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Veseljchak [2.6K]
2 years ago
10

Find the midpoint of A and B where A has coordinates (-3,-5) and B has coordinates (4,4).

Mathematics
1 answer:
snow_lady [41]2 years ago
8 0

Answer:

(\frac{1}{2}, \frac{-1}{2})

Step-by-step explanation:

Use the midpoint formula to solve.

1) Given 2 points: (x_{1}, y_1) and (x_2, y_2)

The midpoint formula would be (\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}).

2) Based on this, we can easily find the midpoint of AB.

  • -3 would be x_1\\
  • -5 would be y_1
  • 4 would be x_2  
  • the next 4 would be y_2

3) With this information, we can solve for the midpoint.  

(\frac{-3+4}{2}, \frac{-5+4}{2}) --> (\frac{1}{2}, \frac{-1}{2}) --> This is your answer.

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F(x) = 2x and g(x) = x + 1, find f(3) and find gf(3)
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Answer:

6 and 7

Step-by-step explanation:

To evaluate f(3), substitute x = 3 into f(x) , that is

f(3) = 2(3) = 6

To evaluate g(f(3)), substitute f(3) = 6 into g(x)

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2 years ago
A projectile is fired with muzzle speed 250 m/s and an angle of elevation 45° from a position 30 m above ground level. Where doe
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The projectile's horizontal and vertical positions at time t are given by

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x=\dfrac{250\frac{\rm m}{\rm s}}{\sqrt2}(36.2458\,\mathrm s)\approx6400\,\mathrm m

The projectile's horizontal and vertical velocities are given by

v_x=\left(250\dfrac{\rm m}{\rm s}\right)\cos45^\circ

v_y=\left(250\dfrac{\rm m}{\rm s}\right)\sin45^\circ-gt

At the time the projectile hits the ground, its velocity vector has horizontal component approx. 176.77 m/s and vertical component approx. -178.43 m/s, which corresponds to a speed of about \sqrt{176.77^2+(-178.43)^2}\dfrac{\rm m}{\rm s}\approx250\dfrac{\rm m}{\rm s}.

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Step-by-step explanation:

The hundreds place is less than 5 so you round down.

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