<span>1. a sine curve with amplitude 2, and period 4pi radians
</span>
the general equation of the sine curve ⇒⇒ y = a sin (nθ)
where: a is the amplitude and n = 2π/perid
∵ <span>amplitude 2, and period 4pi radians
</span>
∴ y = 2 sin (θ/2)
The correct answer is option D. y = 2 sin (θ/2)
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<span>2.The period and amplitude of the function ⇒⇒ y = 5 cos 2θ
</span>
<span>comparing with y = a cos nθ
</span>
where : a is the amplitude and n = 2π/period
<span>amplitude = 5 , period = 2π/n = 2π/2 = π
</span>
The correct answer is option B. Period: pi radians: Amplitude:5
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3. tan (2π/3) = tan 120° = -√3
120° lie in the second quadrant and its reference angle = 180° - 120° = 60°
tan function in the second quadrant is negative
∴ tan 120° = - tan 60 = -√3
The correct answer is C. -sqrt3
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4. <span>Tan 5π/6 = tan 150° = -(√3)/3
</span>
150° lies in the second quadrant and its reference angle = 180° - 150° = 30°
tan function in the second quadrant is negative
∴ tan 150° = - tan 30 = -(√3)/3
The correct answer is <span>B.-sqrt3/3</span>
The relationship between the two variables is inverse proportionality, that is, the greater the number of people, the less the amount of money earned.
Since visitors to a carnival are invited to guess the number of beans in a jar, and the person who guesses the correct number wins $ 300, but if multiple people guess correctly, the prize will be divided evenly among them, to determine what is the relationship between the number of people who guess correctly and the amount of money each person will recieve the following logical reasoning must be performed:
Since the prize is a fixed number, 300, it is a value that will not change. In turn, the more people who have guessed right, the lower the amount of money that each of them will win (because the number 300 will be divided by a greater number).
Therefore, the relationship between the two variables is inverse proportionality, that is, the greater the number of people, the less the amount of money earned.
Learn more in brainly.com/question/2548537
Answer: 140 m3
Step-by-step explanation:
Multiply the area of the trapezoid face by the length .
Since the area is 20, you multiply it by 7 to get 140
Complete question :
Lucy has block letters that are in the shape of cubes with sides 2 3 foot long. She has a box which is 1 1 3 foot long, 2 3 foot wide, and 2 3 foot tall. Find the number of block letters that will fit in the box.
Answer:
1/2
Step-by-step explanation:
Number of block letters that will fit in :
Volume of box ÷ volume of each letter cube
Volume of each letter cube = (side length)³ = (2/3)³ = 8/27 ft³
Volume of box = length * width * height
Volume of box = 1 1/3 * 2/3 * 2/3
Volume of box = 4/3 * 2/3 * 2/3 = 16 / 27 ft³
Therefore ;
8/27 ÷ 16/27
8/27 * 27/16
= 8/16
= 1/2
