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snow_lady [41]
3 years ago
5

a car leaves a town by traveling at 40 mph and two hours later,a second car left the same time in the same road,and the same dir

ections at 60 mph,the question is in how many hours the second car passes the first car????
Mathematics
1 answer:
Shkiper50 [21]3 years ago
3 0
\bf \begin{array}{ccccllll}
&distance&rate&time(hrs)\\
&\textendash\textendash\textendash\textendash\textendash\textendash\textendash\textendash\textendash&\textendash\textendash\textendash\textendash\textendash\textendash&\textendash\textendash\textendash\textendash\textendash\textendash\textendash\textendash\textendash\textendash\\
\textit{first car}&d&40&t\\
\textit{second car}&d&60&t+2
\end{array}
\\ \quad \\\\\\
d=d\implies (40)(t)=(60)(t+2)

"t", is the time the first car has travelled when reaching "d" distance,
whatever that is, at that point, the second car is passing it
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Solve the given differential equation by separation of variables. dy dx = xy + 5x − y − 5 xy − 2x + 6y − 12
Solnce55 [7]

solution:

Consider the differential equation DE

Dy/dx = xy + 5x –y -5 /xy -2x + 6y -12

Write the DE as the follows.

Dy/dx = x(y+5) -1(y+5)/x(y-2) +6(y-2)

Dy/dx = (x-1) (y+5)/(x+6)(y-2)

Separate the variables.

y-2/y+5 dy = x-1/x+6 dx

integrate on the both sides,

∫y-2/y+5 dy = ∫x-1/x+6 dx

7in(x+6) -7in(y+5) = x-y+c

In(x+6)∧7 –in(y+5)∧7 = x-y+c , using bIna =Inab

In [(x+6)∧7/(y+5)∧7] = x-y+c   ,using Ina – Inb = In(b/a)

eIn[(x+6)∧7/(y+5)∧7] = ex-y+c    , taking exponents on both sides

(x+6)∧7/(y+5)∧7 = ec.ex-y       ,use eInx = x

(x+6)∧7/(y+5)∧7 = c1ex-y , take ec =c1

Hence, the solution of the DE is (x+6)∧7/(y+5)∧7 = c1ex-y


3 0
3 years ago
Please help!!!<br><br><br>find the measure of the largest interior angle of this polygon ​
Karolina [17]

Answer:

122 or (3x-4).

Step-by-step explanation:

First, let's take a look at the polygon

The polygon has 5 sides.

We can calculate it's sum of interior angles by using (n-2)*180

Here, number of sides(n)=5

Therefore, (n-2)*180=(5-2)*180=3*180=540

Now that we got that out of the way, let's solve for x

2x+9+3x-8+3x-4+3x-10+2x+7=540

or,13x-6=540

or,13x=546

or,x=42

Now, solve for each interior angle,

2x+9=93

3x-8=118

3x-4=122

3x-10=116

2x+7=91

The largest here s 122 which is 3x-4.

SO, the largest interior angle=122 or (3x-4).

4 0
3 years ago
What is the area of the piece of red paper after the hole for
MakcuM [25]

Answer:

     \large\boxed{\large\boxed{47unit^2}}

Explanation:

The complete question is:

<em>A hole the size of a photograph is cut from a red piece of paper to use in a picture frame.</em>

<em />

<em>On a coordinate plane, 2 squares are shown. The photograph has points (-3, -2), (- 2, 2), (2, 1), and (1, -3). The red paper has points (- 4, 4), (4, 4), (4, -4), and (-4, -4).</em>

<em />

<em>What is the area of the piece of red paper after the hole for the photograph has been cut?</em>

<em />

<h2><em>Solution</em></h2>

<em />

The area of the piece of redpaper after the hole has been cut is equal to the area of the big square less the area of the small rectangle.

<u>1. Area of the big rectangle</u>

Vertices:

  • <em>(- 4, 4) </em>
  • <em>(4, 4)</em>
  • <em>(4, -4)</em>
  • <em>(-4, -4)</em>

<em />

The side length is the distance between two consecutive vertices:

The two points (-4,4) and (4,4) has the same y-coordinate, thus the length is just the absolute value of the difference of the x-coordinates:

  • 4-(-4)=4+4=8

The area of this square is    (8unit)^2=64unit^2

<u>2. Area of the small square</u>

Vertices:

  • <em>(-3, -2)</em>
  • <em>(- 2, 2) </em>
  • <em>(2, 1)</em>
  • <em>(1, -3)</em>

<em />

To find the side length use the distance formula for two consecutive points, for instance (2,1) and (-2,2):

      d=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}\\ \\d=\sqrt{(2-(-2))^2+(2-1)^2}=\sqrt{4^2+1^2}=\sqrt{17}

The area is:

          (\sqrt{17}unit)^2}=17unit^2

<u>3. Area of the piece of red paper after the holw for the photograph has been cut:</u>

<u />

Find the difference:

<u />

         64unit^2-17unit^2=47unit^2

<em />

7 0
3 years ago
Read 2 more answers
The units of the subway map below are in miles. Suppose the routes between
levacccp [35]

Distance between Station E  and Station G  is 8.48 miles (Approx.)

<u>Given:</u>

Distance 3 miles east

Distance 5 miles south

<u>Find:</u>

Distance between Station E  and Station G

<u>Computation:</u>

Co-ordinate of Point E = (-3 , 1)

Co-ordinate of Point G is 3 mile east and 5 mile south

So,

Co-ordinate of Point G = (3 , -5)

Distance between two point = √(x2 - x1)² + (y2 - y1)²

So,

Distance between Station E  and Station G  = √(3 + 3)² + (-5 - 1)²

Distance between Station E  and Station G  = √(6)² + (-6)²

Distance between Station E  and Station G  = √36 + 36

Distance between Station E  and Station G  = √72

Distance between Station E  and Station G  = 8.48 miles (Approx.)

Learn more:

brainly.com/question/12052812?referrer=searchResults

4 0
2 years ago
A jar has five red marbles and 10 blue ones if you were to pick a random marble without replacing it and then select another wha
Andrej [43]
I think the correct answer is 10/15.
4 0
3 years ago
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