Use substitution. 2x + 3y = 5 4x - y = 17 Use linear combinations: 2x + 3y = 5 4x - y = 17
1 answer:
I'll help you get started. To use substitution on the first pair of equations, we want to solve for one of the variables in one of the two equations. It looks like it would be easiest to solve for y in the second equation:
Now we want to substitute this alternate version of y into the first equation:
.
I'll let you finish off that first one. The second problem asks to solve the two equations using linear combination. This means we want to add the two equations together and cancel out one of the variables. Again, it's easiest to cancel out the y since one is negative. First we want to take the second equation and multiply by 3 on both sides:
Now we want to add both equations together. Add the left sides and the right sides on their respective sides of the equals sign:
You can finish that one as well. Your answers for both methods will be the same if you do everything right! Let me know if you have more questions
Now we want to substitute this alternate version of y into the first equation:
I'll let you finish off that first one. The second problem asks to solve the two equations using linear combination. This means we want to add the two equations together and cancel out one of the variables. Again, it's easiest to cancel out the y since one is negative. First we want to take the second equation and multiply by 3 on both sides:
Now we want to add both equations together. Add the left sides and the right sides on their respective sides of the equals sign:
You can finish that one as well. Your answers for both methods will be the same if you do everything right! Let me know if you have more questions
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Answer:
The cosine function to model the height of a water particle above and below the mean water line is h = 2·cos((π/30)·t)
Step-by-step explanation:
The cosine function equation is given as follows h = d + a·cos(b(x - c))
Where:
= Amplitude
2·π/b = The period
c = The phase shift
d = The vertical shift
h = Height of the function
x = The time duration of motion of the wave, t
The given data are;
The amplitude = 2 feet
Time for the wave to pass the dock
The number of times the wave passes a point in each cycle = 2 times
Therefore;
The time for each complete cycle = 2 × 30 seconds = 60 seconds
The time for each complete cycle = Period = 2·π/b = 60
b = π/30 =
Taking the phase shift as zero, (moving wave) and the vertical shift as zero (movement about the mean water line), we have
h = 0 + 2·cos(π/30(t - 0)) = 2·cos((π/30)·t)
The cosine function is h = 2·cos((π/30)·t).