We first integrate the expression to find the oil leaked since we have an expression for leakage rate.
Integrating:
O(t) = -10000exp(-0.2t); substituting t = 10
O(t) = -1,353 gallons
1,353 gallons of oil leak out in the first 10 seconds.
Given the graph, you can assume that f(x) is the y of an equation.
When f(2) is given, this means that what is the y value when x=2?
As you can see, the solution is between 8 and 10. Meaning that the closest answer is 9.
Hope I helped :)
Answer:
f(x) = 2x² - 8x - 10.
This is a parabola open upward (since a>0) with an axis of symmetry = -b/2a:
a) axis of symmetry: x = -(-8)/(2*2) = 8/4 = 2. Then x = 2, which is the x component of the vertex
b) for x = 2, f(x) = f(2) = - 18 (component of y of the vertex)
c) VERTEX(2, - 18)
d) DISCRIMINENT: b² - 4.a.c = 64 - 4*2*(-10) = 144
Hope this helps! :)
