A freight and passenger train share the same track. The average speed of the freight train is 45 mph, whereas that of the passenger train is 70 mph. The passenger train is scheduled to leave 20 minutes after the freight train departs from the same station. Determine the location where a siding would need to be provided to allow the passenger train to pass the freight train. Also determine the time it takes for the freight train to arrive at the siding. As a safety precaution, the separation headway between the two trains at the siding should be at least equal to 6 minutes.

Answer: 2.3 repeating

Please mark me as Brainliest

Answer:

Your answer is absolutely correct

Step-by-step explanation:

The work would be as follows:

[tex]\int _0^{\sqrt{\pi }}4x^3\cos \left(x^2\right)dx,\\\\\mathrm{Take\:the\:constant\:out}:\quad \int a\cdot f\left(x\right)dx=a\cdot \int f\left(x\right)dx\\=> 4\cdot \int _0^{\sqrt{\pi }}x^3\cos \left(x^2\right)dx\\\\\mathrm{Apply\:u-substitution:}\:u=x^2\\=> 4\cdot \int _0^{\pi }\frac{u\cos \left(u\right)}{2}du\\\\\mathrm{Apply\:Integration\:By\:Parts:}\:u=u,\:v'=\cos \left(u\right)\\=> 4\cdot \frac{1}{2}\left[u\sin \left(u\right)-\int \sin \left(u\right)du\right]^{\pi }_0\\\\[/tex]

[tex]\int \sin \left(u\right)du=-\cos \left(u\right)\\=> 4\cdot \frac{1}{2}\left[u\sin \left(u\right)-\left(-\cos \left(u\right)\right)\right]^{\pi }_0\\\\\mathrm{Simplify\:}4\cdot \frac{1}{2}\left[u\sin \left(u\right)-\left(-\cos \left(u\right)\right)\right]^{\pi }_0:\quad 2\left[u\sin \left(u\right)+\cos \left(u\right)\right]^{\pi }_0\\\\\mathrm{Compute\:the\:boundaries}:\quad \left[u\sin \left(u\right)+\cos \left(u\right)\right]^{\pi }_0=-2\\=> 2(-2) = - 4[/tex]

Hence proved that your solution is accurate.

Answer:

[tex]\int\limits^{\sqrt{\pi}}_0 {4x^3\cos(x^2)} \, dx=-4[/tex]

Step-by-step explanation:

So we have the integral:

[tex]\int\limits^{\sqrt{\pi}}_0 {4x^3\cos(x^2)} \, dx[/tex]

As told, let's use u-substitution first and then use integration by parts.

For the u-substitution, we can let u to be equal to x². So:

[tex]u=x^2[/tex]

Differentiate:

[tex]du=2x\, dx[/tex]

We can rewrite our integral as:

[tex]\int\limits^{\sqrt{\pi}}_0 {2x(2x^2)\cos(x^2)} \, dx[/tex]

Therefore, by making our u-substitution, our integral is now:

[tex]\int\limits {2u\cos(u)} \, du[/tex]

We also need to change our bounds. Substitute them into u. So:

[tex]u=\sqrt{\pi}^2=\pi\\u=(0)^2=0[/tex]

Therefore, our integral with our new bounds is:

[tex]\int\limits^{\pi}_{0} {2u\cos(u)} \, du[/tex]

Now, let's use integration by parts. Integration by parts is given by:

[tex]\int\limits {v}\, dy=vy-\int y\, dv[/tex]

(I changed the standard u to y because we are already using u).

Let's let v be 2u and let's let dy be cos(u). Thus:

[tex]v=2u\\dv=2\,du[/tex]

And:

[tex]dy=\cos(u)\\y=\sin(u)[/tex]

So, do integration by parts:

[tex]=2u\sin(u)-\int \sin(u)2\,du[/tex]

Simplify:

[tex]=2u\sin(u)-2\int \sin(u)\,du[/tex]

Evaluate the integral:

[tex]=2u\sin(u)+2\cos(u)[/tex]

Now, use the bounds. So:

[tex](2(\pi)\sin(\pi)+2\cos(\pi))-(2(0)\sin(0)+2\cos(0))[/tex]

Evaluate:

[tex]=(2\pi(0)+2(-1))-(0(0)+2(1))[/tex]

Simplify:

[tex]=(-2)-(2)[/tex]

Subtract:

[tex]=-4[/tex]

And we're done!

Answer:

Center: (0, 0)

Radius: 4

Step-by-step explanation:

Circle Standard Equation: (x - h)² + (y - k)² = r²

(h, k) is center

r is radius

We see that our h and our k are both 0.

∴ Our center is (0, 0), origin.

We see that our r² = 16

√r² = √16

∴ Our radius is equal to 4

Answer:

Step-by-step explanation:

(x₁ , y₁) = (-3.1  , -2.8)   & (x₂ , y₂) = (-4.92 , - 3.3)

[tex]Midpoint=(\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2})\\\\\\=(\frac{-3.1-4.92}{2},\frac{-2.8-3.3}{2})\\\\\\=(\frac{-8.02}{2},\frac{-6.1}{2})\\\\\\=( -4.01 , -3.05)[/tex]

Answer:

$24.400

Step-by-step explanation:

it means you should round to hundredth place

$24.37

Answer:

80 percent because the study was 100 she missed the 20 percent which was mixed because you can't change the psrcent

Step-by-step explanation:

and so if you have 100 percent right take the 20 away its 8 0percent because the 40 per entvdivided it up

Answer:

x=14

Step-by-step explanation:

4x +15 =71

4x =71 - 15

4x =56

x=56 :4

x=14

4 ×14 +15 =71

56 +15 =71

71 =71

Answer: X=14

Step-by-step explanation: Plug 14 in for x. 4*14 equals 56. 56+15 equals 71. and 71=71.

Answer:

putting roots on both sides,

[tex] \sqrt{(2x - 3)} {}^{2} = \sqrt{81} [/tex]

or, 2x-3 =9

or, 2x= 9+3

or, 2x = 12

Or, x = 12÷2

:. x=6

Answer:

  The initial values of the two functions are different and the rates of change of the two functions are the same

Step-by-step explanation:

In order for output values to always be different, the two linear functions must describe parallel lines. That means the rates of change are the same, but the initial values are different.

Answer:

probably too late but the answer is B

Step-by-step explanation:

Answer:

166

Step-by-step explanation:

$15.00-$5.00= $10.00 (subtract five dollars because aiden wants to have at least five dollars left)

10.00 divided by 0.06=  166

I hope this helps! :)

Answer:

Qn.1

{4,5,6,7,8,9,12,15,16}is ans of 1

{8,9}is ans of 2

{4,5,6,7,8,9,18,20}is ans of 3

{}Is the ans of 4

{8,9,12,15,16,18,20}is ans of 5

{}is ans of 6

{4,5,6,7,8,9,12,15,16,18,20} is ans of 7

{8,9,12,15,16} is ans of 8

Qn.2

{0,12}is ans of 9

{0,2,10,12}is ans of 10

{0,4,6,8,12}is ans of 11

{2,4,6,8,10}Is ans of 12

{}is ans of 13

{0,12}is ans 14

{0,12} is ans 15

{0,2,10,12} is ans of 16

{0,12} is ans of 17

{0,12} is ans of 18

{2,10} is ans of 19

{4,6,8} is ans of 20

I haven't made the symbol of union and intersection because i don't how to make.

it may help you at your work

Answer:

let side of square= x

breadth of rectangle= side if square= x

length of rectangle= y

perimeter of both are equal, so

4x= 2(y+x)

4x= 2y+2x

2x=2y

x=y

Mahalia can make a total of 18 napkins using the fabric which she has bought.

The quantity of space enclosing a three-dimensional shape's exterior is its surface area.

In other meaning, if we say side square then it is an area of the square but for a cuboid, there are 6 faces so the surface area will be external to all 6 surfaces area.

Given that,

She has 12 inches wide and 6 yards long fabric.

Since 1 yards = 36 inches.

So,

6 yards = 6 × 36 = 216 inches.

Now,

The total surface area of napkins ⇒ 12 × 216

⇒ 2592 inch²

Area for 1 napkin = 1 foot × 1 foot

Since 1 foot = 12 inches

So,

Area for 1 napkin = 12 × 12 = 144 inch²

Number of napkins can be made = The total surface area of napkins / Area for 1 napkin

Number of napkins that can be made = 2592 inch² / 144 inch²

⇒ 18

Hence "Mahalia can make a total of 18 napkins using the fabric which she has bought".

To learn more about surface area,

https://brainly.com/question/2835293

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Answer:

96 inch,180 inch,216 inch

Step-by-step explanation:

let the sides be 8x,15x,17x

then 8x+15x+17x=480

40x=480

4x=48

x=48/4=12

8x=8×12=96

15x=15×12=180

17x=17×12=216

Answer: B

Step-by-step explanation:

Answer:

option B, square root of 13

Step-by-step explanation:

i took the quiz on edge and got it right. :,)

Answer:

3840

Step-by-step explanation:

Hope this helps you out

Answer:

y=5x+20

Step-by-step explanation:

Answer: false.

Step-by-step explanation: the equation is as follows:

-3 + 7 = 7 - 3, which = 5

-3 times 5 = -15, making the statement false.

Answer:

6

Step-by-step explanation:

-3x+7<-11

-3x<-11-7

-3x<-18

X<-18/-3

X<6

Answer:

[tex]x = \frac{31}{7}[/tex]

Answer:

31/7

Step-by-step explanation:

Plus both sides by 3/7, and on the left it is 4 + 3/7. Transfer that into an improper fraction, and it's 31/7

Answer:

.0456621

Step-by-step explanation:

simpily divide the two and youll get .0456621

Answer:

C. 12x + 40

Step-by-step explanation:

Got 100% on edge.

Answer:

c

Step-by-step explanation:

did the quiz 2021

Answer:

8x≤2.40, x ≤ $0.30

Step-by-step explanation:

Answer:

134,000x 0.08= 10,720= the money you get every year from interest

1,000,000/10,720= 93.28... or 93 years

Step-by-step explanation:

Answer:

-x - 27/ 9 this is it djdjdj

The simplest form of the expression [tex]\frac{5(x-3)-3(2x+4)}{9}[/tex] is [tex]\frac{-x-27}{9}[/tex] .

A mixture of variables, numbers, addition, subtraction, multiplication, and division are called expressions.

An expression is a mathematical proof of the equality of two mathematical expressions.

A statement expressing the equality of two mathematical expressions is known as an equation.

Given the expression

[tex]\frac{5(x-3)-3(2x+4)}{9}[/tex]

⇒ (5x - 15 - 6x - 12) ÷ 9

⇒  (-x - 27)/9

⇒ [tex]\frac{-x-27}{9}[/tex]

Hence "The simplest form of the expression  [tex]\frac{5(x-3)-3(2x+4)}{9}[/tex] is [tex]\frac{-x-27}{9}[/tex] .

To learn more about expression,

https://brainly.com/question/14083225

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Answer:

Given circumference (C) = 16

Radius =  

C  =  

2π

2.5464790894703

Diameter =  

C  =  

π

5.0929581789407

Area =  

C2  =  

4π

20.371832715763

Step-by-step explanation:

We've all seen circles before. They have this perfectly round shape.

Every circle has a center, which is a point that lies exactly at the... well... center of the circle. A circle is a shape where the distance from the center to the edge of the circle is always the same. In order to calculate the radius, you need the circumferance or the diameter.

Answer:

Pi is a number that is approximated by 3.14, or 22/7. It is the ratio of the circumference to the diameter of any circle. This ratio can be rearranged to find circumference of a circle by multiplying pi times diameter

Step-by-step explanation: