We can find an unknown angle in a triangle by applying the fact that total interior
1 answer:
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Answer:
a = . Surface Area =
. and area of the Dish =
+pi
=
+50.27=51.6
Step-by-step explanation:
(1) Constant. y(x) = a that is the curve that we need to rotate around the y axis to get the parabola with diameter of 8 feet and 2 meter depth that statement is translated in mathematics as x = -4 to 4 and y = 0 to 2.
y max = 2, x max = 4 setting up a equation with a unknown gives
2=a4 and a = .
so we have now.
y(x) = (Done with solving for a Constant).
(2) Surface Area.
Setting Up surface integral.
(i) range in x = 0 to 4.
(ii) range in y = 0 to 2.
integral is.
Integral(0-2)[{integral[(0-4)]}]dy
Evaluating this integral gives. .
and area is surface area + area of the circle with 8ft diameter.
= +pi
=
+50.27=51.6
...
Note the Difference between area and aurface area.!
9514 1404 393
Answer:
maximum difference is 38 at x = -3
Step-by-step explanation:
This is nicely solved by a graphing calculator, which can plot the difference between the functions. The attached shows the maximum difference on the given interval is 38 at x = -3.
__
Ordinarily, the distance between curves is measured vertically. Here that means you're interested in finding the stationary points of the difference between the functions, along with that difference at the ends of the interval. The maximum difference magnitude is what you're interested in.
h(x) = g(x) -f(x) = (2x³ +5x² -15x) -(x³ +3x² -2) = x³ +2x² -15x +2
Then the derivative is ...
h'(x) = 3x² +4x -15 = (x +3)(3x -5)
This has zeros (stationary points) at x = -3 and x = 5/3. The values of h(x) of concern are those at x=-5, -3, 5/3, 3. These are shown in the attached table.
The maximum difference between f(x) and g(x) is 38 at x = -3.
