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asambeis [7]
3 years ago
8

Sam drove for 2 hours at 45 mph. He has the same distance remaining. How fast should he drive to make his average speed 60 mph?

Mathematics
1 answer:
Goshia [24]3 years ago
8 0
Speed (S) = Distance (D) / time (t)

First stretch

45 = D / 2

D = 45*2

D = 90 mp

How is the same distance:

Second stretch

S = 90 / t

Average speed (AS):

AS = (S1+S2) / 2

60 = [45+(90/t)] / 2

120 = 45+90/t

120-45 = 90/t

75 = 90/t

t = 90/75

t = 1,2 h

________________________

And now:

S = 90 / t

S = 90 / 1,2

S = 75 mph
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ANSWER
x = ±1 and y = -4.
Either x = +1 or x = -1 will work

EXPLANATION
If -3 + ix²y and x² + y + 4i are complex conjugates, then one of them can be written in the form a + bi and the other in the form a - bi. In other words, between conjugates, the imaginary parts are same in absolute value but different in sign (b and -b). The real parts are the same

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⇒ real part: -3
⇒ imaginary part: x²y

For x² + y + 4i
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⇒ imaginary part: 4

Therefore, for the two expressions to be conjugates, we must satisfy the two conditions. 

Condition 1: Imaginary parts are same in absolute value but different in sign. We can set the imaginary part of -3 + ix²y to be the negative imaginary part of x² + y + 4i so that the 

   x²y = -4 ... (I)

Condition 2: Real parts are the same

   x² + y = -3 ... (II)

We have a system of equations since both conditions must be satisfied

   x²y = -4 ... (I)
   x² + y = -3 ... (II)

We can rearrange equation (II) so that we have

   y = -3 - x² ... (II)

Substituting into equation (I)

   x²y = -4 ... (I)
   x²(-3 - x²) = -4
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Therefore, x = ±1.
Leave alone (x² + 4) as it gives no real solutions.

Solve for y:

   y = -3 - x² ... (II)
   y = -3 - (±1)²
   y = -3 - 1
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   -3 + ix²y 
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   x² + y + 4i
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   = 1 - 4 + 4i
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