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LiRa [457]
3 years ago
14

Rhombus ADEF is inscribed into a triangle ABC so that they share angle A and the vertex E lies on the side BC . What is the leng

th of the side of the rhombus if AB=c, and AC=b.

Mathematics
1 answer:
Alex_Xolod [135]3 years ago
6 0

Answer:

The length of the rhombus is =\frac{bc}{b+c}cm

Step-by-step explanation:

It is given that the Rhombus ADEF is inscribed into a triangle ABC so that they share angle A and the vertex E lies on the side BC.Then,

AE is the angle bisector of ∠A, so divides the sides of the triangle into a proportion:

\frac{BE}{CE}=\frac{BA}{AC}=\frac{c}{b}

⇒\frac{BE}{CE}=\frac{c}{b}

⇒\frac{BE}{BC}=\frac{c}{c+b}

Now, ΔDBE is similar to ΔABC, then

DE=(\frac{BE}{BC}){\times}AC

=(\frac{c}{c+b}){\times}b

=\frac{bc}{b+c}cm

Thus, the length of the rhombus is =\frac{bc}{b+c}cm

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Read 2 more answers
Describe the end behavior of a 14th degree polynomial with a positive leading coefficient.
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<u><em>Answer:</em></u>

1)

f(x)→ ∞ when x→∞ or x→ -∞.

2)

when  x→ ∞ then f(x)→ -∞

        and when x→ -∞ then f(x)→ ∞

<u><em>Step-by-step explanation:</em></u>

<em>" The </em><em>end behavior</em><em> of a polynomial function is the behavior of the graph of as approaches positive infinity or negative infinity. The degree and the leading coefficient of a polynomial function determine the end behavior of the graph "</em>

1)

a 14th degree polynomial with a positive leading coefficient.

Let f(x) be the polynomial function.

Since the degree is an even number and also the leading coefficient is positive so when we put negative or positive infinity to the function i.e. we put x→∞ or x→ -∞ ; it will always lead the function to positive infinity

i.e. f(x)→ ∞ when x→∞ or x→ -∞.

2)

a 9th degree polynomial with a negative leading coefficient.

As the degree of the polynomial is odd and also the leading coefficient is negative.

Hence when x→ ∞ then f(x)→ -∞ since the odd power of x will take it to positive infinity but the negative sign of the leading coefficient will take it to negative infinity.

When x→ -∞ then f(x)→ ∞; since the odd power of x will take it to negative infinity but the negative sign of the leading coefficient will take it to positive infinity.

Hence, when  x→ ∞ then f(x)→ -∞

        and when x→ -∞ then f(x)→ ∞



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