An equation is said to have a constant of proportionality if 'x' is a multiple of 'y' or 'y' is a multiple of 'x'.
Now, we have to determine an equation with constant of proportionality as '1'.
1.
This equation has constant of proportionality as ''.
2.
This equation has constant of proportionality as ''.
3.
This equation has constant of proportionality as ''.
4.
This equation has constant of proportionality as '1'.
Option D is the correct answer.
Answer:
The two airplanes are about 330miles apart.
Step-by-step explanation:
The diagram interpreting the question has been attached to this response.
As shown in the diagram,
i. the airplanes leave at point C.
ii. at 2.00pm the first and second airplanes are at points A and B respectively, where they are 312miles and 487miles away from the starting point C in directions due north and N42E from the point C.
iii. the points A, B and C form a triangle with sides a, b and c.
To solve for the value of c which is the distance between the two planes at 2.00pm, the cosine rule is used.
c² = a² + b² - 2abcosC --------------(i)
where;
b = 312miles
a = 487miles
C = 42°
Substitute these values into equation (i) and solve as follows;
c² = (487)² + (312)² - 2(312)(487)cos(42)
c² = (237169) + (97344) - 303888cos(42)
c² = (237169) + (97344) - 303888(0.7431)
c² = 334513 - 225819.1728
c² = 108693.8272
<em>Take the square root of both sides</em>
√c² = √108693.8272
c = 329.69
c ≅ 330miles
Therefore, the two airplanes are far apart by 330miles
Answer:
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: