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3 years ago

Given: △OKE∼△VDE Prove: EK/EO = ED/EV

Mathematics

1 answer:

harkovskaia [24]3 years ago

6 0

Answer:

The proof is below.

Step-by-step explanation:

Given two triangles similar.

we have to prove that ratio $\frac{EK}{EO}=\frac{VE}{ED}$

As, △OKE∼△VDE

∴ their corresponding sides are in same proportion.

$\frac{OK}{VD}=\frac{EK}{ED}=\frac{OE}{VE}$

⇒ $\frac{EK}{ED}=\frac{EO}{VE}$

⇒ [tex}\frac{EK}{EO}=\frac{VE}{ED}[/tex]

Hence Proved.

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Identify whether the series sigma notation infinity i=1 15(4)^i-1 is a convergent or divergent geometric series and find the sum

const2013 [10]

Answer: The correct option is

(d) This is a divergent geometric series. The sum cannot be found.

Step-by-step explanation: The given infinite geometric series is

$S=\sum_{i=1}^{\infty}15(4)^{i-1}.$

We are to identify whether the given geometric series is convergent or divergent. If convergent, we are to find the sum of the series.

We have the D' Alembert's ratio test, states as follows:

Let, $\sum_{i=1}^{\infty}a_i$ is an infinite series, with complex coefficients $a_i$ and we consider the following limit:

$L=\lim_{i\rightarrow \infty}\dfrac{a_{i+1}}{a_i}.$

Then, the series will be convergent if L < 1 and divergent if L > 1.

For the given series, we have

$a_i=15(4)^{i-1},\\\\a_{i+1}=15(4)^i.$

So, the limit is given by

$L\\\\\\=\lim_{i\rightarrow \infty}\dfrac{a_{i+1}}{a_i}\\\\\\=\lim_{i\rightarrow \infty}\dfrac{15(4)^i}{15(4)^{i-1}}\\\\\\=\lim_{i\rightarrow \infty}\dfrac{15(4)^i}{15(4)^{i}4^{-1}}\\\\\\=\dfrac{1}{4^{-1}}\\\\=4>1.$

Therefore, L >1, and so the given series is divergent and hence we cannot find the sum.

Thuds, (d) is the correct option.

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3 years ago

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*Silly and/or spam answers will not be tolerated*

stepladder [879]

Answer:

-1/8

Step-by-step explanation:

lim x approaches -6 (sqrt( 10-x) -4) / (x+6)

Rationalize

(sqrt( 10-x) -4) (sqrt( 10-x) +4)

------------------- * -------------------

(x+6) (sqrt( 10-x) +4)

We know ( a-b) (a+b) = a^2 -b^2

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-------------------

(x+6) (sqrt( 10-x) +4)

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-------------------

(x+6) (sqrt( 10-x) +4)

Factor out -1 from the numerator

-1( x+6)

-------------------

(x+6) (sqrt( 10-x) +4)

Cancel x+6 from the numerator and denominator

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(sqrt( 10-x) +4)

Now take the limit

lim x approaches -6 -1/ (sqrt( 10-x) +4)

-1/ (sqrt( 10- -6) +4)

-1/ (sqrt(16) +4)

-1 /( 4+4)

-1/8

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