Determine an appropriate domain of the function. Identify the independent and dependent variables. A stone is thrown vertically upward from the ground at a speed of 60 m/s at time t= 0. Its distance d (in m) above the ground (neglecting air resistance) is approximated by the function f(t)= 60t- 5t^2. An appropriate domain is:

the domain of the function = [0,12]

Step-by-step explanation:

Given that:

f(t) = 60 t - 5t²

at time t = 0

f(0) = 60 (0) - 5(0)²

f(0) = 0

the differential of f(t) is:

f(t)' = 60 - 10t

for the maximum height

f'(t)  = 0

i,e

60 - 10t = 0

60 = 10t

t = 60/10

t = 6

Now, t = 6,

f(6) = 60(6) - 5(6)²

f(6) =  360  - 180

f(6) = 180

Hence, after 6 seconds, the stone is noticed to have raise to 180 m and 180 m drop after 6 seconds.

Hence, the domain of the function = [0,12]

the final price would be 29.6925

step-by-step explanation:

39.59 minus 25% equals 29.6925

geometry: triangles

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call the larger triangle abc

then the smaller triangle cde is similar to abc (all angles are equal, aaa).  

ab is the side that is 36, and we wish to find de, the side corresponding to ab

area_cde = area_abc - area_cde --> area_abc / area_cde = 2

let x=length of de

ratio of areas = (ratio of sides)^2

+2+=+%2836%2fx%29%5e2+

+2+=+1296%2fx%5e2+

++x%5e2+=+1296%2f2+=+648+

25.45584