This is an awful question. They mean to say the number of hours practicing <em>per week</em> (we'll call it h) varies inversely with the <em>time</em> (t) she runs her event. Unless they mean to imply more practicing makes Tyler slower, in which case she should just get a pizza.
Inverse variation means the product is a constant, we'll call it k.
ht = k
When h = 1 hour t=6 minutes
(1)(6) = k
k = 6 (hour*minutes, but as long as we're consistent we don't need to sweat the unit.)
Decreasing her time by one minute means t = 6 - 1 = 5. We solve for h.
ht = k
h = k/t = 6/5 = 1.2 hours
Answer: 1.2 hours, second choice
In Cartesian coordinates, the region is given by
,
, and
. Converting to cylindrical coordinates, using
we get a Jacobian determinant of
, and the region is given in cylindrical coordinates by
,
, and
.
The volume is then
Plug in any value for x and then you will get y. Use the coordinates to plot.
Example
x= 2
5/2(2)-6
5-6
-1
(2,-1)
Then continue to do the same.
The product of a number y and 12 or 12 times a number y. These are both equivalent expressions to 12y
