Asinusoidal function whose period is 1/2 , maximum value is 10, and minimum value is −4 has a y-intercept of 3. what is the equation of the function described?

f(x) = 7 sin (4πx) + 3. The function f(x) = 7 sin (4πx) + 3 describe a sinusoidal function whose period is 1/2, maximum value 10, minimum value -4, and it has a y-intercept of 3.

A sinudoidal function whose period is 1/2, maximum value is 10, minimum value is -4, and it has a y-intercept of 3. Let's write to the form f(x) = A sin (ωx +φ) + k, where A is the amplitude, ω is the angular velocity with ω=2πf, (ωx+φ) is the oscillation phase, φ the initial phase (horizontal shift), and k is y-intercept (vertical shift).

Calculating the amplitude:

A = |max - min/2|

A = |10 - (-4)/2| = 14/2

A = 7

calculating the ω:

The period of a sinusoidal is T = 1/f > f = 1 / T

ω = 2πf > ω = 2π ( 1/T) with T = 1/2

ω = 2π (1/(1/2) = 2π (2)

ω = 4π

The y-intercept k = 3

Writing the equation function with A = 7, ω = 4π, k = 3, φ = 0.

f(x) = A f(x) = A sin (ωx +φ) + k > f(x) = 7 sin (4πx) + 3.

something that characterises a right triangle is the fact that we may use pythagoras' theorem to find any one of its sides given that we have the length of the other two sides. here, we have the length of the hypotenuse, √(87) yd, and one other side, √(23) yd, thus we can easily find the length of the remaining side using pythagoras' theorem as defined below:

c^2 = a^2 + b^2, where c is the length of the hypotenuse, and a and b are the lengths of the other two sides.

thus, given that c = √(87) and a = √(23), we may substitute these into the formula we defined above to get:

c^2 = a^2 + b^2

(√87)^2 = (√23)^2 + b^2 (substitute c = √87 and a = √23 into the equation)

87 = 23 + b^2 (evaluate (√87)^2 = 87 and (√23)^2 = 23 - remember that the square root of a number, squared will equal that very same number)

64 = b^2 (subtract 23 from both sides)

√64 = b (take the square root of both sides)

8 = b (evaluate √64 = 8)

therefor, the length of the unknown leg in the right triangle is 8 yd (first answer).