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).
Hello! In slope-intercept form, y=mx+b. M is the slope and b is the y-intercept. The rate of change and slope are interchangeable, therefore, they both create a line through the slope-intercept form.
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Answer:
28 students
Step-by-step explanation:
Let number of students in cooking club = x
Number of students in fencing club = 1/5 x
Number of students in chess club = 2(1/5)x
Since, There are 42 more students in the cooking club than in the chess club
Then ;
Number of students in chess club = Number of students in cooking club - 42
2(1/5)x = x - 42
(2/5)x - x = - 42
(2/5)x - x = - 42
-0.6x = - 42
x = 42 / 0.6
x = 70
Hence, number of students in chess club :
(2/5) * 70 = 28
3 goes into 96 32 times, so 96/3=32. There is no decimal (unless you insist on including one, then it'd be 32.0) because 3 goes into 96 perfectly.
Answer:
-4, 0, and 4
Step-by-step explanation:
