1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
goldfiish [28.3K]
3 years ago
7

A plane flies from atlanta to new york to los angeles angainst the wind in 5 hr the return trip back to atlanta with the wind on

ly 4 hr if the diatance between atlanta and los angeles is 3200 km find the speed of the plane in still air and the speed of the wind
Mathematics
1 answer:
dimulka [17.4K]3 years ago
4 0

Answer: speed of plane is 720 km/h

Speed of wind is 80km/h

Step-by-step explanation:

Let x represent the speed of the plane.

Let y represent the speed of the wind.

The plane flies from Atlanta to los Angeles and against the wind in 5hrs and the distance between Atlanta and los Angeles is 3200 km.

Since it flew against the wind, the speed would be x-y km/hour

Distance = speed × time. Therefore

3200 = 5(x - y )

3200 = 5x - 5y - - - - - - - - - 1

the return trip back to Atlanta with the wind only 4 hr. This means that the speed is x+y km/hour. Therefore

3200 = 4(x+y)

3200 = 4x + 4y - - - - - - - - 2

Multiplying equation 1 by 4 and equation 2 by 5, it becomes

12800 = 20x - 20y

16000 = 20x - 20y

Adding both equations, it becomes

28800 = 40x

x = 28800/40 = 720

Substituting x = 720 into 3200 = 5(x - y )

x - y = 3200/5 = 640

y = 720 - 640 = 80

You might be interested in
A school trip requires students to score at least a total of 335 points on four tests. Each test is worth 100 points. If a stude
HACTEHA [7]

Answer:

D. 81

Step-by-step explanation:

You need to first add 77, 95 and 82 to get 254, Then you do 335 - 254 which is 81.

6 0
2 years ago
Read 2 more answers
The perimeter of a triangle is 25 feet.
shutvik [7]

25 = 5.2 + 8 + x

5.2 + 8 = 13.2

25 = 13.2 + x

25 - 13.2 = 11.8

11.8 = x

The unknown side is 11.8 ft.

3 0
3 years ago
4x+4=-2x+10<br><br> Alguien que me explique porfas ,el mejor doy corona
ehidna [41]

Answer:

X = 1

Step-by-step explanation:

4x+4=-2x+10 \\4 - 10 =  - 2x - 4x \\  - 6 =  - 6x \\  - 6x =  - 6 \\ x =  \frac{ - 6}{ - 6}  \\ x = 1

6 0
2 years ago
Find the equation of the sphere if one of its diameters has endpoints (4, 2, -9) and (6, 6, -3) which has been normalized so tha
Pavel [41]

Answer:

(x - 5)^2 + (y - 4)^2 + (z - 6)^2 = 14.

(Expand to obtain an equivalent expression for the sphere: x^2 - 10\,x + y^2 - 8\, y + z^2 - 12\, z + 63 = 0)

Step-by-step explanation:

Apply the Pythagorean Theorem to find the distance between these two endpoints:

\begin{aligned}&\text{Distance}\cr &= \sqrt{\left(x_2 - x_1\right)^2 + \left(y_2 - y_1\right)^2 + \left(z_2 - z_1\right)^2} \cr &= \sqrt{(6 - 4)^2 + (6 - 2)^2 + ((-3) - (-9))^2 \cr &= \sqrt{56}}\end{aligned}.

Since the two endpoints form a diameter of the sphere, the distance between them would be equal to the diameter of the sphere. The radius of a sphere is one-half of its diameter. In this case, that would be equal to:

\begin{aligned} r &= \frac{1}{2} \, \sqrt{56} \cr &= \sqrt{\left(\frac{1}{2}\right)^2 \times 56} \cr &= \sqrt{\frac{1}{4} \times 56} \cr &= \sqrt{14} \end{aligned}.

In a sphere, the midpoint of every diameter would be the center of the sphere. Each component of the midpoint of a segment (such as the diameter in this question) is equal to the arithmetic mean of that component of the two endpoints. In other words, the midpoint of a segment between \left(x_1, \, y_1, \, z_1\right) and \left(x_2, \, y_2, \, z_2\right) would be:

\displaystyle \left(\frac{x_1 + x_2}{2},\, \frac{y_1 + y_2}{2}, \, \frac{z_1 + z_2}{2}\right).

In this case, the midpoint of the diameter, which is the same as the center of the sphere, would be at:

\begin{aligned}&\left(\frac{x_1 + x_2}{2},\, \frac{y_1 + y_2}{2}, \, \frac{z_1 + z_2}{2}\right) \cr &= \left(\frac{4 + 6}{2},\, \frac{2 + 6}{2}, \, \frac{(-9) + (-3)}{2}\right) \cr &= (5,\, 4\, -6)\end{aligned}.

The equation for a sphere of radius r and center \left(x_0,\, y_0,\, z_0\right) would be:

\left(x - x_0\right)^2 + \left(y - y_0\right)^2 + \left(z - z_0\right)^2 = r^2.

In this case, the equation would be:

\left(x - 5\right)^2 + \left(y - 4\right)^2 + \left(z - (-6)\right)^2 = \left(\sqrt{56}\right)^2.

Simplify to obtain:

\left(x - 5\right)^2 + \left(y - 4\right)^2 + \left(z + 6\right)^2 = 56.

Expand the squares and simplify to obtain:

x^2 - 10\,x + y^2 - 8\, y + z^2 - 12\, z + 63 = 0.

8 0
3 years ago
Find the value of x.<br> 6x+3(-3x+4)=13
iren [92.7K]

Answer:

x= -1/3 or -0.3

Step-by-step explanation:

6 0
2 years ago
Read 2 more answers
Other questions:
  • 4a-3a+21+6 in standard form
    8·1 answer
  • michael found a job listed in the classified ads that pays a yearly salary of $57.3k what is the weekly salary based on this ann
    6·1 answer
  • The table shows the charge for renting a bicycle from a rental shop on Cumberland Island, Georgia, for different amounts of time
    6·2 answers
  • Which shows faster decay 0.8 or 0.9
    11·1 answer
  • While at the beach Daniel buys lunch for his family from a food stand he purchased one hotdog for $2.50 and three hamburgers if
    10·1 answer
  • A shadow 2 meters long is cast by a statue that is 2.1 meters tall. If a stucco column close by casts a shadow 4 meters long, ho
    10·1 answer
  • I’m failing my math class and I need help with math because I don’t understand some stuff.
    12·2 answers
  • Helppppppp meee plzz
    5·2 answers
  • -4x – y = 24<br> Complete the missing value in the solution to the equation.
    14·2 answers
  • If x = 3 and y = 6, evaluate the following expression:<br> 100 – 3(3y - 4x)
    8·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!