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3 years ago

The equation of a circle is x2 + (y - 10)2 = 16.

Mathematics

1 answer:

vekshin13 years ago

5 0

Answer:

radius 4

center (0,10)

Step-by-step explanation:

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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

2 years ago

I wasn't in school today can someone explain how to do this

Pachacha [2.7K]

You have to multiply 7 3/4 to 9.

First, turn 7 3/4 to an improper fraction which is 31/4.
Next, you multiply 31/4 to 9/1(same thing as 9) across from each other.
Then, you get the answer 279/4(31 x 9 = 279 ;4 x 1 = 4; 279/4).
Last divide 279 to 4 and get 67.75( .75 = 3/4 ; 69 3/4).

7 0

3 years ago

A company is expanding its building area from 11,000 square feet to 13,750 square feet. What is the percentage increase of the a

hjlf

2.5=is the answer to the question

5 0

3 years ago

Read 2 more answers

PLEASE HELP V IMPORTANT the answers I input were just so I could see other questions.

marishachu [46]

Step-by-step explanation:

(T-S)(2000), when T(x) and S(x) are functions, is equivalent to T(2000)-S(2000), which is 17-7=10

We know that T(x) is equal to everything else, and everything else is S(x)+G(x), so T(x)-S(x) = G(x), or dollars spent on general science

6 0

2 years ago

Two students from a group of eight boys and 12 girls are sent to represent the school in a parade.

Deffense [45]

Answer

c. 62/95

Explanation

Probability is the chance of an event happening.

Probability = (favorable outcome)/(total outcome)

P(girl) = 12/20 × 11/19

= (12×11)/(20×19)

= 132/380

= 33/95

P( not a girl) = 1 - 33/95

= 62/95

8 0

2 years ago

Read 2 more answers