What are the lengths of line segments AB and BC?
2 answers:
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Answer:
- 0.5 + 2.985i
- 1 + 2.828i
- 1.5 + 2.598i
- 2 + 2.236i
Explanation:
Complex numbers have the general form a + bi, where a is the real part and b is the imaginary part.
Since, the numbers are neither purely imaginary nor purely real a ≠ 0 and b ≠ 0.
The absolute value of a complex number is its distance to the origin (0,0), so you use Pythagorean theorem to calculate the absolute value. Calling it |C|, that is:
Then, the work consists in finding pairs (a,b) for which:
You can do it by setting any arbitrary value less than 3 to a or b and solving for the other:
I will use b =0.5, b = 1, b = 1.5, b = 2
Then, four distinct complex numbers that have an absolute value of 3 are:
- 0.5 + 2.985i
- 1 + 2.828i
- 1.5 + 2.598i
- 2 + 2.236i
Answer:
Hence, Grasshopper will land on the ground after 1.5 sec.
Step-by-step explanation:
It s given that:
The height, in feet, of the grasshopper above the ground after t seconds is modeled by the function:
Now we are asked to find:
In how many seconds will the grasshopper land on the ground?
i.e. we have to find the value of t such that h(t)=0
i.e.
i.e. we need to find the roots of the given quadratic equation.
On solving the quadratic equation or plotting it's graph we could observe that the point where h(t)=0 are:
As time can't be negative hence we will consider:
Hence, grasshopper will land on the ground after 1.5 sec.