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2 years ago

Find equation of this line.

Mathematics

1 answer:

ohaa [14]2 years ago

6 0

Answer:

2/5 and 1/4 yw hope it helps

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Given that cot θ = 1/√5, what is the value of (sec²θ - cosec²θ)/(sec²θ + cosec²θ) ?

Bogdan [553]

Step-by-step explanation:

$\mathsf{Given :\;\dfrac{{sec}^2\theta - co{sec}^2\theta}{{sec}^2\theta + co{sec}^2\theta}}$

$\bigstar\;\;\textsf{We know that : \large\boxed{\mathsf{{sec}\theta = \dfrac{1}{cos\theta}}}}$

$\bigstar\;\;\textsf{We know that : \large\boxed{\mathsf{co{sec}\theta = \dfrac{1}{sin\theta}}}}$

$\mathsf{\implies \dfrac{\dfrac{1}{cos^2\theta} - \dfrac{1}{sin^2\theta}}{\dfrac{1}{cos^2\theta} + \dfrac{1}{sin^2\theta}}}$

$\mathsf{\implies \dfrac{\dfrac{sin^2\theta - cos^2\theta}{sin^2\theta.cos^2\theta}}{\dfrac{sin^2\theta + cos^2\theta}{sin^2\theta.cos^2\theta}}}$

$\mathsf{\implies \dfrac{sin^2\theta - cos^2\theta}{sin^2\theta + cos^2\theta}}$

Taking sin²θ common in both numerator & denominator, We get :

$\mathsf{\implies \dfrac{sin^2\theta\left(1 - \dfrac{cos^2\theta}{sin^2\theta}\right)}{sin^2\theta\left(1 + \dfrac{cos^2\theta}{sin^2\theta}\right)}}$

$\bigstar\;\;\textsf{We know that : \large\boxed{\mathsf{cot\theta = \dfrac{cos\theta}{sin\theta}}}}$

$\mathsf{\implies \dfrac{1 -cot^2\theta}{1 + cot^2\theta}}$

$\mathsf{Given :\;cot\theta = \dfrac{1}{\sqrt{5}}}$

$\mathsf{\implies \dfrac{1 - \left(\dfrac{1}{\sqrt{5}}\right)^2}{1 + \left(\dfrac{1}{\sqrt{5}}\right)^2}}$

$\mathsf{\implies \dfrac{1 - \dfrac{1}{5}}{1 + \dfrac{1}{5}}}$

$\mathsf{\implies \dfrac{\dfrac{5 - 1}{5}}{\dfrac{5 + 1}{5}}}$

$\mathsf{\implies \dfrac{5 - 1}{5 + 1}}$

$\mathsf{\implies \dfrac{4}{6}}$

$\mathsf{\implies \dfrac{2}{3}}$

Hence, option (a) 2/3 is your correct answer.

3 0

3 years ago

Multiply (2x+3) (-x -2)

Marysya12 [62]

Answer:

$-2x^{2} -7x-6$

Step-by-step explanation:

(2x + 3) (-x - 2)

distribute first term, to the second term:

2x(-x) + 2x(-2) + 3(-x) + 3(-2)

multiply:

$(-2x^{2})$ + (-4x) + (-3x) + (-6)

$-2x^{2} -4x-3x-6$

combine the like terms:

$-2x^{2}$ - 4x - 3x - 6

-7x

$-2x^{2}$ - 7x - 6

final answer :

$-2x^{2}$ - 7x - 6

hope this helped !!

mark me brainliest :D

6 0

3 years ago

Write the equation of the line Screenshot attached

andrew-mc [135]

Answer:

y = -3/2x + 4

Step-by-step explanation:

Do rise over run to get the -3/2x

the y-intercept is 4, hence the ‘+4’

6 0

3 years ago

Read 2 more answers

F and H are sets of real numbers defined as follows.

Marina CMI [18]

Answer:

$(a)F \cup H=(3, \infty)\\(b)F \cap H=(6, \infty)$

Step-by-step explanation:

Given the sets F and H of real numbers defined as given:

F={w | w>3}

H={w | w>6}

To write a set in interval notation, we use these brackets, ( ) for < or > while we use [ or ] for $\leq $ or \geq$ .

Since our sets are defined by strict inequalities(< or >)

In interval notation

$F=(3,\infty), H=(6,\infty)$

$(a) F \cup H =(3,\infty) \cup (6,\infty) \\\\F \cup H=(3, \infty)\\\\(b) F \cap H =(3,\infty) \cap (6,\infty) \\\\F \cap H=(6, \infty)$

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3 years ago

If today is friday what day of the week will it be 101 days from today

lys-0071 [83]

If the date were to be October 23rd, 2015.. In 101 days, it would be a Monday. -J

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3 years ago