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Gre4nikov [31]
3 years ago
13

Without the wind, a plane would fly due east at a rate of 150 mph. The wind is blowing southeast at a rate of 50 mph. The wind i

s blowing at a 45 angle from due east. What is the actual speed of the plane with the wind?
Mathematics
1 answer:
ch4aika [34]3 years ago
8 0
The actual speed of the plane with the wind:
v² = ( 150 + 50 · cos 45°)² + ( 50 · sin 45°)²
v² = ( 150 + 35.355 )² + 35.355²
v² = 34,356.467 + 1,249.976
v = √35,606.452
v = 188.7 mph
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solve the system of equations by finding the reduced row-echelon form of the augmented matrix for the system of equations. x-2y+
Alekssandra [29.7K]

Answer:

x = -5, y = -6, z = -3

Step-by-step explanation:

Given the system of three equations:

\left\{\begin{array}{l}x-2y+3z=-2\\6x+2y+2z=-48\\x+4y+3z=-38\end{array}\right.

Write the augmented matrix for the system of equations

\left(\begin{array}{ccccc}1&-2&3&|&-2\\6&2&2&|&-48\\1&4&3&|&-38\end{array}\right)

Find the reduced row-echelon form of the augmented matrix for the system of equations:

\left(\begin{array}{ccccc}1&-2&3&|&-2\\6&2&2&|&-48\\1&4&3&|&-38\end{array}\right)\sim \left(\begin{array}{ccccc}1&-2&3&|&-2\\0&-14&16&|&36\\0&-6&0&|&36\end{array}\right)\sim \left(\begin{array}{ccccc}1&3&-2&|&-2\\0&16&-14&|&36\\0&0&-6&|&36\end{array}\right)

Thus, the system of three equations is

\left\{\begin{array}{r}x+3z-2y=-2\\16z-14y=36\\-6y=36\end{array}\right.

From the last equation:

y=-6

Substitute it into the second equation:

16z-14\cdot (-6)=36\\ \\16z=36-84\\ \\16z=-48\\ \\z=-3

Substitute y = -6 and z = -3 into the first equation:

x+3\cdot (-3)-2\cdot (-6)=-2\\ \\x=-2+9-12\\ \\x=-5

7 0
3 years ago
Help me plz now plz help me asap​
loris [4]

\\ \sf\longmapsto 0.49=\dfrac{49}{100}

\\ \sf\longmapsto 0.093=\dfrac{93}{1000}

\\ \sf\longmapsto 0.021=\dfrac{21}{1000}

\\ \sf\longmapsto 0.103=\dfrac{103}{1000}

6 0
3 years ago
Which equation is equivalent to the equation 6x+9=12? A: x + 9 = 6 B: 2 x + 3 = 4 C: 3 x + 9 = 6 D: 6 x + 12 = 9
Pachacha [2.7K]

Answer: B

Step-by-step explanation:

3 0
2 years ago
Please help me this is for 95 points ​
uranmaximum [27]
Y=12
The angles are 45°, 114°,105°,96° & 84°
7 0
2 years ago
It takes 12 cups of chicken broth to make a chicken soup recipe. How much is this in quarts?
slava [35]
3 quarts.

4 cups equal 1 quart according to the US standards.
Using that, we get an equation like:
4c = 1q
if you want 12 cups, you have to multiply the left side by 3 meaning you would also have to multiply the right side by 3.
3(4c) = 3(1q)
12c = 4q
you get 12 cups equals 4 quarts.
4 0
3 years ago
Read 2 more answers
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