Mathematics, 22.11.2019 01:31 simegustachocolate

Given: ∆dln, lf ⊥ dn , df = 4 m∠n = 23º, m∠d = 47º find: dl, ln, dn

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Answer from: giigigihyys2111

DL = 5.87 un.

LN = 10.98 un.

DN = 14.4 un.

Step-by-step explanation:

Given:

∆DLN,

LF ⊥ DN ,

DF = 4

m∠N = 23º,

m∠D = 47º

Find:

DL, LN, DN

Solution:

In right triangle DFL, DF = 4, m∠D = 47º, so

$LF=DF\tan \angle D\\ \\LF=4\cdot \tan 47^{\circ}\approx 4.29 \ units$

and

$DL=\dfrac{DF}{\cos \angle D}\\ \\DL=\dfrac{4}{\cos 47^{\circ}}\approx 5.87\ units$

In right triangle LFN, LF = 4.29 units, m∠N = 23º, so

$FN=LF\cot \angle N\\ \\FN=4.29\cdot \cot 23^{\circ}\approx 10.11\ units$

and

$LN=\dfrac{LF}{\sin \angle N}\\ \\LN=\dfrac{4.29}{\sin 23^{\circ}}\approx 10.98\ units$

Hence,

DN = 4.29 + 10.11 = 14.4 units

Given: ∆dln, lf ⊥ dn , df = 4 m∠n = 23º, m∠d = 47º find: dl, ln, dn

Answer from: Quest

(2 x^3 + 7 x^2 + 5 x + 2)/(x (x + 2))

step-by-step explanation:

simplify the following:

x/x^2 + 3 x + 2 - (x (x + 1))/(x + 2)

combine powers. x/x^2 = x^(1 - 2):

x^(1 - 2) + 3 x + 2 - (x (x + 1))/(x + 2)

1 - 2 = -1:

x^(-1) + 3 x + 2 - (x (x + 1))/(x + 2)

put each term in 1/x + 3 x + 2 - (x (x + 1))/(x + 2) over the common denominator x (x + 2): 1/x + 3 x + 2 - (x (x + 1))/(x + 2) = (x + 2)/(x (x + 2)) + (3 x^2 (x + 2))/(x (x + 2)) + (2 x (x + 2))/(x (x + 2)) - (x^2 (x + 1))/(x (x + 2)):

(x + 2)/(x (x + 2)) + (3 x^2 (x + 2))/(x (x + 2)) + (2 x (x + 2))/(x (x + 2)) - (x^2 (x + 1))/(x (x + 2))

(x + 2)/(x (x + 2)) + (3 x^2 (x + 2))/(x (x + 2)) + (2 x (x + 2))/(x (x + 2)) - (x^2 (x + 1))/(x (x + 2)) = ((x + 2) + 3 x^2 (x + 2) + 2 x (x + 2) - x^2 (x + 1))/(x (x + 2)):

(2 + x + 3 x^2 (x + 2) + 2 x (x + 2) - x^2 (x + 1))/(x (x + 2))

3 x^2 (x + 2) = 3 x^3 + 6 x^2:

(2 + x + 3 x^3 + 6 x^2 + 2 x (x + 2) - x^2 (x + 1))/(x (x + 2))

2 x (x + 2) = 2 x^2 + 4 x:

(2 + x + 6 x^2 + 3 x^3 + 2 x^2 + 4 x - x^2 (x + 1))/(x (x + 2))

-x^2 (x + 1) = -x^2 - x^3:

(-x^2 - x^3 + 3 x^3 + 6 x^2 + 2 x^2 + 4 x + x + 2)/(x (x + 2))

grouping like terms, 3 x^3 - x^3 + 6 x^2 + 2 x^2 - x^2 + 4 x + x + 2 = (3 x^3 - x^3) + (6 x^2 + 2 x^2 - x^2) + (x + 4 x) + 2:

((3 x^3 - x^3) + (6 x^2 + 2 x^2 - x^2) + (x + 4 x) + 2)/(x (x + 2))

3 x^3 - x^3 = 2 x^3:

(2 x^3 + (6 x^2 + 2 x^2 - x^2) + (x + 4 x) + 2)/(x (x + 2))

6 x^2 + 2 x^2 - x^2 = 7 x^2:

(2 x^3 + 7 x^2 + (x + 4 x) + 2)/(x (x + 2))

x + 4 x = 5 x:

answer: (2 x^3 + 7 x^2 + 5 x + 2)/(x (x + 2))

Answer from: Quest

the answer is 1/4

step-by-step explanation:

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Given: ∆dln, lf ⊥ dn , df = 4 m∠n = 23º, m∠d = 47º find: dl, ln, dn...

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