A circular oil slick is expanding with radius, r in yards, at time t in hours given by r=2t-0.1t^2, for t in hours, 0<t<10. find a formula for the area in square yards, A= F(t), as a function of time.
Same as your other question
Area of circle = πr^2
= π(2t - 1t^2)^2
But with units.. how would it be?? cause it remarks be sure to include units! pleasee
To find a formula for the area of the circular oil slick as a function of time, we need to calculate the area of a circle with radius r at a given time t.
The area of a circle is given by the formula: A = πr^2, where π is a mathematical constant approximately equal to 3.14159.
Substituting the given expression for r into the formula, we have:
A = π(2t - 0.1t^2)^2
Expanding and simplifying, we get:
A = π(4t^2 - 0.4t^3 + 0.01t^4)
Therefore, the formula for the area of the circular oil slick as a function of time is:
A = 4πt^2 - 0.4πt^3 + 0.01πt^4
To find the formula for the area of the circular oil slick as a function of time, we need to use the formula for the area of a circle, which is A = πr², where r is the radius of the circle.
Given that the radius, r, of the circular oil slick is given by r = 2t - 0.1t², we can substitute this expression into the formula for the area of a circle.
A = π(2t - 0.1t²)²
Now, we can simplify the expression by expanding the square:
A = π(4t² - 0.4t³ + 0.01t⁴)
Using the distributive property:
A = 4πt² - 0.4πt³ + 0.01πt⁴
Therefore, the formula for the area of the circular oil slick, A, as a function of time, t, is:
A = 4πt² - 0.4πt³ + 0.01πt⁴