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Lorico [155]
2 years ago
12

Solve the equation by first using a sum-to-product formula. (enter your answers as a comma-separated list. let k be any integer.

round terms to three
Mathematics
1 answer:
kykrilka [37]2 years ago
8 0

Solutions of the equation are 22.5°, 30°.

The given equation is sin(5θ) - sin(3θ) = cos(4θ)

We take left side of the equation

sin(5θ) - sin(3θ) = 2cos ((5θ+3θ)/2) (sin(5θ-3θ)/2)

=2cos4θsinθ  [From sum-product identity]

Now we can write the equation as

2cos(4θ)sin(θ) = cos(4θ)

2cos(4θ)sinθ - cos(4θ) = 0

cos(4θ)[2sinθ - 1] = 0

cos(4θ) = 0

4θ = 90°

θ = 90/4

θ = 22.5°

and (2sinθ - 1) = 0

sinθ = 1/2

θ = 30°

Therefore, solutions of the equation are 22.5°, 30°

For more information about trigonometric identities, visit

brainly.com/question/24496175

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2 years ago
Below are the supply and demand equations for blenders in a certain market. In these equations, p represents price, D represents
Reptile [31]

The value of p at the point of equilibrium, where supply and demand are equal, is 43.3 (the nearest tenth).

<h3>What is equilibrium point of supply and demand?</h3>

The equilibrium point of supply and demand is the point where, the value of demand of a product is exactly equal to the value of supply of that product.

The supply and demand equations for blenders in a certain market is given as,

D=\dfrac{-5}{8}p+35

S=\dfrac{6}{5}p-44

Here, in these equations, p represents price, D represents demand, and S represents supply.

At the point of equilibrium, the supply and demand are equal. Therefore,

D=S\\\dfrac{-5}{8}p+35=\dfrac{6}{5}p-44

Solve it further to get the value of p as,

\dfrac{6}{5}p-\dfrac{-5}{8}p=35+44\\\dfrac{6}{5}p-\dfrac{-5}{8}p=35+44\\p=\dfrac{3160}{73}\\p\approx43.3

Hence, the value of p at the point of equilibrium, where supply and demand are equal is 43.3 (the nearest tenth).

Learn more about the equilibrium point of supply and demand here;

brainly.com/question/1915798

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