Over the past several years, the owner of a boutique on aspen avenue has observed a pattern in the amount of revenue for the store. the revenue reaches a maximum of about $ 59000 in april and a minimum of about $ 29000 in october. suppose the months are numbered 1 through 12, and write a function of the form f(x)=asin(b[x−c])+d that models the boutique's revenue during the year, where x corresponds to the month. if needed, you can enter π=3. as 'pi' in your answer.

Step-by-step explanation:

Given that the revenue reaches a maximum of about $ 59000 in April and a minimum of about $ 29000 in October. Suppose the months are numbered 1 through 12, where the months are numbered 1 through 12

Then minimum when x=10 and maximum when x = 4

Average = 44000 correspond to middle line

Amplitude =

Hence the function roughly would be

So we found out two values for A and D

To find values for B and C

The minimum of sine function corresponds to -pi/2 here it is 10 and maximum pi/2 here is 4.

Period = 12 months

So B = coefficient of X =

Because symmetrical about x=7 we have x-7 with a negative sign since min atx =10

answer: ratio of volume of cone (with 3 times the height and equal diameter) to volume of cylinder is 2 to 1. the value of π is not used.

step-by-step explanation:

radius is diameter/2 = 4.

area of circle is π r^2.

volume of cylinder is height × area of base = hπr^2 = 3(4^2) π = 48π cubic inches.

not knowing the formula for volume of cone, i calculate it using calculus (which is for calculating things).

volume of cone is integral 0 to h area(y) dy. area(y) is π r(y)^2. r(y) runs r to zero as y runs zero to h, r(0) = r, r(h) = 0.

r(y) = r - r/h y

area(y) = π (r - r/h y)^2 = π (r^2 - 2r^2y/h + r^2y^2/h^2) = π r^2(1-2y/h+y^2/h^2)

antiderivative area(y) = π r^2 (y-y^2/h+y^3/(3h^2))

integral 0 to h = π r^2(h-h^2/h+h^3/(3h^2) - (0)) = π r^2(h - h + h/3) = π r^2(h/3) = π/3 r^2 h

volume of this cone is π/3(4^2)18 cubic inches.

= 6 16 π = 96π cubic inches.

cone has twice the volume, 96/48.

cone height is 6 times the cylinder.

ratio of volume formula: π r^2 cancels.

cone over cylinder ratio is 6h/3 to h, 2 to 1.

the answer for this question is : 360°

step-by-step explanation:

we have been given a triangle   we need to tell which one of these is a triangle below to map onto itself.

360° rotation is the complete rotation which eventually leads to the same figure which is given.

the correct will be, that is 360° that will cause the triangle below to map onto itself.