7200[/tex]
I need help please !!!
Answer:
isosceles triangle
Step-by-step explanation:
the first one is isosceles triangle
ASAPPPPPPPP DUE IN 3 MIN
Answer:
72
Step-by-step explanation:
Answer:
h = 6
Step-by-step explanation:
Area of a trapezoid formula:
[tex]A=\frac{a+b}{2} *h\\\\h=2*\frac{A}{a+b}[/tex]
Given:
A = 48
a = 4
b = 12
Work:
[tex]h=2*\frac{A}{a+b} \\\\h=2*\frac{48}{12+4} \\\\h=2*\frac{48}{16}\\\\h=2*3\\h=6[/tex]
A simple random sample from a population with a normal distribution of 103 body temperatures has x = 98.30°F and s = 0.61°F. Construct a 95% confidence interval estimate of the standard deviation of body temperature of all healthy humans.
Answer:
(98.2884 ; 98.3116)
Step-by-step explanation:
Given :
x = 98.30°F and s = 0.61°F
Sample size. n = 103
Zcritical at 95% = 1.96
Using the confidence interval relation :
x ± margin of error
Margin of Error :
Zcritical * s/√n
1.96 * 0.61/√103 = 0.0116
Lower boundary = (98.30 - 0.0116) = 98.2884
Upper boundary = (98.30 + 0.0116) = 98.3116
(98.2884 ; 98.3116)
help please? anyone?
Answer:
"so i need to find e missing side of each right triangle, side c is the hypotenuse!! a = 8.8ft, b= 9ft i have to round the answers to the nearest tenth if necessary "
Step-by-step explanation:
Sure! So remember that the Pythagorean theorem is a squared plus b squared = c squared.
= 8.8 squared + 9 squared = c squared
= 77.44 + 81 = c squared
[tex]\sqrt{158.44}[/tex] = c squared
c squared = (rounded) 12.6 ft
7. The answer is letter A or letter D
Find the next two terms in the sequence.
40, 10, –20, –50, . . .
A.
60, 80
B.
–80, –110
C.
–70, –100
D.
–70, –90
Answer:
B.
–80, –110
Step-by-step explanation:
-80 and -110
It is an arithmetic sequence. The difference = -30. It is the difference between each number in the sequence: 10-40=-30
-50-30=-80
-80-30 =-110
-80
First Identify the sequence being made here.
10-40 = -30
-20-10 = -30
-50-(-20) = -30
Therefor this pattern is decreasing by a rate of 30 so to continue this, just subtract 30 from -50.
-50-30 = -80
The next term is -80.
Hope I helped!
I need help with this question
Answer:
I thinks its F because you cant factor it
Step-by-step explanation:
Answer:
F) The expression does not have a real factor
2x-2y>6 in y=Mx+b form
Answer:
y=−x+3
Step-by-step explanation:
The slope-intercept form is y=mx+b, where m is the slope and b
is the y-intercept.
y=mx+b
Please someone help I need to turn this in soon !!
Answer:
6
Step-by-step explanation:
18/3=6
Work out size of Angle x
Answer:
106
Step-by-step explanation:
all 3 of the angles add up to 360
you already know one is 164 and one is a right angle so
164 + 90 = 254
360 - 254 = 106
what's the area of this shape
Answer:
L x W x H
Step-by-step explanation:
if my calculations are correct the length is 2 the width is 3 and the height is 3
Therefore the answer is (2 x 3) = 6 x3
So the answer is 18.
Hope it helps, if it is incorrect than i am extremely sorry, wish you the best of luck and have a great day/midday/evening. BYYEEEEEEE
What is the value of x?
a . 75
b . 25.5
c . 8
d . 4.5
help meeee
Answer:
d. 4.5
Step-by-step explanation:
10x-5=16x+22
-22 -22
10x-27=16x
-10x -10x
-27=6x
x=4.5
Simplify this expression
(√2+√3)(√5 -√7)
Answer:
Step-by-step explanation:
Answer:
pretty sure its the second one
Step-by-step explanation:
Please help me so i don't fail :(
Answer:
y = 2x + 6
Step-by-step explanation:
slope-intercept form => y = mx + b
substitute two of the (x, y) into the equations: y = mx + b to solve for m and b
=> 0 = -3m + b, 6 = 0m + b
6 = 0m + b => b = 6
substitute b = 6 into 0 = -3m + b to solve for m:
=> 0 = -3m + 6 => -3m = -6 => m = 2
plug in b = 6 and m = 2 into the equation y = mx + b:
=> y = 2x + 6
Suppose a runner travels 5200 feet in 5 minutes. At what rate does she run?
Answer:
1040 ft./min
Step-by-step explanation:
It's Right :)
What is 1?1?1?1=6 pls help my brain id hurt rn
Answer:
(1+1+1)!*1=6
Step-by-step explanation:
what is the sale price of $149 sneakers with 15% off?
Answer: $ 126.65
Step-by-step explanation:
149/100)*15 =
(149*15)/100 =
2235/100 = 22.35
15% of $149 is 22.35
so ,
real price-15% of real price= sale preice
$149-$22.35=$126.65
Answer:
$ 126.65
Step-by-step explanation:
$ 149 multiply 15 % which is 0.15
Which is $ 22.35
Take $ 149 - $22.35 = $126.65
Match the equivalent expressions.
Pls help me
Answer:
1/9 = 3^-2
1/8 = 2^-3
9 = 3²
8 = 2³