Ronaldo applies a constant force of F⃗ =⟨24,−7⟩ newtons to a box. His brother Federico applies a force −2F⃗ to another heavier box. What is the magnitude and direction of Federico's force? A 34 newtons in the same direction as Ronaldo's force B 34 newtons in a direction opposite to Ronaldo's force C 50 newtons in the same direction as Ronaldo's force D 50 newtons in a direction opposite to Ronaldo's force

9514 1404 393

  D  50 newtons in a direction opposite to Ronaldo's force

Step-by-step explanation:

The factor -2 means the magnitude is doubled and the direction is opposite that of F. We know the magnitude of F is more than 24, so -2F will have a magnitude more than 48. The appropriate choice is ...

  50 newtons in a direction opposite to Ronaldo's force

You can recognize that the components of Ronaldo's force are the smaller numbers of the Pythagorean triple 7-24-25. That recognition tells you the magnitude of Federico's force is 2×25=50 N. Or, you can figure it out using the Pythagorean theorem:

  |Federico's force| = √((-48)² +(14)²) = √(2304 +196) = √2500 = 50

d

step-by-step explanation:

by observation, we can see that the the graph is simply the graph of y = |x| that has been shifted 4 units downwards and 3 units to the left.

we can recognize in choice d :

y = | x + 3 |   - 4 (rewriting in general form)

y = | x - (- 3) |   - 4

the "-4 " term means   that the graph has been shifted by 4 units in the negative y direction

the "-3 " term means   that the graph has been shifted by 3 units in the negative x direction

this matches our observation of the graph described above.

12/11c

or

12

c

11