Answer:
C
Step-by-step explanation:
there are six spots, which the arrow will land on only one, making it 1/6
Answer:
A) When using the shell method, the axis of the cylindrical shells is parallel to the axis of revolution. True.
The Shell method is a technique used to find the volume of a solid of revolution. Here, we take thin shells with axis coinciding with the axis about which the region whose volume is to be found, is revolved.
B) If a region is revolved about the y-axis, then the shell method must be used. False.
This method can be used with any axis of rotation.
C) If a region is revolved about the x-axis, then in principle it is possible to use the disk/washer method and integrate with respect to x or the shell method and integrate with respect to y. True.
The washer method uses thin disks with infinite width but the shell method uses thin concentric shells with infinite width about the axis of revolution. So, the statement is true.
Answer: (4,6)
Explanation:
x - 3y = -14
x - y = -2
Multiply a -1 to the first equation so the x’s can cancel out.
-x + 3y = 14
x - y = -2
Subtract the two equations together.
2y = 12
y=6
Now, plug in y to one of the original equations.
x - (6) = -2
x=4
Therefore, the answer is: (4,6)
Domain: Set of all real numbers.
The domain in interval notation is (-infinity, infinity)
The reason why the domain is the set of all real numbers is because we can pick any number we want for x, without having to worry about division by zero errors or taking the square root of negative values. There are no restrictions for x.
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Range: Set of all non-negative numbers.
As an inequality, you would write (y is greater than or equal to 0)
In interval notation, the range is written as [0, infinity)
The absolute value result cannot be negative. The smallest y = |x| can get is y = 0. This applies to y = |x-3| as well. The use of square brackets tells the reader "include y = 0 as part of the range". You always use curved parenthesis for infinity because you can never actually reach infinity.