Two trains leave a station, one headed due west and the other headed due south. How fast is the southern bound train moving if the west bound train is 15 miles from the station traveling at a constant speed of 35 mph, the distance between the trains is 24 miles, and the distance between them is increasing at a rate of 25 mph.

Answers

Answer 1

Answer:

dx/dt = 4 mph

Step-by-step explanation:

The two trains, with the station ( origin of the coordinates system) all, form a right triangle when we considered the distance between the two trains.

In that triangle:

distance between trains  D = 24 miles

leg (1 ) distance of train going west to origin  y = 15 miles

leg (2) distance of train going south x = ??

When d = 24 and y = 15

D² = y² + x²      ⇒   x² = D² - y²

x = √ (24)² - (15)²

x = √351

x = 18,73 miles

Now according to Pythagoras theorem

D² = x² + y²

Taking derivatives (respect to time) on both sides of the equation we get

2*D*dD/dt = 2*y*dy/dt  + 2*x*dx/dt

In this expression we are looking for dx/dt, all the rest of variables are known

2*24*25 = 2* 15*35  +  2*(18,73)* dx/dt

(1200 - 1050 )/37,46 = dx/dt

dx/dt = 4 mph


Related Questions

Consider each expression. if x = -2, is the value of the expression
a positive number? Select Yes or No.
A. -2(x - 2)
Yes
No
B. –3x(5 – 4x)
Yes
No
C. x + 6x
O Yes O No

Answers

Answer:

Yes

Yes

No

Step-by-step explanation:

Given value x = -2;

    Problem, is the expression a positive number ?

A. -2(x - 2)

  if x = -2

     -2(-2 - 2)

     = -2 (-4)

     = 8

Yes

B.  -3x(5 - 4x)

   if x = -2

     -3 x -2(5  - 4(-2))

    = 6 (5 + 8)

     = 6 x 13

     = 78

Yes

C. x + 6x

if x = -2

    -2 + 6(-2)

   = -2 - 12

   = - 14

No

At the supermarket you can fill your own honey bear container. A customer buys 12 oz of honey for $5.40.
How much honey can you buy per dollar?\

Answers

I believe about 2.22 this is average because you have to divide to find what the average is so if you divide 12oz by $5.40. Your answer would be about 2.222 so your answer should be 2.22 and as you check your work you can use addition I really hope this has helped :)

Which rational number equals 0 point 4 with bar over 4?

Answers

Answer:   4/9

==============================================

Work Shown:

[tex]x = 0.\overline{4}\\\\x = 0.4444\ldots\\\\10x = 4.4444\ldots\\\\10x-x = 4.4444\ldots-0.4444\ldots\\\\9x = 4\\\\x = \frac{4}{9}\\\\\frac{4}{9} = 0.\overline{4}= 0.4444\ldots\\\\[/tex]

The idea is that when we subtract 10x and x, the infinite decimal pattern (the 4s that go on forever) will cancel. That leads to 9x = 4 which solves to x = 4/9

Find the value of x so that the function has given value
M(x)=4x+15; m(x)=7

Answers

Mx=4x+15
7=4x+15
Subtract 15 from both sides
-8=4x
Divide each sides by 4
X=-2

how do I write an equation in standard form with the points (3,3) (0,-3) (2,-3)

Answers

First:
-3-3= -6 2-3=-1
-6/-1=6

Y=6x+b
3=6 x 3
3=18

Subtract both sides by 18

B=-15

Answer= y=6x-15

What is the value of sin-1(1)?

Answers

The value of sin^(-1) 1 is; π/2

We want to find the value of sin^(-1) 1

Now, when using trigonometric functions, we know that; If sin θ = x Then; θ = sin^(-1) x

Now, we want to find the angle.

We know that in radians the value of θ at which sin θ = 1 is; π/2 radians

Thus; sin^(-1) 1 = π/2

Read more about trigonometric angles at; https://brainly.com/question/22591162

Web crawlers need to estimate the frequency of changes to Web sites to maintain a current index for Web searches. Assume that the changes to a Web site follow a Poisson process with a mean of 6 days. Let a random variable X denote the time (in days) until the next change. What is the probability that the time until the next change is greater than 9.5 days

Answers

Answer:

The probability will be "0.205".

Step-by-step explanation:

The probability that perhaps the time remains greater than 9.5 days before the next shift will indeed be:

⇒  [tex]P(X>9.5)[/tex]

⇒  [tex]1-P(X<9.5)[/tex]

⇒  [tex]1-(1-exp(\frac{-9.5}{6} ))[/tex]

⇒  [tex]0.205[/tex]

secx- cosx = sinx tanx

Answers

Answer:

See Explanation

Step-by-step explanation:

[tex] \sec \: x - cos \: x = \sin \: x \tan \: x \\ \\ LHS = \sec \: x - cos \: x \\ \\ = \frac{1}{ \cos x} - cos \: x \\ \\ = \frac{1 - { \cos x}^{2} }{ \cos x} \\ \\ = \frac{ { \sin x}^{2} }{ \cos x} \\ \\ = \frac{ \sin \: x \times \sin x}{ \cos x} \\ \\ = \sin x \: tan x \\ \\ = RHS \\ \\ thus \: proved \\ [/tex]

Rachel estimates the weight of her dog to be 50 pounds the actual weight of the dog is 52.5 pounds what is the percent error of Rachel’s estimate

Answers

Answer:

It is unidentified.

Step-by-step explanation:

The sum of three times a number and seven is 22

Answers

Answer:

3x+7=22

Step-by-step explanation:

three times a number is

[tex]3\times x=3x[/tex]

so the sum of 3x and 7 is 22

[tex]3x+7=22\\\\3x=15\\\\x=5[/tex]

you can leave it here

[tex]3x+7=22[/tex]

if you need the value of x

then

[tex]x=5[/tex]

Solve x2 - 4x + 1 = 0.
x= 2 + 2i15
x = 4+ V3
x = 2/3
x= -2-3

Answers

Answer:

x = 2 ± √ 3

Step-by-step explanation:

You are buying fruit to make fruit baskets. Apples come in bags of 20. Oranges come in bags of 16, and bananas come in bags of 32. You have one bag of each fruit. Each fruit basket must be identical. What is the greatest number of fruit baskets that you can make using all of the fruit? *

Answers

Answer:

4 fruit baskets.

Step-by-step explanation:

Use GCF to find the answer. 20 divided by 4 is 5, 16 divided by 4 is 4, and 32 divided by 4 is 8.

Find the solution set for this inequality -2 x + 4 > -4x + 8.

Answers

Answer:

x > 2

Step-by-step explanation:

Evaluate the following expression,
5x [7+ (10-2) + 4)

Answers

Answer: 95x

Step-by-step explanation: Remove parentheses. 5x(7+10-2+4)

Add 7 and 10.

5x(17-2+4)

Add 15 and 4.

5x multiped by 19

Multiply 19 by 5

95x

In which number is the digit 7 ten times larger than it is in the number 175?

A) 379
B) 607
C) 730
D) 7,513

Answers

Answer:

c 730

Step-by-step explanation:

because the 7 in 730 is one digit to the left

Answer:

C. 730

Step-by-step explanation:

The 7 in the original number is in the tens place. So if you multiply that by 10, the seven moves into the hundreds place.

The price of a technology stock was $9.71 yesterday today the price rose to $9.84 find the percentage increase round your answer to the nearest 10th of a percent

Answers

Answer:

1.34%

Step-by-step explanation:

In order to find the percentage increase between these two prices, we must first find the difference in price. We calculate this by subtracting the final price by the initial price like so...

$9.84 - 9.71 = 0.13

Now we divide the difference by the initial price to find what percentage of the initial price this difference is, since this percentage difference was added to the initial price to get the new and final price point.

0.13 / 9.71 = 0.013388 ... multiply by 100 to get percent value

0.013388 * 100 = 1.3388% or 1.34% rounded.

If 4 adult elephants eat 320 pounds of food, how many ounces of food should the zookeeper purchase?

Answers

Answer:

Step-by-step explanation:

Water is an example of a solvent true or false !
Hurry up and answer

Answers

Yes water is a solvent

PLEASE HELPPPPPP
the side length of the base of a rectangular prism with a height of 18 inches can be found with the equation b=(v/18)^1/2 v is the volume of the prism find the side length of the base of the volume of the prism is 4050 cubic meters

Answers

Answer:

15 if b is supposed to the side length, √15 if b is the base which is a square.

Step-by-step explanation:

Playing golf, Mike got a + 2on the first hole and - 2 on the second hole. What is his combined score for the first two holes?

Answers

Answer:

0

Step-by-step explanation:

he had a score of 2 on the first hole and then he go a birdie i think and it subtracted 2 from that leaving 0

The snack table had 48 cookies displayed. After the first round of students came by, the number decreased by 25%. How many cookies were left on the table?

Answers

Answer:

36 cookies left

Step-by-step explanation:

48×.25=12

48-12=36 cookies

The figure shows the design of a greenhouse with a rectangular floor. The front and back sides of the greenhouse are semicircles with a diameter of w and the roof is half a cylinder. Consider greenhouse A with floor dimensions w=16 feet and l =18 feet.
A concrete slab 4 inches deep will be poured for the floor of greenhouse A. How many cubic feet of concrete are needed for the floor?

Answers

9514 1404 393

Answer:

  96 cubic feet

Step-by-step explanation:

A volume that is 16 ft by 18 ft by 1/3 ft will be ...

  V = LWH

  V = (16 ft)(18 ft)(1/3 ft) = 96 ft³

96 cubic feet of concrete are needed.

6x(24÷2) equals what?

Answers

6x(24 divided into 2 is 72 .

Answer:

72

Step-by-step explanation:

do 24/2=12x6=72

A bread company has a total of 12 packages of buns to sell. Each package of buns contains 6 buns and sells for $2.50. The cost of the buns, in dollars, is a function of the number of packages bought.
Which of the following values are NOT in the domain of the function described?
a) -2
b) 0
c) 0.5
d) 6
e) 14

Answers

Answer:

a) -2, c) 0.5, e) 14

Step-by-step explanation:

The domain is the x value, which is the number of packages sold in this case.

a) -2: You can't sell a negative number of packages

c) 0.5: You can't sell half a package

e) 14: The company only has 12 packages

The answer to this questions is A

Determine whether the given relations are functions.

Answers

Answer:

Yes, this relation is a function.

Step-by-step explanation:

It is a function because every input (left side) only has one output (right side). It doesn't matter if an output has multiple inputs. As long as an input has only one output, it is a function

Ex: 3 = 8 & 7     NOT an input

4 & 3 = 8          AN input

What is a perfect squares​

Answers

Answer:

A square number or perfect square is an integer that is the square of an integer; in other words, it is the product of some integer with itself. For example, 9 is a square number, since it can be written as 3 ×3

HOPE IT WILL HELP U!!!!!!

"The intersection of two planes is a line" is a statement that is generally accepted as true, but
cannot be proven to be true. What type of statement is this?
1. defined
2. undefined
3. postulate
4. proof

Answers

Answer:  3. Postulate

A postulate is something that is assumed to be true and there isn't a proof for it as its something foundational to help set up further proofs later down the road. Another example of a postulate is that a line is defined by two distinct points.

Toni is shopping for clothes at the store she buys 8 shirts for $8.00 what is the unit rate for the shirts?

Answers

Answer:

$1.00

Step-by-step explanation:

The unit rate in this scenario would be $1.00 , meaning that Toni is paying $1.00 for every shirt. This can be calculated by dividing the total price that she is paying for the shirts by the total number of shirts that Toni is purchasing like so...

$8.00 / 8 = $1.00 per shirt

The unit rate is basically the value over the denominator of 1 which would be the case as seen above since $1 buys 1 shirt ([tex]\frac{1 dollar}{1 shirt}[/tex]) as opposed to $8 dollars 8 shirts ([tex]\frac{8 dollars}{8 shirts}[/tex]) as mentioned in the question.

Howard's pawn shop bought an antique clock at the wholesale price of $725. Howard marked up the price of the clock
30%. What was the list price of the clock?
holour

Answers

Answer:

942.50

Step-by-step explanation:

725×30% or 0.3 = 217.5

217.5+725=942.5

Listed below are the 35 members of the Metro Toledo Automobile Dealers Association. We would like to estimate the mean revenue from dealer service departments. The members are identified by numbering them 00 through 34.

Answers

Answer:

Metro Toledo Automobile Dealers Association

a) The mean revenue

= Total Revenue from the dealer service departments/35

b) The sample of five include 27, 23, 32, 11,  and 13

c) Using systematic random sampling, the dealers included in the sample are: 7, 13, 19, 25, and 31.

Step-by-step explanation:

a) The mean value is the total value divided by the number of elements. The mean revenue is, therefore, the total revenue from the dealer service departments divided by the number of dealers.  This gives an average revenue from each dealer, which is a statistic to describe the population.

b) The sample of five cannot include any number that is outside the population.  For example, 85 is not a number allocated to any dealer in the indicated population, therefore, it cannot form part of the population sample.

c) The systematic random sampling starts from 7 and chooses the sixth number after 7.  Therefore, the next four numbers are multiples of 6.  This is why we choose 13, 19, 25, and 31.

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