Solve the following trigonometric question: cos x=3 cos x-2
1 answer:
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Answer:
Step-by-step explanation:
Let the numbers be x,y, where x>y
The geometric mean is
The Arithmetic mean is
The ratio of the geometric mean and arithmetic mean of two numbers is 3:5.
We can write the equation;
or
l
and
or
Make y the subject in equation 2
Put equation 3 in 1
When x=1, y=10-1=9
When x=9, y=10-9=1
Therefore x=9, and y=1
The ratio of the smaller number to the larger number is
Answer:
y = -x + 11
Step-by-step explanation:
The equation of a straight line is is given by:
y = mx + b; where m is the slope and b is the y intercept
The equation of the line joining G(9, 8) and H(3, 2) is given as:
The perpendicular bisector of the line joining G(9, 8) and H(3, 2) is perpendicular to the line joining G(9, 8) and H(3, 2) and passes through the midpoint of line joining G(9, 8) and H(3, 2).
Let (x, y) be the midpoint of the line joining G(9, 8) and H(3, 2). Hence:
x = (9 + 3)/2 = 6
y = (8 + 2)/2 = 5
The midpoint = (6, 5)
Two lines are perpendicular if the product of their slopes is -1.
The line joining G(9, 8) and H(3, 2) has a slope of 1, hence, the slope of the perpendicular bisector would be -1.
This means that the perpendicular bisector has a slope of -1 and passes through (6, 5). Using:
The equation of the perpendicular bisector is y = -x + 11
Consider the center of the nonagon. If we join the center to all the vertices, the central angle of 360°, is divided into 9 equal angles, each with a measure of:
360°/9=40°
So to a nonagon rotated 40°, clockwise or counterclockwise, is indistinguishable from the original one.
similarly if we rotate 80 ° c.wise or c.c.wise
in general, a nonagon has a rotational symmetry of 40°n,
where n∈{...-3, -2, -1, 0, 1, 2, 3}...
where 40°n, for n negative, means we are rotating clockwise.
Answer: any angle which is a multiple of 40°
360°/9=40°
So to a nonagon rotated 40°, clockwise or counterclockwise, is indistinguishable from the original one.
similarly if we rotate 80 ° c.wise or c.c.wise
in general, a nonagon has a rotational symmetry of 40°n,
where n∈{...-3, -2, -1, 0, 1, 2, 3}...
where 40°n, for n negative, means we are rotating clockwise.
Answer: any angle which is a multiple of 40°