Mathematics, 11.01.2020 01:31 Goodgirlkl12k

The line with equation a + 4b = 0 coincides with the terminal side of an angle θ in standard position and cos θ > 0. what is the value of sinθ ?
a. -(√17/17)
b. -(17/√17)
c. -(14/√17)
d. -(17/√14)

Answers: 3

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Answer from: Magalaki8999

Option A. -( $\frac{\sqrt{17}}{17}$ )

Step-by-step explanation:

Equation of a given line is a + 4b = 0 or b = - $\frac{1}{4}a$

This in the form of y = mx + b, which is slope-intercept form.

Here slope of the line is ( $-\frac{1}{4}$ ).

Or tanθ = $\frac{(-1)}{4}$

This line coincides with the terminal side of the angle in standard position where cosθ > 0

Since tanθ = $\frac{\text{Height}}{\text{Base}}$

and sinθ = $\frac{\text{height}}{\txt{Hypotenuse}}$

Hypotenuse = $\sqrt{\text{height}^{2}+\text{Base}^{2}}$

= $\sqrt{(1^{2}+4^{2})}$

= $\sqrt{17}$

Since tanθ is negative and cosθ > 0 that means θ lie in fourth quadrant.

Therefore, sinθ will be negative.

[ $\frac{-sin\theta}{+cos\theta}=-tan\theta$ ]

sinθ = - $\frac{1}{\sqrt{17}}$

= - $\frac{1}{\sqrt{17}}\times \frac{\sqrt{17} }{\sqrt{17}} = -\frac{\sqrt{17}}{17}$

Answer will be option A.

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

answer: what do you mean

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The line with equation a + 4b = 0 coincides with the terminal side of an angle θ in standard positio...