Answer:
The dimensions of rectangular fence are 14 feet and 20 feet.
Step-by-step explanation:
We are given the following in the question:
Length of rectangular fence = 14 feet
Width of fence = (14+x) feet
Area of rectangular field = 280 square feet
Area of rectangular field =
Putting the values, we get,
Thus, the dimensions of rectangular fence are 14 feet and 20 feet.
Answer: Space was alloted for each subject is 8 dm, 8 dm, 12 dm.
Explanation:
Since we have given the length of bulletin board =28 dm
Let the share of three subject areas be 2x,2x,3x
According to question,
so x=4 dm
Now,
Space was alloted for each subject is given as below:
First subject =
Second subject =
Third subject =
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).