<span>The line tangent to the graph of y = f(x) at x = a has slope f'(a) and goes through the point (a, f(a)). So it has the equation
(y - f(a))/(x - a) = f'(a)
[sometimes called the 'point-slope' form of the line] which can be rewritten in perhaps the more familiar form
y = f'(a) (x - a) + f(a).
Plugging in a = 2 and using the given information, we see the tangent line to the graph of y = f(x) at x = 2 has equation
y = f'(2) (x - 2) + f(2) = 4 (x - 2) + 1.
To compute an "approximation of f(1.9) using the line tangent to the graph of f at x = 2" means to use the equation for the tangent line with x = 1.9 plugged into it as a substitute for f(1.9). When you plug 1.9 in here you get
4 (1.9 - 2) + 1 = 4(-0.1) + 1 = -0.4 + 1 = 0.6
which is the answer. So, I guess I don't know how they got 0.4 either; it's wrong.
You may wonder what happened with f''(2) = 3. Well, it doesn't enter into it at all. (The tangent line to the graph, the only thing we need, is determined by f(2) and f'(2).) Presumably its value was given to test the understanding of people solving the problem--- if they somehow bring f''(2) into it, it shows that they are just trying random things involving the given information and don't get the problem. This may be useful if the grader wants to distinguish between different levels of wrongness when assigning partial credit.</span>
Answer:
<h2>The value of D is 6 and the value of F is -26.</h2>
Step-by-step explanation:
Givens
- The center of the circle is at (1, -3), and its radius is 6 units.
The best way to find the general form of the circle, it's to use the center-radius form
In this case, , and . Replacing all these values in the formula, we have
Now, we solve each power
Where:
However, Ben wrote the expression with F as the constant. So,
Therefore, the value of D is 6 and the value of F is -26.
.51 You add 15 +36 to get 51
Answer: 18.125 lbs
Explanation: The baby weighed 18.125 pounds at the end of eight months.
The baby weighed 7.25 lbs at birth. Eight months later, he weighed 2.5 or 2½ times its birth weight. Multiply 7.25 by 2.5 (which equals 18.125).
So now eight months later, he's 18.125 pounds.
What is 2,722 rounded to the nearest thousand