What is the general equation of a sine function with an amplitude of 6, a period of startfraction pi over 4 endfraction, and a horizontal shift of startfraction pi over 2 endfraction?

C:

Step-by-step explanation:

Amplitude is changed by multiplying the entire trig function by a number, by default the amplitude is 1, so multiplying by 6 is necessary; eliminate A and B

Horizontal shift is going through the x axis, so it must be subtracted from the x value. This is only seen in choice C of the remaining answers.

Calculating the period isn't necessary because we already found the right answer but in case you need it in the future; the period is by default 2pi, to get to pi/4, it had to be 8 times smaller, so multiplying x and translations on x by 8 will get you the correct period.

  f(x) = 6·sin(8(x -π/2))

Step-by-step explanation:

A transformed sine function with amplitude A, period P, and horizontal shift S can be written as ...

  f(x) = A·sin(2π/P(x -S))

__

The equation for A=6, P=π/4, and S=π/2 is then ...

  f(x) = 6·sin(8(x -π/2))

_____

Additional comment

The horizontal shift is equal to two full periods, so the shifted function is indistinguishable from the unshifted function.

The answer is in the image 

SI=(P*R*T)/100

P=2000

R=1.5

T=6

SI=(2000*1.5*6)/100

=(2000*9)/100

=180

Neil will earn interest of 180

Cost of 7 gallons=$24.50

Cost of 1 gallon=24.50/7=3.5

Cost of 15 gallons=15*3.5=52.5

Cost of 15 gallons will be $52.5

For 1 flavor there are 9 topping

Therefore, for 5 different flavors there will be 5*9 choices

No of choices= 5*9

=45 

y=2x+15

where y=Value of coin

x=Age in years

Value of coin after 19 years=2*19+15

=$53

Therefore, Value after 19 years=$53

F=ma

where F=force

m=mass

a=acceleration

Here,

F=4300

a=3.3m/s2

m=F/a

    =4300/3.3

    =1303.03kg

The answer is in the image 

Salesperson will make 6% of 1800

=(6/100)*1800

=108

Salesperson will make $108 in $1800 sales