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2 years ago

Triangle ABC is equilateral. Find the height of BD

Mathematics

2 answers:

Oksana_A [137]2 years ago

4 0

Answer:

C) 4√3

Step-by-step explanation:

The given triangle is an equilateral triangle. BD is angle bisector.

Triangle BCD is a 30-60-90 degree triangle in the ration of 1:√3:2

Here we are given BC, that is highest length of the side.

So 2x = 8

x = 8/2

x = 4.

BD = √3 x

Now plug in x =4, we get

Height (BD) = 4√3

Thank you.

MA_775_DIABLO [31]2 years ago

4 0

Answer:

Step-by-step explanation:

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A 4-foot tree was planted in 1984. The tree grows continuously by 22% each year from this point forward. Find the height of the

nata0808 [166]

Answer:

the tree will be 11.04 feet tall

Step-by-step explanation:

4 x 0.22 (22%) = 0.88

every year it grows 0.88 foot.

0.88 x 8 = 7.04

4 + 7.04 = 11.04 feet tall

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2 years ago

Determine the singular points of the given differential equation. Classify each singular point as regular or irregular. (Enter y

ludmilkaskok [199]

Answer:

Step-by-step explanation:

Given that:

The differential equation; $(x^2-4)^2y'' + (x + 2)y' + 7y = 0$

The above equation can be better expressed as:

$y'' + \dfrac{(x+2)}{(x^2-4)^2} \ y'+ \dfrac{7}{(x^2- 4)^2} \ y=0$

The pattern of the normalized differential equation can be represented as:

y'' + p(x)y' + q(x) y = 0

This implies that:

$p(x) = \dfrac{(x+2)}{(x^2-4)^2} \$

$p(x) = \dfrac{(x+2)}{(x+2)^2 (x-2)^2} \$

$p(x) = \dfrac{1}{(x+2)(x-2)^2}$

Also;

$q(x) = \dfrac{7}{(x^2-4)^2}$

$q(x) = \dfrac{7}{(x+2)^2(x-2)^2}$

From p(x) and q(x); we will realize that the zeroes of (x+2)(x-2)² = ±2

When x = - 2

$\lim \limits_{x \to-2} (x+ 2) p(x) = \lim \limits_{x \to2} (x+ 2) \dfrac{1}{(x+2)(x-2)^2}$

$\implies \lim \limits_{x \to2} \dfrac{1}{(x-2)^2}$

$\implies \dfrac{1}{16}$

$\lim \limits_{x \to-2} (x+ 2)^2 q(x) = \lim \limits_{x \to2} (x+ 2)^2 \dfrac{7}{(x+2)^2(x-2)^2}$

$\implies \lim \limits_{x \to2} \dfrac{7}{(x-2)^2}$

$\implies \dfrac{7}{16}$

Hence, one (1) of them is non-analytical at x = 2.

Thus, x = 2 is an irregular singular point.

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2 years ago

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Sav [38]

Answer:

x=17

Step-by-step explanation:

ok so since lines PR and RQ are congruent (we know because of the lines on them), that means angles P and Q are also equal.

now we can set up the equation to find x like this:

29+29+(8x-14)=180 (180 because the three angles of a triangle always equal 180)

x=17

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