a. Given that y = f(x) and f(0) = -2, by the fundamental theorem of calculus we have

Evaluate the integral to solve for y :



Use the other known value, f(2) = 18, to solve for k :

Then the curve C has equation

b. Any tangent to the curve C at a point (a, f(a)) has slope equal to the derivative of y at that point:

The slope of the given tangent line
is 1. Solve for a :

so we know there exists a tangent to C with slope 1. When x = -1/3, we have y = f(-1/3) = -67/27; when x = -1, we have y = f(-1) = -3. This means the tangent line must meet C at either (-1/3, -67/27) or (-1, -3).
Decide which of these points is correct:

So, the point of contact between the tangent line and C is (-1, -3).
<h3>Given</h3>
The current balance is $420.
The current balance is 7/6 of the original balance, b
<h3>Find</h3>
equation to use to find b
<h3>Solution</h3>
Equate the two descriptions of the current balance.
... $420 = (7/6)b . . . . . equation to use to find b
Answer:
28. the second and third one
29. 687.50 dollars
Step-by-step explanation:
2.49(2) + 1.79(2) + 0.89(4) = 12.12 no
2.49(3) + 1.79(2) = 11.05 yes
2.49(2) + 1.79(3) + 0.89 = 11.24 yes
2.49(4) + 1.79 + 0.89 = 12.64 no
area = length times width
a = 6.25 times 5
a = 31.25 square feet
31.25(22) = 687.50
Answer:
105 is the part.
Step-by-step explanation:
175 is the whole
60% is the percent
x is the part
175 * 0.60 = 105