Answer:
The volume is increasing at a rate of 1508 cubic millimeters per second when the diameter is 60 mm.
Step-by-step explanation:
Volume of a sphere:
The volume of a sphere is given by the following equation:
In which r is the radius.
Implicit derivatives:
This question is solving by implicit derivatives. We derivate V and r, implicitly as function of t. So
The radius of a sphere is increasing at a rate of 4 mm/s.
This means that 
How fast is the volume increasing (in mm^3/s) when the diameter is 60 mm?
This is 
when 
. So
The volume is increasing at a rate of 1508 cubic millimeters per second when the diameter is 60 mm.
Answer:
A length=24ft, width=15ft
Step-by-step explanation:
the side AB have x values of 5 and the side with CD have x values of 10 so the width from b to d or a to c is 5 so the width of the drawing is 5cm
the bottom side AC has y values of 8 and the top side BD has y values of 16 so they are 8 apart so the length of the rectangular drawing is 8cm
then the scale says that 1 cm = 3 ft so multiply the length and width each by 3 to get the answer that the length of the sail is 24ft and the width is 15ft
Hope this helps! :)
Answer:
-1
Step-by-step explanation:
∫x^2 -x +1 dx = x^3/3 -x^2/2 +x evaluated at 1 subtracting the value at 0
1/3 -1/2 +1 - (0/3 -0/2 +0)
5/6
Now lets find
∫x^2 -x +1 dx=x^3/3 -x^2/2 +x evaluated at 2 subtracting the value at 1
2^3/ 3 -2^2/2 +2 - (1/3 -1/2 +1 )
8/3 -2 +2 - (5/6)
8/3 -5/6
11/6
The total is 5/6 - 11/6 = -6/6 or -1
Think: 25 less what number is 18?
18 less what number is 11?
11 less what number is 4?
Note that "less" indicates "negative" or "subtraction."
Answer:
63 = 1 x 63, 3 x 21, or 7 x 9. Factors of 63: 1, 3, 7, 9, 21, 63. Prime factorization: 63 = 3 x 3 x 7, which can also be written 63 = 3² x 7.
Step-by-step explanation:
hope this is right
