Dr. Bayer measured the masses of newborn twins. Baby A weighs 2.8 kilograms. Baby B weighs 2,950 grams. What is the difference b
1 answer:
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Answer:
a = -3/2
Step-by-step explanation:
You can set x=0 and solve for y to find the y-intercept in each case.
first equation: y-intercept = -3/2
second equation: y-intercept = a
To make these equal, we must have ...
a = -3/2
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).