An object dropped from a height of 600 feet has a height, h(t), in feet after t seconds have elapsed, such that h(t)=600 - 16t^2. Express t as a function of height h, and find the time to reach a heigh of 50 feet

t as a function of height h is  t = √600 - h/16

The time to reach a height of 50 feet is 5.86 minutes

Step-by-step explanation:

Function for height is h(t) = 600 - 16t²

where t = time lapsed in seconds after an object is dropped from height of 600 feet

t  as a function of height h

replacing the function with variable h

h = 600 - 16t²

Solving for t

Subtracting 600 from both side

h - 600 = -16t²

Divide through by -16

600 - h/ 16 = t²

Take square root of both sides

√600 - h/16 = t

Therefore, t = √600 - h/16

Time to reach height 50 feet

t = √600 - h/16

substituting h = 50 in the equation

t = √600 - 50/16

t = √550/16

t= 34.375

t = 5.86 minutes

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.