Solve the system by graphing. (Enter your answers as a comma-separated list. If the system is inconsistent, enter INCONSISTENT.
If the system is dependent, enter DEPENDENT.) x + y = 6 x − y = 2
1 answer:
Answer:
(4,2). DEPENDENT
Step-by-step explanation:
As each equation consist on two variable, both can be represented graphically on a cartesian plane. First, each expression is rewritten in explicit form:
(red line) and
(blue line)
By the resource of graphing software, the solution is (4,2). The representation is presented below as attachment. As solution exists, both expression are linearly DEPENDENT.
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Answer:
Volume:
Ratio:
Step-by-step explanation:
First of all, we need to find the volume of the hemispherical tank.
The volume of a sphere is given by:
where
r is the radius of the sphere
V is the volume
Here, we have a hemispherical tank: a hemisphere is exactly a sphere cut in a half, so its volume is half that of the sphere:
Now we want to find the ratio between the volume of the hemisphere and its surface area.
The surface area of a sphere is
For a hemisphere, the area of the curved part of the surface is therefore half of this value, so . Moreover, we have to add the surface of the base, which is
. So the total surface area of the hemispherical tank is
Therefore, the ratio betwen the volume and the surface area of the hemisphere is