Find the Area of the figure below, composed of a rectangle and a semicircle. There radius of the circle is shown. Round to the n
earest tenths place.
1 answer:
You might be interested in
Answer: 25 games
Step-by-step explanation:
Take the fractions 76/100 and 19/x
Cross multiply. 76 times x equally 76x and 100 times 19 equals 1900.
Divide 76x by 76 which equals just x.
Divide 1900 by 76 which equals 25.
x=25
See the attached picture.
- Create an equation for the volume of the box, find the zeroes, and sketch the graph of the function.
The resulting box has a volume
because the volume of a box is the product of its width , length
, and height
.
- find the zeroes
You know right away from the factored form of that the zeroes are
. (zero product property)
- sketch the graph of the function
Easy to plot by hand. You know the zeroes, and you can check the sign of for any values of
between these zeros to get an idea of what the graph of
looks like. See the second attached picture.
Here's what I mean by "check the sign" in case you don't follow. We know when
and
. So we pick some value of
between them, say
, and find that
which is positive, so will be positive for any other
between 0 and 8. Similarly we would find that
for
between 8 and 12, and so on.
- What is the size of the cutout he needs to make so that he can fit the most marbles in the box?
It's impossible to answer this without knowing the volume of each marble...
- If Thomas wants a volume of 12 cubic inches, what size does the cutout need to be?
Thomas wants , so you solve
While this is possible to do by hand, the procedure is tedious (look up "solving the cubic equation"). With a calculator, you'd find three approximate solutions
but you throw out the third solution because, realistically, the cutout length can't be greater than either of the sheet's dimensions.
- What would be the dimensions of this box?
The box's dimensions are ( in) x (
in) x (
in).
If , then
and
.
If , then
and
.
