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impura12713
20.07.2019 •
Mathematics
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a bucket of paint has spilled on a tile floor. the paint flow can be expressed with the function p(t) = 5t, where t represents time in minutes and p represents how far the paint is spreading.
the flowing paint is creating a circular pattern on the tile. the area of the pattern can be expressed as a(p) = πp2.
part a: find the area of the circle of spilled paint as a function of time, or a[p(t)]. show your work. (6 points)
part b: how large is the area of spilled paint after 2 minutes? you may use 3.14 to approximate π in this problem. (4 points)
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Ответ:
A) A(p(t)) = 25πt²
B) 314 square units.
Step-by-step explanation:
Part A)
Flow of paint can be expressed by the function:
p(t) = 5t
Area of the pattern is expressed as:
A(p) = πp²
Since area is given in terms of p, we can use the expression of p to express the area of pattern in terms of time(t). Using the value, we get:
A(p(t)) = π (5t)²
A(p(t)) = 25πt²
Part B)
We have to calculate the area of the pattern after time t. Substituting the value of t in above expression, we get:
A(p(2)) = 25 x 3.14 x 4 = 314 square units.
Therefore, the area of spilled paint after 2 minutes will be 314 square units.
Ответ:
C or D
Step-by-step explanation: