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Anastasy [175]
2 years ago
6

Sheleah and her family are planning a trip from Los Angeles, California to Melbourne, Australia. While booking her family's plan

e tickets, she notices on the itinerary that the airline is offering a sixteen hour straight flight from Los Angeles to Melbourne on a Boeing 747-8 Intercontinental Jet. In an effort to learn more about the capabilities of the Jet, Sheleah does a little research and stumbles upon the following graph and facts about the Jet's gasoline consumption.
The Boeing 747-8 Intercontinental Jet can carry approximately 422,000 gallons of gasoline, making it possible for the jet to travel 14,430 kilometers before needing to refuel.
Use a linear model to predict the amount of gasoline that is present on the Jet after it has been in flight for 18 hours without stopping to refuel. In two or more complete sentences, explain your answer.

Mathematics
1 answer:
Shkiper50 [21]2 years ago
3 0

Answer:

Step-by-step explanation:

According to the graph, the amount of gasoline after 16 hours is 0 gallons. ⇒ Jet has to land to refuel after 15 hours of flying.

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Consider the initial value problem: 2ty′=8y, y(−1)=1. Find the value of the constant C and the exponent r so that y=Ctr is the s
VikaD [51]

The correct question is:

Consider the initial value problem

2ty' = 8y, y(-1) = 1

(a) Find the value of the constant C and the exponent r such that y = Ct^r is the solution of this initial value problem.

b) Determine the largest interval of the form a < t < b on which the existence and uniqueness theorem for first order linear differential equations guarantees the existence of a unique solution.

c) What is the actual interval of existence for the solution obtained in part (a) ?

Step-by-step explanation:

Given the differential equation

2ty' = 8y

a) We need to find the value of the constant C and r, such that y = Ct^r is a solution to the differential equation together with the initial condition y(-1) = 1.

Since Ct^r is a solution to the initial value problem, it means that y = Ct^r satisfies the said problem. That is

2tdy/dt - 8y = 0

Implies

2td(Ct^r)/dt - 8(Ct^r) = 0

2tCrt^(r - 1) - 8Ct^r = 0

2Crt^r - 8Ct^r = 0

(2r - 8)Ct^r = 0

But Ct^r ≠ 0

=> 2r - 8 = 0 or r = 8/2 = 4

Now, we have r = 4, which implies that

y = Ct^4

Applying the initial condition y(-1) = 1, we put y = 1 when t = -1

1 = C(-1)^4

C = 1

So, y = t^4

b) Let y = F(x,y)................(1)

Suppose F(x, y) is continuous on some region, R = {(x, y) : x_0 − δ < x < x_0 + δ, y_0 −ę < y < y_0 + ę} containing the point (x_0, y_0). Then there exists a number δ1 (possibly smaller than δ) so that a solution y = f(x) to (1) is defined for x_0 − δ1 < x < x_0 + δ1.

Now, suppose that both F(x, y)

and ∂F/∂y are continuous functions defined on a region R. Then there exists a number δ2

(possibly smaller than δ1) so that the solution y = f(x) to (1) is

the unique solution to (1) for x_0 − δ2 < x < x_0 + δ2.

c) Firstly, we write the differential equation 2ty' = 8y in standard form as

y' - (4/t)y = 0

0 is always continuous, but -4/t has discontinuity at t = 0

So, the solution to differential equation exists everywhere, apart from t = 0.

The interval is (-infinity, 0) n (0, infinity)

n - means intersection.

7 0
2 years ago
An object is moving at a speed of 850 miles per hour. Express this speed in meters per minute. Round your answer to the nearest
lorasvet [3.4K]

Answer:it would be 1385

Step-by-step explanation:because 850 miles per hour converted into meter per min would be 22799.04 meters per sec and then u would Find the number in the whole number place

4

and look one place to the right for the rounding digit on the right side of the decimal point

7

.Round up if this number is greater than or equal to

5

and round down if it is less than

5

1385

5 0
2 years ago
A shoe manufacture reported earnings of -$453,000 for 2012. In 2013 the company reported earnings of $813,000, and in 2014 the c
vitfil [10]
D $837,000 because your dealing with a negative number. -$453 - 384 = 744 because your still going down in the negatives.<span />
5 0
2 years ago
Read 2 more answers
Which measure is the largest? 1.2 km, 120,600 cm, 1,220,000 mm, 120 meters
aalyn [17]
The answer would be 1,220,000mm.

You can do this if you convert all the measures into one unit. Let us convert all into km. 

The first one is already in km, so we do not need to covert it. 

Let's start with converting 1,220,000mm to km. 


There are 1, 000,000 mm in one km. 

1,220,000X \frac{1km}{1,000,000mm} = 1.22km

So there are 1.22km 
in 1,220,000mm.

Next, we have 120m. There are 1,000m in 1km.

120mX \frac{1km}{1,000} =0.12km

There are 0.12km in 120m

Now you can see that 1,220,000mm is the longest. 


4 0
2 years ago
You jog 623623 miles around a track each day. If you jogged that distance 44 times last week, how many miles did you jog?
jasenka [17]

the answer would be : 2,942

you multiply 623 times 4

8 0
2 years ago
Read 2 more answers
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