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.!
Hey the answer to your question is -6.4
Answer:
3 miles
Step-by-step explanation:
5-1+2=3
12.

13.

16.

is already in simplest form.
Answer:
The speed of the first train is 45 mph and the speed of the second train is 75 mph
Step-by-step explanation:
Let x represent the speed of the first train in mph. Since the second train, is 30 mph faster then the first, therefore the speed of the second train is (x + 30).
The first train leaves at 1:00 pm, therefore at 6:00 pm, the time taken is 5 hours. Therefore the distance covered by the first train at 6:00 pm = x mph * 5 hours = 5x miles
The second train leaves at 3:00 pm, therefore at 6:00 pm, the time taken is 3 hours. Therefore the distance covered by the second train at 6:00 pm = (x + 30) mph * 3 hours = (3x + 90) miles
Since the second train overtakes the first at 6:00 pm, hence:
3x + 90 = 5x
2x = 90
x = 45
Therefore the speed of the first train is 45 mph and the speed of the second train is 75 mph (45 mph + 30 mph).