Without the length of BC given, we cannot find the exact value of AB using the Pythagorean theorem.
To find x, we can use the fact that the two vertical lines in the image are parallel, creating alternate interior angles. We know that the angle labeled as 55 degrees is congruent to the angle labeled as 2x+10 degrees.
55 = 2x + 10
Subtracting 10 from both sides:
45 = 2x
Dividing by 2:
x = 22.5
Therefore, the value of x is 22.5 degrees.
Find AB. Round to the nearest tenth if necessary.
What is the value of x? Round the answer to the nearest tenth.
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5 answers
Find the period range and amplitude of the cosine function y=-4 cos 8x
The general form of a cosine function is y = A cos(Bx - C) + D, where A is the amplitude, B is the frequency (or period), C is the horizontal shift, and D is the vertical shift.
Comparing this to the given function y = -4 cos 8x, we can see that:
A = -4 (amplitude)
B = 8 (frequency or period)
C = 0 (no horizontal shift)
D = 0 (no vertical shift)
To find the period, we can use the formula:
period = 2π/B
period = 2π/8
period = π/4
So the period range is from 0 to π/4.
Therefore, the amplitude of the function is 4 and the period range is from 0 to π/4.
Comparing this to the given function y = -4 cos 8x, we can see that:
A = -4 (amplitude)
B = 8 (frequency or period)
C = 0 (no horizontal shift)
D = 0 (no vertical shift)
To find the period, we can use the formula:
period = 2π/B
period = 2π/8
period = π/4
So the period range is from 0 to π/4.
Therefore, the amplitude of the function is 4 and the period range is from 0 to π/4.
Find the period range and amplitude of the cosine function y=-4 cos 8xA.
A. period= 1/4, amplitude=4
B. period= 1/4 pi, amplitude=4
C. period= 1/2 pi, amplitude=-4
D. period= 1/2, amplitude=-4
A. period= 1/4, amplitude=4
B. period= 1/4 pi, amplitude=4
C. period= 1/2 pi, amplitude=-4
D. period= 1/2, amplitude=-4
The correct answer is B.
To find the period and amplitude of the given cosine function y = -4 cos 8xA, we need to rewrite the equation in standard form:
y = -4 cos 8xA
y = -4 cos (8A)x
Comparing this to the general form of a cosine function y = A cos(Bx - C) + D, we can see that:
A = -4 (amplitude)
B = 8A (frequency or period)
C = 0 (no horizontal shift)
D = 0 (no vertical shift)
To find the period, we use the formula:
period = 2π/B
period = 2π/8A
period = π/4A
Therefore, the period range of the function is from 0 to π/4A.
Substituting A=1/4 pi gives:
period = π/4(1/4 pi) = π/pi = 1
So the period range is from 0 to 1.
Therefore, the amplitude of the function is 4 and the period range is 1/4 pi.
Therefore, the correct answer is B.
To find the period and amplitude of the given cosine function y = -4 cos 8xA, we need to rewrite the equation in standard form:
y = -4 cos 8xA
y = -4 cos (8A)x
Comparing this to the general form of a cosine function y = A cos(Bx - C) + D, we can see that:
A = -4 (amplitude)
B = 8A (frequency or period)
C = 0 (no horizontal shift)
D = 0 (no vertical shift)
To find the period, we use the formula:
period = 2π/B
period = 2π/8A
period = π/4A
Therefore, the period range of the function is from 0 to π/4A.
Substituting A=1/4 pi gives:
period = π/4(1/4 pi) = π/pi = 1
So the period range is from 0 to 1.
Therefore, the amplitude of the function is 4 and the period range is 1/4 pi.
Therefore, the correct answer is B.
1 answer