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scoray [572]
3 years ago
6

Mr Daniels is organizing a class field trip on a budget of $900.The bus rental costs $600. Mr.daniels will also buy tickets that

will cost $9.50 per student. Write an inequality to represent the number students,y, that he can bring on the trip.
Mathematics
2 answers:
solmaris [256]3 years ago
8 0
600 + 9.5x (less than or equal to) 900

600 fixed amount
9.5 is the variable changing amount and differs among number of students taken
DENIUS [597]3 years ago
8 0

Answer:

y ≤ 31 students

Step-by-step explanation:

The rental cost is a fixed cost that will be incurred irrespective of the number of students embarking on the class field trip. This cost added to the total ticket cost must be less than or equal to the budget.

the total ticket cost for y number of students

= 9.5y

Hence the total cost = 9.5y + 600 ( measured in $)

In inequality form,

9.5y + 600 ≤ 900 (all in $)

9.5y ≤ 900 - 600

9.5y ≤ 300

y ≤ 300/9.5

y ≤ 31 students

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Debby pays rent twice a year, buys groceries once every quarter, and buys a transit pass
Natasha2012 [34]
<h3>Answer: 2x+4y+12z (choice B)</h3>

Work Shown:

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3 years ago
Consider the following equation of the form dy/dt = f(y)dy/dt = ey − 1, −[infinity] &lt; y0 &lt; [infinity](a) Sketch the graph
kotegsom [21]

Complete Question:

The complete question is shown on the first uploaded image

Answer:

a) The graph of  f(y) versus y. is shown on the second uploaded image

b) The critical point is at y = 0  and the solution is asymptotically unstable.

c)The phase line is shown on the third uploaded image

d) The sketch for the several graphs of solution in the ty-plane  is shown on the fourth uploaded image

Step-by-step explanation:

Step One: Sketch The Graph of  f(y) versus y

Looking at the given differential equation

       \frac{dy}{dt} = e^{y} - 1 for -∞ < y_{o} < ∞

 We can say let \frac{dy}{dt} = f(y) =e^{y} - 1

Now the dependent value is f(y) and the independent value is y so to sketch is graph we can assume a scale in this case i cm on the graph is equal to 2 unit for both f(y) and y and the match the coordinates and after that join the point to form the graph as shown on the uploaded image.

Step Two : Determine the critical point

   To fin the critical point we have to set   \frac{dy}{dt} = 0

       This means e^{y} - 1 = 0

                          For this to be possible e^{y} = 1

                          which means that  e^{y} = e^{0}

                          which implies that y = 0

Hence the critical point occurs at y = 0

meaning that the equilibrium solution is y = 0

As t → ∞, our curve is going to move away from y = 0  hence it is asymptotically unstable.

Step Three : Draw the Phase lines

A phase line can be defined as an image that shows or represents the way an ODE(ordinary differential equation ) that does not explicitly depend on the independent variable behaves in a single variable. To draw this phase line , draw the y-axis as a vertical line and mark on it the equilibrium, i.e. where  f(y) = 0.

In each of the intervals bounded  by the equilibrium draw an upward

pointing arrow if f(y) > 0 and a downward pointing arrow if f(y) < 0.

      This phase line would solely depend on y does not matter what t is

On the positive x axis it would get steeper very quickly as you move up (looking at the part A graph).

For  below the x-axis which stable (looking at the part a graph) we are still going to have negative slope but they are going to be close to 0 and they would take a little bit longer to get steeper  

Step Four : Draw a Solution Curve

A solution curve is a curve that shows the solution of a DE (deferential equation)

Here the solution curve would be drawn on the ty-plane

So the t-axis(x-axis) is its the equilibrium  that is it is the solution

If we are above the x-axis it is going to increase faster and if we are below it is going to decrease but it would be slower (looking at part A graph)

5 0
3 years ago
Can someone plz help me with me homework
riadik2000 [5.3K]
The answer to #3 is 52.
4 0
3 years ago
The cost of vacation to a cabin resort for a night is $95 for each person. Each cabin also has to pay a $25 recreational equipme
Blababa [14]
(x) = 95x + 25 is correct, since the $25 cost is fixed, but the $95 cost increases as x increases.
7 0
3 years ago
Read 2 more answers
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