Answer:
A triangle has three sides, three vertices, and three angles. The sum of the three interior angles of a triangle is always 180°.
The sum of the length of two sides of a triangle is always greater than the length of the third side.
<u>EXPLANATION</u><u>:</u>
Given that
sin θ = 1/2
We know that
sin 3θ = 3 sin θ - 4 sin³ θ
⇛sin 3θ = 3(1/2)-4(1/2)³
⇛sin 3θ = (3/2)-4(1/8)
⇛sin 3θ = (3/2)-(4/8)
⇛sin 3θ = (3/2)-(1/2)
⇛sin 3θ = (3-1)/2
⇛sin 3θ = 2/2
⇛sin 3θ = 1
and
cos 2θ = cos² θ - sin² θ
⇛cos 2θ = 1 - sin² θ - sin² θ
⇛cos 2θ = 1 - 2 sin² θ
Now,
cos 2θ = 1-2(1/2)²
⇛cos 2θ = 1-2(1/4)
⇛cos 2θ = 1-(2/4)
⇛cos 2θ = 1-(1/2)
⇛cos 2θ = (2-1)/2
⇛cos 2θ = 1/2
Now,
The value of sin 3θ /(1+cos 2θ
⇛1/{1+(1/2)}
⇛1/{(2+1)/2}
⇛1/(3/2)
⇛1×(2/3)
⇛(1×2)/3
⇛2/3
<u>Answer</u> : Hence, the req value of sin 3θ /(1+cos 2θ) is 2/3.
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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.
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Answer: Danny can make 15 sundaes from 11 1/4 cups of chocolate
Step-by-step explanation:
number of cups of chocolate syrup= 11 1/4 cups
For ever sundae, he decides to make, it will require 3/4 cup of chocolate
Number of sundae , Danny can make = number of cups of chocolate syrup /3/4 cup of sundae
= 11 1/4 / 3/4
45/4 x 4/3= 15 sundaes
Therefore, Danny can make 15 sundaes from 11 1/4 cups of chocolate
