Outside temperature over a day can be modelled as a sinusoidal function. Suppose you know the high temperature of 64 degrees occurs at 4 PM and the average temperature for the day is 50 degrees. Assuming t is the number of hours since midnight, find an equation for the temperature, D, in terms of t.

The sinusoidal wave can be represented by the equation:y=A∗sin[ω(x−α)]+Cy=A∗sin[ω(x−α)]+C

where, A is the amplitude; ω=2π/periodω=2π/period; α=α= phase shift on the Y-axis; and C = midline.

With the information given in this problem,

Midline (C) is the average calculated as: (72+38)/2=55(72+38)/2=55;

Amplitude (A) is 72-55= 17;

Period = 24 hours;

ω=2π/24ω=2π/24;

α=10α=10;

Substituting in the equation,

y=17∗sin[2π/24(x−10)]+55y=17∗sin[2π/24(x−10)]+55

Solving this equation for y=51y=51 gives the value of x as 9.09.

Thus, the temperature first reaches 51 degrees about 9.09 hours after midnight.

Step-by-step explanation:

the volume is the product of the area of the base, 3x(3x+4), and the height, 3x-1

step-by-step explanation:

the simplified form is

step-by-step explanation:

we want to simplify the expression,

let us change the middle bar to a normal division sign to obtain,

we multiply the first fraction by the reciprocal of the second fraction to obtain,

we factor to obtain,

we cancel the common factors to get,

we simplify to get,

the correct answer is b