Mathematics College

A plane flies against the wind 288 miles from Los Angeles to San Jose and then returns home with the same wind. The wind speed is 60 mph. If the total flying time was 2 hours, what is the speed of the plane?

Answers

Answer 1

Answer:

The speed of the airplane is 300 miles per hour.

Step-by-step explanation:

Let consider that plane travels at constant speed, which is the sum of the velocity of the plane in still air (velocity of the plane relative to wind) and the velocity of the wind. Hence, the total time spent by the plane is described by following kinematic formula:

[tex]t = s\cdot \left(\frac{1}{v_{P}-v_{W}}+\frac{1}{v_{P}+v_{W}} \right)[/tex] (1)

Where:

[tex]t[/tex] - Total time, in hours.

[tex]s[/tex] - Distance between Los Angeles and San Jose, in miles.

[tex]v_{P}[/tex] - Velocity of the plane in still air, in miles per hour.

[tex]v_{W}[/tex] - Velocity of the wind, in miles per hour.

Then, we proceed to simplify the formula and clear the speed of the plane in still air:

[tex]\frac{t}{s} = \frac{2\cdot v_{P}}{v_{P}^{2}-v_{W}^{2}}[/tex]

[tex]\left(\frac{t}{s}\right)\cdot (v_{P}^{2}-v_{W}^{2}) = 2\cdot v_{P}[/tex]

[tex]\left(\frac{t}{s} \right)\cdot v_{P}^{2} - 2\cdot v_{P}- \left(\frac{t}{s} \right)\cdot v_{W}^{2} = 0[/tex]

Which is a Second Order Polynomial, whose roots can be found analytically by Quadratic Formula. If we know that [tex]t = 2\,h[/tex], [tex]s = 288\,mi[/tex] and [tex]v_{W} = 60\,\frac{mi}{h}[/tex], then we have the following polynomial:

[tex]\frac{1}{144}\cdot v_{P}^{2}-2\cdot v_{P} -25 = 0[/tex]

The two roots associated with this polynomial are, respectively:

[tex]v_{P,1} = 300\,\frac{mi}{h}[/tex], [tex]v_{P,2} = -12\,\frac{mi}{h}[/tex]

Since speed is the magnitude of velocity, then solution must be positive. First root satisfies all these conditions.

In a nutshell, the speed of the airplane is 300 miles per hour.

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Answer:

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Step-by-step explanation:

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54 - 3 = 51

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Step-by-step explanation:

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Answer:

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Step-by-step explanation:

Answer:

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Step-by-step explanation:

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Answer:

Mean: 20

Median: 21

Mode: 14

Range: 16

Answer:

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Step-by-step explanation:

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Step-by-step explanation:

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Answers

Answer:

4/20 or 1/5 if you want it simplified

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Answers

Answer:

<CFE = 28

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Step-by-step explanation:

1)

<CFE + 152 = 180

<CFE = 180 - 152

<CFE = 28

2)

Complementary means the angles add up to 90 so:

<RPQ + 37 = 90

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Which point is located at (0.25, -0.50)?
A
C
T

Answers

Answer:

i would say R

Step-by-step explanation:

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Step-by-step explanation:

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Answers

Answer:

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Step-by-step explanation:

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Answers

Answer:

No,

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Obviously, 12.800 < 12.815.

[tex] \infty \infty [/tex]

Answer:

[tex]12.8 < 12.815 \: \\ with \: a \:range \: of \: 0.015[/tex]

What is the radian measure of an angle of 75º?

Answers

The second answer is correct.

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Answers

Answer: x=6  x=5

Step-by-step explanation:

Answer:

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Five friends shared 1 1/2 pounds of fudge equally. How much did each friend get?

Answers

Answer:

each friend gets 0.1 fudge

Step-by-step explanation:

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Answers

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Answer:

the volume of the cone is about 56.52

Step-by-step explanation:

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Answer:

We have

selling price=Discount + sales price

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Sales price =selling price - discount

Mark of price=mark up price rate ×original price

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Answers

Answer:

9:59

Step-by-step explanation:

Answer:

C) 9:59

Step-by-step explanation:

Now 9:29

in 30 min 9:59

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Answers

Answer:

69.9 sq units

Step-by-step explanation:

find area of entire rectangle then subtract out area of semi-circle

(14 x 6) - (3²π ÷ 2)

84 - 14.1 = 69.9

69.9

Step-by-step explanation:

nick is baking fudge. what is the minimum amount of plastic wrap needed to cover this piece of fudge?

Answers

Answer:

4 inches

Step-by-step explanation:

Answer:

where is the picture?

Step-by-step explanation:

HELP ASAP PLS NO LINKS
Which of the following values in the set below will make the equation 5x + 6 = 6 true? (Only input the number.)
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Answer for Blank 1:

Answers

Answer:

0

Step-by-step explanation:

0

No bots. No bots. No bots Please, someone please answer this, and No bots!!

Answers


t/5 = 2.9
For the first step, I would multiply both sides by 5, to get rid of the fraction.

That will leave
t = 14.5

So with what you have on your screen, I would drag “x” and “5” to both sides of the equation.

Dennis Hampton earns a straight com-
mission of 7% on sales of $5,000 or less
and 9% on sales in excess of $5,000. One
week Dennis had a gross pay of $578.
What were his total sales for that week?

Answers

Answer:

Denis's total sales that week were $ 6,422.22.

Step-by-step explanation:

Since Dennis Hampton earns a straight commission of 7% on sales of $ 5,000 or less and 9% on sales in excess of $ 5,000, if one week Dennis had a gross pay of $ 578, to determine what were his total sales for that week the following calculations must be performed:

7 = 578

100 = X

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57,800 / 7 = X

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100 = X

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57.800 / 9 = X

6,422.22 = X

Therefore, Denis's total sales that week were $ 6,422.22.

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Answers

Option 1 because they both need to start sequence from 2

Kam
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Answers

Answer:

c

Step-by-step explanation:

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Answers

Answer:

Depends

Step-by-step explanation:

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1 Remy has 4 monster trucks, 3 firetrucks, 1 ambulance, and 2 taxis. He will randomly choose. what is the probability that Remy will choose a taxi
A 1/10
B 1/5
C 2/4
D 1/3

Answers

Answer:

B) 1/5

Step-by-step explanation:

Remy has 2 taxis, and 10 cars in all. It is asking for the probability that Remy will choose a taxi. Divide the amount of taxis from the total amount of cars. Simplify the fraction:

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B) 1/5 is your answer.

~

Answer:

Mmmmm maybe is A 1/10 por que se suman todas las posibilidades y luego se le coloca la cantidad que podria elegir

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Answers

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2

Step-by-step explanation:

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Answers

Answer:

x = 5

Step-by-step explanation:

[tex]\frac{4.5}{7.5}[/tex] = [tex]\frac{3}{x}[/tex]

cross multiply

4.5x = 7.5(3)

4.5x = 22.5

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Answers

Answer:

100%

Step-by-step explanation:

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Answer:

An event that is guaranteed to happen has a probability of exactly 1

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Answers

9514 1404 393

Answer:

  B.  line AB

Step-by-step explanation:

The terminal point must be named first when naming a ray.

The vertex must be named in the middle when naming an angle.

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Answers

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Answer:

750160 ez

Step-by-step explanation:

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