The function given represents the temperature of a sauna set to 180°F. The temperature goes up and down throughout the day. Find the period: 30 Find how many times the function reaches a maximum temperature in one hour: 180 f(x)=5sin(π15x)+180, where x is measured in minutes, and f(x) is measured in degrees Fahrenheit.

The answer is below

Step-by-step explanation:

Given the function as:

f(x)=5sin(πx / 15)+180,

a) The angular frequency (ω) = 2π * frequency

but ω = π/15, hence:

π/15 = 2π * frequency

frequency = (π/15)/2π

frequency = 1/30 hertz

Period (T) = 1/frequency = 1/(1/30) = 30 seconds

b) The period is 30 seconds. This means that it reaches the maximum temperature every 30 seconds.

In one hour (3600 s), the number of times the function reaches a maximum temperature = 3600 s / 30 s = 120

he used the algebra tiles correctly.

step-by-step explanation:

given : 3x(2x-1)

solution :

since he used algebra tiles .

armando's solution is the same in the solution shown in figure

as he distributed 2x into x and x and wrote them vertically

and also write   -1 vertically

and 3x into x and x and x and wrote it horizontally

performing the multiplication in the algebra tiles we get

and solving the given expression :

3x(2x-1)

since solving the expression using tiles   and solving the expression algebraically we get the same answer

thus   we can choose the first statement as the answer to this problem which is "he used the algebra tiles correctly".

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

step-by-step explanation: