Write a sine function that has a midline of 5, an amplitude of 4 and a period of 3pi/2

Step-by-step explanation:

The standard form for this function is

y = Asin(Bx - C) + D where

A is the amplitude,

B is used to find the period in the formula ,

C is used to find the phase shift in the formula ,

and D is the midline which either moves the function up or down from its natural midline of 0.

We have no given phase shift, so there is no C value. The amplitude is easy; we just fill in A as 4. The period is another story:

and we solve for B by cross multiplying:

3πB = 4π and

so

so the function is

3. parallelogram

step-by-step explanation:

we turn each of our sides into direction vectors

ab=b-a=(3 - 7, 1 - 0) = (-4, 1)

bc=c-b=(1,6)

cd=d-c=(4,-1)

da=a-d=(-1,-6)

we see how the opposite sides have negated direction vectors; this is characteristic of a parallelogram.   we have congruent sides ab=cd and bc=da with unequal lengths because 1^2+6^2 is different from (-4)^2+1^2.   so it's not a square or a rhombus.  

we check the dot product of direction vectors of adjacent sides.   we have

ab dot bc = -4(1) + 1(6) = 2

that's not zero so the sides are not perpendicular.   we've ruled out rectangle.

the direction vectors indicate two pairs of congruent parallel sides, so we choose parallelogram over trapezoid.

n

step-by-step explanation: