A line passes through (-5,8) and (4,-1) what is the point slope method?
1 answer:
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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).
Negative exponents work like this:
So, in order to evaluate a negative exponent, you simply have to invert the base, and then raise to the positive equivalent of the exponent.
As an example, here are the first three exercises:
You can work out the rest applying this logic.
Answer:
The other endpoint is (-33, 17)
Step-by-step explanation:
The rule of the mid-point of a segment whose endpoints are
(,
) and (
,
) is
In our question
∵ The coordinates of the endpoints of a segment are (-15, 13) and (x, y)
∴ = -15 and
= x
∴ = 13 and
= y
∵ The coordinates of the mid-point of this segment are (-24, 15)
∴ = -24 and
= 15
→ Use the rule of the mid-point to find x and y
∵
→ Multiply both sides by 2
∴ -48 = -15 + x
→ Add 15 to both sides
∴ -33 = x
∵
→ Multiply both sides by 2
∴ 30 = 13 + y
→ Subtract 13 from both sides
∴ 17 = y
∴ The other endpoint is (-33, 17)