Help Arduino #4

[Aokiji_Master]

swing servo motor back and forth when detected a sound by sound sensor or a rain sensor has detected and stop when thiers no detected

 

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72. Using the cosine rule, we have:

cos 0 = cos 05° cos 55° + sin 05° sin 55°
cos 0 = cos² 05° + sin² 05° (since cos² θ + sin² θ = 1)
cos 0 = 1
Therefore, 8 = 0 radians.

Answer: A. 0.765

73. We know that cot θ = cos θ / sin θ. Using the fact that sin θ = 0.6, we can find cos θ using the Pythagorean identity:

cos² θ + sin² θ = 1
cos² θ + 0.36 = 1
cos² θ = 0.64
cos θ = ±0.8 (since θ is acute, we take the positive value)

Therefore, cot θ = cos θ / sin θ = 0.8 / 0.6 = 4/3.

Answer: C. 4/5

74. Using the identity sec² θ - 1 = tan² θ, we can rewrite the expression as:

sec 6 - (sec 0) sin² 0 = sec² 6 - sec² 0
= (1/cos² 6) - (1/cos² 0)
= (1/cos² 6) - (1/1)
= (1/cos² 6) - 1

Using the identity 1 - sin² θ = cos² θ, we can rewrite this as:

(1/cos² 6) - 1 = 1 - sin² 6 - 1
= cos² 6 - sin² 6
= cos 12 (using the double angle formula for cosine)

Therefore, the answer is cos 12.

Answer: A. cos² 0

75. The time difference between two longitudes can be found using the formula:

time difference = (longitude difference / 15) hours

Using this formula, we have:

longitude difference = 139°E - 121°E = 18°E
time difference = (18°E / 15) hours = 1 hour and 12 minutes

Answer: A. 1 hour and 12 minutes

76. Using the spherical law of cosines, we have:

cos a = cos b cos c + sin b sin c cos A
cos 46° = cos b cos 75°
cos b = cos 46° / cos 75°

Using a calculator, we get:

cos b ≈ 0.5209
b ≈ 59.9°

However, since this is a spherical triangle, we need to convert this to a spherical angle by using the formula:

Spherical angle = 180° - angle in degrees

Therefore, b = 180° - 59.9° = 120.1°.

Answer: Not in options.

77. Using the spherical law of sines, we have:

sin a / sin A = sin c / sin C
sin 80° / sin 72° = sin 115° / sin 90°
sin a = (sin 80° / sin 72°) sin 90°
a = sin⁻¹ (sin 80° / sin 72°)

Using a calculator, we get:

a ≈ 96.2°

Using the fact that the angles in a triangle add up to 180°, we can find angle C:

C = 180° - A - a
C = 180° - 72° - 96.2°
C ≈ 11.8°

Answer: Not in options.

78. The spherical excess of a spherical triangle is given by the formula:

Excess = sum of angles - (n - 2) × 180°

where n is the number of sides of the triangle. Since all angles of a right spherical triangle are 90°, we have:

Excess = 90° + 90° + 90° - (3 - 2) × 180°
Excess = 270° - 180°
Excess = 90°

Therefore, the spherical excess of the given spherical triangle is 90°.

Answer: A. 45°

79. Using the distance formula, we have:

distance = sqrt [(x2 - x1)² + (y2 - y1)²]
distance = sqrt [(-2 - 4)² + (5 - (-3))²]
distance = sqrt [(-6)² + 8²]
distance = sqrt [36 + 64]
distance = sqrt 100
distance = 10

Therefore, the distance between A and B is 10 units.

Answer: C. 10

80. Since the points (a,1), (b,2), and (c,3) are collinear, we can use the slope formula to find the slope of the line passing through them:

slope = (y2 - y1) / (x2 - x1)
slope = (3 - 1) / (c - a)
slope = 2 / (c - a)

Since they are collinear, the slope must be the same for all pairs of points. Therefore, we have:

2 / (c - a) = 1 / (b - a)
2(b - a) = c - a

Using the given choices, we can substitute in values for a, b, and c to see which one satisfies this equation:

A. c - b = c - a
B. c - b = b - a
C. c - a = a - b
D. c - a = b - a

Trying option D, we have:

c - a = b - a
2(b - a) = b - a
b - a = 0
b = a

Therefore, option D is true.

Answer: D. c - a = b - a

81. Using the slope formula, we have:

slope = (y2 - y1) / (x2 - x1)
slope = (7 - 3) / (10 - (-5))
slope = 4 / 15

The inclination of a line is the angle it makes with the positive x-axis. We can find this angle using the tangent function:

tan θ = slope
θ = tan⁻¹ (slope)

Using a calculator, we get:

θ ≈ 14.93°

Therefore, the inclination of the line passing through (-5,3) and (10,7) is approximately 14.93°.

Answer: B. 14.93