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3 years ago

( PLEASE HELP ) What is the solution to the inequality below?

Mathematics

1 answer:

Lunna [17]3 years ago

5 0

Answer:

Step-by-step explanation:

You are to take the square root across the inequality sign to make it plus or minus 3 squared.

The answer will therefore be C

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Please Help! This is a trigonometry question.

liraira [26]

$\large\begin{array}{l} \textsf{From the picture, we get}\\\\ \mathsf{tan\,\theta=\dfrac{2}{3}}\\\\ \mathsf{\dfrac{sin\,\theta}{cos\,\theta}=\dfrac{2}{3}}\\\\ \mathsf{3\,sin\,\theta=2\,cos\,\theta}\qquad\mathsf{(i)} \end{array}$

$\large\begin{array}{l} \textsf{Square both sides of \mathsf{(i)} above:}\\\\ \mathsf{(3\,sin\,\theta)^2=(2\,cos\,\theta)^2}\\\\ \mathsf{9\,sin^2\,\theta=4\,cos^2\,\theta}\qquad\quad\textsf{(but }\mathsf{cos^2\theta=1-sin^2\,\theta}\textsf{)}\\\\ \mathsf{9\,sin^2\,\theta=4\cdot (1-sin^2\,\theta)}\\\\ \mathsf{9\,sin^2\,\theta=4-4\,sin^2\,\theta}\\\\ \mathsf{9\,sin^2\,\theta+4\,sin^2\,\theta=4} \end{array}$

$\large\begin{array}{l} \mathsf{13\,sin^2\,\theta=4}\\\\ \mathsf{sin^2\,\theta=\dfrac{4}{13}}\\\\ \mathsf{sin\,\theta=\sqrt{\dfrac{4}{13}}}\\\\ \textsf{(we must take the positive square root, because }\theta \textsf{ is an}\\\textsf{acute angle, so its sine is positive)}\\\\ \mathsf{sin\,\theta=\dfrac{2}{\sqrt{13}}} \end{array}$

________

$\large\begin{array}{l} \textsf{From (i), we find the value of }\mathsf{cos\,\theta:}\\\\ \mathsf{3\,sin\,\theta=2\,cos\,\theta}\\\\ \mathsf{cos\,\theta=\dfrac{3}{2}\,sin\,\theta}\\\\ \mathsf{cos\,\theta=\dfrac{3}{\diagup\!\!\!\! 2}\cdot \dfrac{\diagup\!\!\!\! 2}{\sqrt{13}}}\\\\ \mathsf{cos\,\theta=\dfrac{3}{\sqrt{13}}}\\\\ \end{array}$

________

$\large\begin{array}{l} \textsf{Since sine and cosecant functions are reciprocal, we have}\\\\ \mathsf{sin\,2\theta\cdot csc\,2\theta=1}\\\\ \mathsf{csc\,2\theta=\dfrac{1}{sin\,2\theta}\qquad\quad\textsf{(but }}\mathsf{sin\,2\theta=2\,sin\,\theta\,cos\,\theta}\textsf{)}\\\\ \mathsf{csc\,2\theta=\dfrac{1}{2\,sin\,\theta\,cos\,\theta}}\\\\ \mathsf{csc\,2\theta=\dfrac{1}{2\cdot \frac{2}{\sqrt{13}}\cdot \frac{3}{\sqrt{13}}}} \end{array}$

$\large\begin{array}{l} \mathsf{csc\,2\theta=\dfrac{~~~~1~~~~}{\frac{2\cdot 2\cdot 3}{(\sqrt{13})^2}}}\\\\ \mathsf{csc\,2\theta=\dfrac{~~1~~}{\frac{12}{13}}}\\\\ \boxed{\begin{array}{c}\mathsf{csc\,2\theta=\dfrac{13}{12}} \end{array}}\qquad\checkmark \end{array}$

If you're having problems understanding this answer, try seeing it through your browser: brainly.com/question/2150237

$\large\textsf{I hope it helps.}$

Tags: trigonometry trig function cosecant csc double angle identity geometry

8 0

3 years ago

Solve each question using square root property (5x-1)^2=16

Goshia [24]

Answer:

(5x-1)^2=16

Step-by-step explanation:

7 0

3 years ago

REALLY URGENT. 1 3/5 divided by 2/5

Nikolay [14]

Answer:

Step-by-step explanation:

1 3/5(2/5) = 4

7 0

3 years ago

Read 2 more answers

A woman plans to use one fourth of a 48 foot x 100 foot rectangular backyard to plant garden. Find the perimeter of the garden i

nataly862011 [7]

Answer: 160ft.

Step-by-step explanation:

First find the area of the 48ft x 100ft rectangular back yard.

Area of a rectangular = L x B

= 48 x 100

= 4800ft²

Now, find 1/4 of the rectangular backyard meant for garden

= 1/4 of 4800

= 1200ft²

Step 2:

To find the perimeter of the garden,first find the length and breath of the garden. From the dimension of the garden, the length is 40ft > width. In interpreting this,

We make the width of the garden to be. B = xft,

Therefore. L = (x + 40)ft

Now equate the product of this to 1200ft

x(x + 40) = 1200

Open the bracket

x² + 40x = 1200

x² + 40x - 1200 = 0

This is now a quadratic expression. Solving for x using any methods

x² + 60x - 20x - 1200 = 0

Solving by grouping

x(x + 60) - 20(x + 60) = 0

Collect common factors here

(x + 60)(x - 20) = 0

Therefore, x = -60 or 20

Remember, x cannot be negative, so x = 20ft. The width = 20ft, and the length = 60ft.

With this, we can determine the perimeter.

Formula for perimeter of a rectangular block

= 2( L + B )

= 2( 60 + 20 )

= 2(80)

= 2 x 80

= 160ft.

8 0

3 years ago

Which of the following inequalities represent the number line below?

MrRissso [65]

Answer:

greater than or equal to 250

x < or = 250

Step-by-step explanation:

hopefully this helps

6 0

3 years ago