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3 years ago

In the figure, FL=5 and HL=8 what is FM?

Mathematics

1 answer:

liq [111]3 years ago

6 0

We know that
GL=HL/2---------> GL=8/2----> GL=4

in the right triangle FGL
FL=5
GL=4
FG=?
Applying the Pythagoras theorem
FL²=GL²+FG²-----> FG²=FL²-GL²-----> FG²=5²-4²----> FG²=9
FG=3
FG is the radius of the smaller circle
and
FM also is the radius of the smaller circle
so
FM=FG--------> FM=3

the answer is
FM is 3

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The partial fraction decomposition is $\frac{- 4 x^{2} + 13 x - 12}{\left(x + 1\right)^{2} \left(x + 2\right)}=\frac{50}{x + 1}+\frac{-29}{\left(x + 1\right)^{2}}+\frac{-54}{x + 2}$ .

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Partial-fraction decomposition is the process of starting with the simplified answer and taking it back apart, of "decomposing" the final expression into its initial polynomial fractions.

To find the partial fraction decomposition of $\frac{- 4 x^{2} + 13 x - 12}{\left(x + 1\right)^{2} \left(x + 2\right)}$ :

First, the form of the partial fraction decomposition is

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Write the right-hand side as a single fraction:

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