Answer:
The umbrella will fit in, but there will be a lot of extra room.
Step-by-step explanation:
Remember the Pythagorean theorem:
x^(2) + y^(2) = n^(2)
where "x" and "y" are the legs of the right triangle and "n" is the hypotenuse
In this problem it is given that the sides (legs) are:
38in, and 24in
and diagonally across is 29in
so the hypotenuse is 29in
therefore we can form the equation:
38^(2) + 24^(2) = 29^(2)
without solving it is clear that
38^(2) + 24^(2) > 29^(2)
because 38 is a leg, but it is greater than 29, which means that 38 - 24 - 29 is not a Pythagorean triple,
but because 38 > 29, then the 29 in umbrella will fit into the suitcase, but it will not be a snug fit, there will be a lot of extra room
The ratio of the areas is 340/1158 = 170/579thus the ratio of the side lengths is sqrt(170)/sqrt(579) = .5418the ratio of volumes is the side length ratio cubed = .5418^3 = .159Volume of smaller solid = (.159)(1712) = 272.37
By the fundamental theorem of algebra, we can write
Expanding the right hand side, we get
We want 
to be an integer, which means 
must also be integers. This means must be factors of 10. There are several possibilities:
So there are 4 possible values for : -11, -7, 7, and 11.
R + 3 = 2
First, subtract 3 from both sides. / Your problem should look like: r = 2 - 3
Second, simplify 2 - 3 to -1. / Your problem should look like: r = -1
Answer: r = -1
