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).
You can show that (y) is proportional to (x) by writing:
This would mean that:
Whereby (k) would be the constant of proportionality.
This value can be an element of a real number.
k∈R
What are real numbers?
Integers, rational numbers and irrational numbers.
Example of a graph which would show that 2 objects are proportional:y=2x
Answer:
b = 73°
Step-by-step explanation:
Since SR and ST are congruent then the triangle is isosceles.
Thus the base angles R and T are congruent, so
b = 73°
Answer: 125x exponent 3-100x exponent 2 +675x-540
Step-by-step explanation:
Answer:
2+3+2+3+2+3+2=17 because each was worth 2 or 3