Mathematics College

Two cargo trains each leave their respective stations at 1:00 p.m. and approach each other, one traveling west at 6 miles per hour and the other on separate tracks traveling east at 14 miles per hour. The stations are 40 miles apart. Find the time when the trains meet and determine how far the eastbound train has traveled.

A). 3 p.m, 28 mi
B). 12 p.m., 20 mi
C). 2 p.m., 18 mi.
D). 1 p.m., 15 mi

Answers

Answer 1

let x = hours

6x + 14x = 40

20x=40

x = 40/20 = 2 hours

1 pm + 2 hours = 3 pm

eastbound trains is going 14 miles per hour, 14 mph x 2 hours = 28 miles

Answer is A. 3 pm and 28 miles

Answer 2

The eastbound train has traveled 28 miles and they met at 3:00 pm

Speed is the ratio of total distance to total time taken. It is given by:

Speed = distance / time

Let both cargo trains meet each other at time t.

For the train traveling west:

6 = d₁ / t

d₁ = 6t

For the train traveling east:

14 = d₂ / t

d₂ = 14t

Since both trains are 40 miles apart, hence:

d₁ + d₂ = 40

6t + 14t = 40

20t = 40

t = 2 hours

t = 3:00 pm (1:00 pm + 2 hours)

Distance travel by east bound train = d₂ = 14t = 14(2) = 28 miles

The eastbound train has traveled 28 miles and they met at 3:00 pm

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Related Questions

"assume that josh throws the discus 36 times. let y denote the sum of the lengths of the 36 throws.
a. what is the expected value of y

Answers

Assuming that Josh throws the discus 36 times, the expected value of y will be the length each discus reaches for each throw all added together. Specifically, it will be discus throw one, plus discus throw two -- all the way to discus throw thirty-six. Adding all of those throws together will provide the expected value of Y.

How to estimate 208 + 569

Answers

Well just lookin at it and guessing I would say the estimate would be 777 bc u know that 8+9=17 den carry the one and u know that 1+6=7 and u know that 5+2=7 and yea
Hope this help good luck have a nice nite

Fraction 4 over 5n = Fraction 2 over 3. n = ___? Fraction 2 over 15 Fraction 5 over 6 1Fraction 1 over 5 1Fraction 7 over 15

Answers

So, we know that

4/5n = 2/3

n = 2/3 x 5/4 . . . . .. if fraction is moved to other side of the equation the numerator and denominator will be swithced

n = 10/12 ......................... divide numerator and denominator by 2

n = 5/6

The answer is Fraction 5 over 6

Answer:

what?

Step-by-step explanation:

What is 2 2/5 ÷ (- 1/4) And how?

Answers

-9.6 is the answer.
first you turn both fractions into decimals, then you just divide the two.

Turn 2 2/5 into a fraction of 12/5 and when dividing fractions, just flip and multiply! So 12/5 x -4/1 = your answer

What happens to the average kinetic energy of water molecules as water freezes? A. It decreases as the water releases energy to its surroundings.
B. It increases as the water releases energy to its surroundings.
C. It increases as the water absorbs energy from its surroundings.
D. It decreases as the water absorbs energy from its surroundings.

Answers

Answer: Option (A) is the correct answer.

Explanation:

Kinetic energy is defined as the energy possessed by an object because of it's motion.

Whereas average kinetic energy is the sum of kinetic energy of all the particles of a substance.

Therefore, when water freezes then there will decrease in kinetic energy of particles and thus, particles will gain potential energy.

Hence, we can conclude that when water freezes average kinetic energy of water molecules decreases as the water releases energy to its surroundings.

The average "kinetic-energy" of water molecules decreases as water freezes, because water releases energy to its surroundings, option (a) is correct.

When water freezes, it undergoes a phase transition from a liquid to a solid state. During this process, water molecules lose energy and slow down, causing decrease in their average kinetic energy.

As temperature decreases, water molecules arrange themselves into a more structured pattern due to the formation of hydrogen bonds.

In order for water to freeze, it needs to release energy to its surroundings, in form of heat. This release of energy is necessary to facilitate transformation from a higher-energy liquid state to lower-energy solid state. As a result, average kinetic energy of water molecules decreases as water freezes.

Therefore, the correct option is (a).

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What is the third term of the sequence defined by the recursive rule f(1)=2, f(n)=2f(n-1) +1

Answers

The function is defined recursively. In order to calulate f(3), f(2) and f(1) must be known. f(1) is given f(1) = 2 f(2) is then calculated f(2) = 2 * f(1) + 1 = 2 * 1 + 1 = 2 + 1 = 3 Finally f(3) can be calculated given f(2)=3 f(3)= 2 * f(2) + 1 = 2 * 3 + 1 = 6 + 1 = 7

Mira has breakfast at a restaurant. She leaves a 20% tip of $1.80. What is the price of Mira’s breakfast,before tip?

Answers

Ok so
9×20%=1.80
So the original price of her breakfast is $9.00
hope this helps!

Hey there,
20% = $1.80
1% = $1.80 / 20%
= $0.09
100 % = $0.09 x 100
= $9

Hope this helps :))

~Top

What is the area of a regular polygon with 100 sides and a perimeter of 100 units?

Answers

now, if the regular polygon has 100 sides, and the perimeter is 100 units, that simply means that each side is 1 unit, foot, meter, else.

so, we know each side is 1 unit long, and we know there are 100 sides,

[tex]\bf \textit{area of a regular polygon}\\\\ A=\cfrac{1}{4}ns^2cot\left( \frac{180}{n} \right)\quad \begin{cases} n=\textit{number of sides}\\ s=\textit{length of a side}\\ \frac{180}{n}=central~angle\\ \qquad~~ in~degrees\\ ----------\\ n=100\\ s=1 \end{cases} \\\\\\ A=\cfrac{1}{4}\cdot 100\cdot 1^2\cdot cot\left( \frac{180}{100} \right)\implies A=25cot\left(\frac{9}{5}^o \right) \\\\\\ A\approx 795.51289884[/tex]

solve this system of linear equations. separate the x- and y- values with a coma. 6x+20y=-62
3x-9y=-12

Answers

Final answer:

To solve the system of linear equations, use the method of substitution by solving for one variable and substituting it into the other equation.

Explanation:

To solve the system of linear equations:

6x + 20y = -62

3x - 9y = -12

We can use the method of substitution:

From the first equation, solve for x: x = (-62 - 20y) / 6Substitute the value of x into the second equation: 3((-62 - 20y) / 6) - 9y = -12Simplify and solve for y:

After finding the value of y, substitute it back into the first equation to solve for x. The solution is: x = -2, y = 4.

Find the limit. use l'hospital's rule if appropriate. if there is a more elementary method, consider using it. lim x→0 2x − sin(2x) 2x − tan(2x)

Answers

Final answer:

Using the L'Hospital's Rule, we differentiate the numerator and denominator of the given function separately, substitute these derivatives back into the function, and then attempt to evaluate the limit as x approaches 0.

Explanation:

To find the limit of the given function as x approaches 0, we will use the L'Hospital's Rule since the function gets an indeterminate form 0/0 as x approaches 0. L'Hospital's Rule states that the limit of a quotient of two functions as x approaches a certain value is equal to the limit of the quotients of their derivatives.

First, we differentiate the numerator and the denominator separately. For the numerator, the derivative of 2x is 2, and the derivative of sin(2x) is 2cos(2x). So the derivative of the numerator is 2 - 2cos(2x).

For the denominator, the derivative of 2x is 2, and the derivative of tan(2x) is 2sec²(2x), since the derivative of tan(x) is sec²(x) and because of the chain rule, we multiply by 2. So, the derivative of the denominator is 2 - 2sec²(2x).

Now, we substitute these derivatives back into the original function and take the limit as x approaches 0: lim x→0 (2 - 2cos(2x)) / (2 - 2sec²(2x)).

After further simplifying the above expression, you can evaluate the limit.

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The limit is 0.

We need to find the limit:

lim x→0 (2x − sin(2x)) / (2x − tan(2x))

Both the numerator and the denominator approach 0 as x approaches 0, which means it is in the indeterminate form 0/0. This suggests that we can use L'Hôpital's Rule.

According to L'Hôpital's Rule, we can differentiate the numerator and the denominator and then take the limit of the resulting fraction.

First, let's compute the derivative of the numerator:

Numerator: 2x - sin(2x)Derivative: 2 - 2cos(2x)

Next, let's compute the derivative of the denominator:

Denominator: 2x - tan(2x)Derivative: 2 - 2sec²(2x)

Now, we apply L'Hôpital's Rule:

lim x→0 (2 - 2cos(2x)) / (2 - 2sec²(2x))

As x approaches 0, cos(2x) approaches 1 and sec²(2x) also approaches 1, so:

lim x→0 (2 - 2(1)) / (2 - 2(1)) = 0 / 0

This fraction again gives an indeterminate form. Applying L'Hôpital's Rule a second time will be helpful. We need to differentiate the numerator and the denominator again:

Second derivative of the numerator: d/dx [2 - 2cos(2x)] = 4sin(2x)

Second derivative of the denominator: d/dx [2 - 2sec²(2x)] = -8sec²(2x)tan(2x)

Applying L'Hôpital's Rule once more, we get:

lim x→0 (4sin(2x)) / (-8sec²(2x)tan(2x))

Substitute x = 0:

lim x→0 (4sin(2x)) / (-8sec²(2x)tan(2x)) = 0

Therefore, the limit is 0.

The distance from Talamunda to Velcratia is 700 miles. The train takes 5 hours to travel the distance. At what unit rate is the train traveling?

Answers

[tex]\bf \stackrel{distance}{d}=\stackrel{rate}{r}\cdot \stackrel{time}{t}\quad \begin{cases} d=700\\ t=5 \end{cases}\implies 700=5r\implies \cfrac{700}{5}=r \\\\\\ \stackrel{mph}{140}=r[/tex]

Answer: 140 miles per hour

Step-by-step explanation:

Find the distance the point p(0,0,−4)p(0,0,−4) is to the line through the two points q(−4,1,−2q(−4,1,−2 ), and r(−2,0,−5r(−2,0,−5 ).

Answers

r(2,0-5r) is the correct answer !!!!!

Betty correctly determined that the ordered pair (–3, 5) is a solution to the system of linear equations mc004-1.jpg and x + 4y = 17. Based on this information, which statement is correct? (–3, 5) satisfies neither the equation 6x + 5y = 7 nor the equation x + 4y = 17. (–3, 5) satisfies the equation 6x + 5y = 7 but not the equation x + 4y = 17. (–3, 5) satisfies the equation x + 4y = 17 but not the equation 6x + 5y = 7. (–3, 5) satisfies both the equation 6x + 5y = 7 and the equation x + 4y = 17

Answers

She correctly found the solution to be (-3, 5).
Since (-3, 5) is a solution of the system of equations, then (-3, 5) must satisfy both equations.
Answer is choice D.

answer is d foo on my mama

20 points! Suppose you find six articles related to the topic of your research paper. In how many ways can you choose four articles to read

a.720

b.30

c.360

d.15

Answers

B s the correct answer

Find three positive numbers whose sum is 100 and whose product is a maximum. (enter your answers as a comma-separated list.)

Answers

Let's start by solving this problem when there are only two positive numbers involved, and then see whether we can apply the same technique when there are three positive integers.

Let the two positive integers be x and y.
Then x + y = 100, and xy = the product.

Let's eliminate x. Solve x + y = 100 for x: x = 100 - y. Now subst. this last result into P = xy: P = product = (100 - y)(y) = 100y - y^2

Differentiating, dP/dy = 100 - 2y. Set this = to 0 and solve for y: -2y = -100, and y = 50. Since x + y = 100, x is thus also = to 50.

Solution set: (50,50).

Now suppose that three positive integers add up to 100, and that we want to maximize their product.

Then x + y + z = 100. Let's maximize f(x,y,z) = xyz (the product of x, y and z).

Since x + y + z = 100, we can eliminate z by solving x + y + z = 100 for z and subst. the result back into f(x,y,z) = xyz:

We get f(x,y) =xy(100-x-y), a function of two variables instead of three.

I won't go through the entire procedure of maximizing a function in three variables, but will get you started:

Find the 'partial of f with respect to x' and then the 'partial of f with respect to y'. Set each of these partial derivatives = to 0:

f = 0 = (partial of xy(100-x-y) with respect to x
x

= xy(partial of 100-x-y with respect to x) + (100-x-y)(partial of xy with respect to x)

= xy(-1) + (100-x-y)(y)

We must set this partial = to 0: -xy+100y-xy-y^2 = 0

-2xy + 100y - y^2 = 0

or y(-2x + 100 - y) = 0

of which y=0 is one solution and in which -2x + 100 - y = 0

You must now go through the same procedure with respect to the partials with respect to y.

If you'd like to continue this discussion, please respond with questions and comments.

How long will it take for the object to fall all the way down to the ground? The function for objects dropped from a height where t is the time in seconds, h is the height in feet at time t, and h is the intial height is h(t)=-16t^2+h. The building is 162 feet tall.
Thanks so much!

Answers

Since the initial height of the bldg is 162 ft, h(t)= -16t^2+h becomes

-16t^2+162, or 16t^2 = 162. Taking the + square root of both sides,

we get t = 162/16 seconds, or 10 1/8 seconds.

The ice cream Palace received 3 gallons of strawberry ice cream, 5 pints of mocha ice cream, and 1 quart of vanilla ice cream today. How many pints of ice cream did they receive?

Answers

They recived 31 pints of ice cream

A student has three mangos, two papayas, and two kiwi fruits. if the student eats one piece of fruit each day, and only the type of fruit matters, in how many different ways can these fruits be consumed

Answers

7! / ( 3! * 2! * 2! ) = 210

There are 210 different ways for the fruits can be consumed.

What is Multiplication?

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Given that;

A student have 3 mangos, 2 papayas, and 2 kiwi fruits.

And, The student eats one piece of fruit each day, and only the type of fruit matters.

Now,

Total number of fruits = 3 + 2 + 2

= 7

And, There are 3 mangos, 2 papayas, and 2 kiwi fruits.

So, Number of ways for the fruits can be consumed, is calculated as;

= 7! / 3! 2! 2!

= 7 x 6 x 5 x 4 x 3! / 3! 2! 2

= 7 x 6 x 5 x 4 / 2 x 1 x 2 x 1

= 7 x 6 x 5

= 210

Thus, There are 210 different ways for the fruits can be consumed.

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One hundred pounds of co2 is contained in a 10:0-ft3 tank. the safety limit of the tank is 1600 psig.

Answers

Final answer:

To answer the question, we need to convert the mass from pounds to kilograms, use the ideal gas law equation to calculate the pressure in atmospheres, and then convert atmospheres to psig.

Explanation:

In this question, we are given that 100 pounds of CO2 is contained in a 10.0-ft3 tank and the safety limit of the tank is 1600 psig. To convert pounds to kilograms, we can use the conversion factor of 1 pound = 0.4536 kilograms. So, 100 pounds of CO2 is equal to 45.36 kilograms. Now, we can use the ideal gas law equation PV = nRT to find the pressure in bar. Rearranging the equation, we have P = (nRT) / V. Plugging in the values given, n = mass / molar mass, R = 0.0821 atm L / mol K, T = 273 + degrees Celsius, and V = 10.0 ft3 converted to liters, we can calculate the pressure in atmospheres. Finally, we can convert atmospheres to psig by multiplying by 14.7.

In 2015, in Buffalo, New York, there were 8,625 arrests, 2,678 robberies, 865 assaults, and 20 murders. The population of Buffalo is 258,959. What is the ratio of the number of assaults to the number of robberies in simplest form?

Answers

I'm pretty sure simplest form would still be 865:2678
I could be wrong tho

Answer:

The simplest form of the ratio is: [tex]\dfrac{865}{2678}[/tex]

Step-by-step explanation:

We are given information about the buffalo in New york in the year 2015 as:

Number of arrests= 8,625

Number of robberies=2678

Number of assaults= 865

Number of murders= 20

The population of Buffalo is 258,959.

he ratio of the number of assaults to the number of robberies in simplest form is given by:

[tex]\dfrac{865}{2678}[/tex]

As the number in the numerator and the denominator do not have a common factor. hence the simplest form of the ratio is:

[tex]\dfrac{865}{2678}[/tex]

A local little league has a total of 85 players, of whom 80% are left-handed. How many left-handed players are there?

Answers

Final answer:

The question is asking us to find out how many players are left-handed from a total of 85 players, given that 80% of the players are left-handed. For this, we perform a simple calculation by finding 80% of 85, which equals 68. So, there are 68 left-handed players in the league.

Explanation:

The subject of this question falls under the category of Mathematics, more specifically, it is about percentage calculations. In order to figure out how many left-handed players there are out of the total 85 players, we need to remember that percent means 'per 100'. So, 80% translates to 80 out of 100. Therefore, to find out how many are left-handed, we need to take 80% of 85.

The calculation is as follows:

Left-handed players = 85 * (80/100)

= 85 * 0.80

= 68

So, there are 68 left-handed players in the local little league.

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A laptop computer is purchased for $1300. After each year, the resale value decreases by 35%. What will the resale value be after 3 years?

Answers

[tex]\bf \qquad \textit{Amount for Exponential Decay}\\\\ A=I(1 - r)^t\qquad \begin{cases} A=\textit{accumulated amount}\\ I=\textit{initial amount}\to &1300\\ r=rate\to 35\%\to \frac{35}{100}\to &0.35\\ t=\textit{elapsed time}\to &3\\ \end{cases} \\\\\\ A=1300(1-0.35)^3\implies A=1300(0.65)^3[/tex]

The speed of the car was 45 mph. A driver noticed that while moving with this speed it took him 40 seconds to cross a bridge. On the way back crossing the same bridge, it took him 30 seconds. What was the speed of the car on the way back?

Answers

distance = speed*time

Each time the car travels the same distance across the bridge.

By setting the distances equal you get the following equation:

[tex]30x = 40*45 \\ \\ x = \frac{40*45}{30} = 60[/tex]

Answer: Car was going 60 mph

Answer:

Speed of car on the way back = 30 mph

Step-by-step explanation:

Speed of car on the way = 45 mph = 45 x 1.6 = 72 kmph = 20 m/s

Time taken to cross bridge on the way = 40 seconds

Length of bridge = Speed of car on the way x Time taken on the way = 20 x 40 = 800 m

Time taken to cross bridge on the way back = 30 seconds

Length of bridge = Speed of car on the way back x Time taken on the way back

800 = Speed of car on the way back x 30

Speed of car on the way back = 26.67 m/s =96 kmph = 30 mph

Speed of car on the way back = 30 mph

For which real numbers x and y is it true that x + y = x+y?

Answers

By the general application of cumulative property of addition :

x + y = y + x

For sure

If 300 cm2 of material is available to make a box with a square base and an open top, find the maximum volume of the box in cubic centimeters

Answers

check the picture below, recall the base is a square, so each side being equally "x".

[tex]\bf V(x)=x^2\left( \cfrac{300-x^2}{4x} \right)\implies V(x)=x^2\left( \cfrac{75}{x}-\cfrac{x}{4}\right) \\\\\\ V(x)=75x-\cfrac{x^3}{4}\implies \cfrac{dV}{dx}=75-\cfrac{1}{4}\cdot 3x^2\implies \cfrac{dV}{dx}=75-\cfrac{3x^2}{4} \\\\\\ \cfrac{dV}{dx}=\cfrac{300-3x^2}{4}\impliedby \textit{now, let's set the derivative to 0} \\\\\\ 0=\cfrac{300-3x^2}{4}\implies 0=300-3x^2\implies 3x^2=300\implies x^2=100 \\\\\\ x=\pm\sqrt{100}\implies x=\pm 10[/tex]

now, if you do a first-derivative test on +10, say check 9.99 and 10.01 for example, you'll notice you'd get + and - value respectively, meaning is a maximum.

If two parallel lines are cut by a transversal and corresponding angles measure 10x – 1 and 8x + 21, what is the value of x?

Answers

Since corresponding angles are congruent:

10x -1 = 8x + 21
-8x -8x
2x -1 = 21
+1 +1
2x = 22
x = 11

Hope this helps!

find the equation in general form of the circle with center at the origin and radius equal 6.

Answers

[tex]\bf \textit{equation of a circle}\\\\ (x-{{ h}})^2+(y-{{ k}})^2={{ r}}^2 \qquad \begin{array}{lllll} center\ (&{{ h}},&{{ k}})\qquad radius=&{{ r}}\\ &0&0&6 \end{array}\\\\ -------------------------------\\\\ (x-0)^2+(y-0)^2=6^2\implies x^2+y^2=36[/tex]

Find the area of the part of the plane 5x + 4y + z = 20 that lies in the first octant.

Answers

This part of the plane is a triangle. Call it [tex]\mathcal S[/tex]. We can find the intercepts by setting two variables to 0 simultaneously; we'd find, for instance, that [tex]y=z=0[/tex] means [tex]5x=20\implies x=4[/tex], so that (4, 0, 0) is one vertex of the triangle. Similarly, we'd find that (0, 5, 0) and (0, 0, 20) are the other two vertices.

Next, we can parameterize the surface by

[tex]\mathbf s(u,v)=\langle4(1-u)(1-v),5u(1-v),20v\rangle[/tex]

so that the surface element is

[tex]\mathrm dS=\|\mathbf s_u\times\mathbf s_v\|=20\sqrt{42}(1-v)\,\mathrm du\,\mathrm dv[/tex]

Then the area of [tex]\mathcal S[/tex] is given by the surface integral

[tex]\displaystyle\iint_{\mathcal S}\mathrm dS=20\sqrt{42}\int_{u=0}^{u=1}\int_{v=0}^{v=1}(1-v)\,\mathrm dv\,\mathrm du[/tex]
[tex]\displaystyle=20\sqrt{42}\int_{v=0}^{v=1}(1-v)\,\mathrm dv=10\sqrt{42}\approx64.8074[/tex]

Final answer:

The area of the plane 5x + 4y + z = 20 in the first octant is calculated using a double integral over the xy-plane. The limits are defined by the intersection of x and y with the xy-plane when z=0, and the solution is approximately 66.67 square units.

Explanation:

To solve for the area of the part of the plane that lies in the first octant, we first need to isolate z in our equation. z = 20 - 5x - 4y. The limits for x and y in the first octant are from 0 to positive infinity, but in this case, they will be limited by the plane defined by z = 0 (the xy-plane). x and y will range from 0 to the point where they meet the plane. Therefore, we set z = 0 and solve for both x and y, giving us x = 4 and y = 5.

Now in order to calculate the area, we must interpret this integral on the xyz-plane as a double integral on the xy-plane. Now, we integrate over the region in the xy-plane that x and y range over:

Area = ∫ from 0 to 4 ∫ from 0 to (5 - 1.25x) (20 - 5x - 4y) dy dx

And that is the integral you need to calculate to find the area. Attempting to calculate this integral results in the area ≈ 66.67 square units.

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The fifth term of a geometric sequence is 781.25. Each previous term is 1/5 of the value of the current term. Which recursive formula represents the situation?

Answers

Answer:

[tex]a_n=5a_{n-1}[/tex]

Step-by-step explanation:

Given fifth term of a geometric sequence is 781.25.

[tex]a_5= 781.25[/tex].

Also, each previous term is 1/5 of the value of the current term.

Therefore, common ratio would be 5.

But we just need to find the recursive formula .

Recursive formula of a geometric sequence is given by

[tex]a_n=ra_{n-1}[/tex]

Plugging value of r in above formula, we get

[tex]a_n=5a_{n-1}[/tex]

Therefore, recursive formula would be [tex]a_n=5a_{n-1}[/tex] represents the situation.

Answer: c

Step-by-step explanation:

buddy beneath me is blabbin to much

What are the values of the mean and standard deviation after converting?

Answers

Example:Pulse rates of women are normally distributed with a mean of 77.5beats per minute and a standard deviation of 11.6 beats per minute.a) What are the values of the mean and standard deviation afterconverting all pulse rates of women to z-scores usingz=(x−μ)/σ?µ = 0;σ= 1b) The original pulse rates are measured with units of “beats perminute.” What are the units of the corresponding z-scores?The z-scores are numbers without units of measurement.

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