Please help me with this!!

Answer:

[tex]\tan(\theta) \cdot \cot(\theta) + \csc(\theta) = \frac{5 - 3\sqrt 5}{5}[/tex]

Step-by-step explanation:

Given

[tex]\cos(\theta) = -\frac{2}{3}[/tex]

[tex]\theta \to[/tex] Quadrant III

Required

Determine [tex]\tan(\theta) \cdot \cot(\theta) + \csc(\theta)[/tex]

We have:

[tex]\cos(\theta) = -\frac{2}{3}[/tex]

We know that:

[tex]\sin^2(\theta) + \cos^2(\theta) = 1[/tex]

This gives:

[tex]\sin^2(\theta) + (-\frac{2}{3})^2 = 1[/tex]

[tex]\sin^2(\theta) + (\frac{4}{9}) = 1[/tex]

Collect like terms

[tex]\sin^2(\theta) = 1 - \frac{4}{9}[/tex]

Take LCM and solve

[tex]\sin^2(\theta) = \frac{9 -4}{9}[/tex]

[tex]\sin^2(\theta) = \frac{5}{9}[/tex]

Take the square roots of both sides

[tex]\sin(\theta) = \±\frac{\sqrt 5}{3}[/tex]

Sin is negative in quadrant III. So:

[tex]\sin(\theta) = -\frac{\sqrt 5}{3}[/tex]

Calculate [tex]\csc(\theta)[/tex]

[tex]\csc(\theta) = \frac{1}{\sin(\theta)}[/tex]

We have: [tex]\sin(\theta) = -\frac{\sqrt 5}{3}[/tex]

So:

[tex]\csc(\theta) = \frac{1}{-\frac{\sqrt 5}{3}}[/tex]

[tex]\csc(\theta) = \frac{-3}{\sqrt 5}[/tex]

Rationalize

[tex]\csc(\theta) = \frac{-3}{\sqrt 5}*\frac{\sqrt 5}{\sqrt 5}[/tex]

[tex]\csc(\theta) = \frac{-3\sqrt 5}{5}[/tex]

So, we have:

[tex]\tan(\theta) \cdot \cot(\theta) + \csc(\theta)[/tex]

[tex]\tan(\theta) \cdot \cot(\theta) + \csc(\theta) = \tan(\theta) \cdot \frac{1}{\tan(\theta)} + \csc(\theta)[/tex]

[tex]\tan(\theta) \cdot \cot(\theta) + \csc(\theta) = 1 + \csc(\theta)[/tex]

Substitute: [tex]\csc(\theta) = \frac{-3\sqrt 5}{5}[/tex]

[tex]\tan(\theta) \cdot \cot(\theta) + \csc(\theta) = 1 -\frac{3\sqrt 5}{5}[/tex]

Take LCM

[tex]\tan(\theta) \cdot \cot(\theta) + \csc(\theta) = \frac{5 - 3\sqrt 5}{5}[/tex]

Answer:

77, 48

Step-by-step explanation:

the area of a rectangle is length times width.

the area of a triangle is length x height divided by 2

Answer:

√29

Step-by-step explanation:

You would use the distance formula in this case to solve the problem:

(8-3)^2+(1-3)^2=29

Now square root 29, leaving you with √29.

Answer:

5.39

Step-by-step explanation:

√(x2 - x1)² + (y2 - y1)²

√(3 - 8)² + (1 - 3)²

√(-5)² + (-2)²

√25 + 4

√29

= 5.39

Answer:

-90 degree is the correct answer

Answer:4.12

Step-by-step explanation: I need brainliest for next rank I’d appreciate it

Answer:

5, 9,13,17

Step-by-step explanation:

5 +4 +4+4

Answer:

Alr

Step-by-step explanation:

Brainliest???

Answer:

Step-by-step explanation:

Answer:

The circle's area is 380.13 square miles.

Step-by-step explanation:

A = pie * r^2 = pie * 11^2 = 380.13

I hope this somewhat helped you find your answer.

Answer:

379.94

Step-by-step explanation:

3.14 x (11x11) = 379.94

Answer:

i think its b

Step-by-step explanation:

Answer: im pretty sure this is correct

- 1/42 x (21x233y)

Step-by-step explanation:

first convert the expressions (2 3/10x x5/7 x y-2 4/5 x x )

then factor the expression (23/10 x- 5/7 y- 29/6 y- 14/5x )

then collect like terms (1/210 x 483 x - 150 y - 1015 - 588x)

factor the expression (1/210 x 105x 1165y)

Multiply reduce (1/210 x -5 (21x + 233y ))

= -1/42 x (21x233y)

Answer:

The answer is 13, 21

Step-by-step explanation:

9x2=18

18-5=13

13x2=26

26-5=21

The next two terms of the pattern are 13, 21.

Arithmetic operations can also be specified by the subtract, divide, and multiply built-in functions.

The operator that perform arithmetic operation are called arithmetic operators .

Operators which let do basic mathematical calculations

+ Addition operation : Adds values on either side of the operator.

For example 4 + 2 = 6

- Subtraction operation : Subtracts right hand operand from left hand operand.

for example 4 -2 = 2

* Multiplication operation : Multiplies values on either side of the operator

For example 4*2 = 8

/ Division operation : Divides left hand operand by right hand operand

For example 4/2 = 2

Given,

The pattern is  6, 7, 9...

To determine the next two terms follows the rule multiply by 2, then subtract 5,

Firstly multiply by 2

⇒ 9 x 2 = 18

Then subtract 5,

⇒ 18 - 5 = 13

So, the term is 13

Firstly multiply by 2

⇒ 13 x 2 = 26

Then subtract 5,

⇒ 26 - 5 = 21

So, the term is 26

Hence, the next two terms of the pattern are 13, 21.

Learn more about Arithmetic operations here:

brainly.com/question/25834626

#SPJ2

Answer:

B

Step-by-step explanation:

[tex]F = \frac{9}{5} c + 32[/tex]

This Equation Is Used For Conversion Of Celcius To Fahrenheit.

Answer: Uhmm ok the answer i got would have been F = C x 9/5 + 32 But since there isn't a choice like that I think it's the second one- its the closest to what i got--

Step-by-step explanation:

Answer:

option 2

Step-by-step explanation:

Answer:

Option 2

Step-by-step explanation:

Option 2

x is 4

y is -4

Answer:

Macaroni, spaghetti, and bow tie are all types of pasta.

Answer:

C

Step-by-step explanation:

hope this helps with the work

Answer:

201

Step-by-step explanation:

use πr^2 formula here

Step-by-step explanation:

.....................

Answer:

10

Step-by-step explanation:

Answer:

30

Step-by-step explanation:

Answer:

Step-by-step explanation:

5^4 = 625. I hope your calculator will do this.

625 / 5 = 125

There is a more general way to do this which will be in harmony with the rest of the question.

5^4 / 5^1 = 5^(4 - 1) = 5^3 = 125

b^4 / b2 = b^(4 - 2) = b^2

a remains as it is at a^3

So the answer is 125 a^3 b^2

Answer:

a = [tex]4\sqrt{3}[/tex]

b= 4

Step-by-step explanation:

It's a 30-60-90 triangle based on the given picture. A right triangle too

Use sine, cosine, and tangent to solve for the side.

To find b, you can use sin(30) = b/8 because sin(angle) = opposite/hypotenuse.

OR you can use the rule for 30-60-90 triangle, which is x for short leg, 2x for hypotenuse, and [tex]x\sqrt{3}[/tex] for long leg

So either way, b = 4

To find a, you can use cos(30) = a/8 because cos(angle) = adjacent/hypotenuse.

OR you can use the same rule, 30-60-90 triangle to save time

a will end up = [tex]4\sqrt{3}[/tex]

Answer:

352

Step-by-step explanation:

originally 351.86 but 352 when rounded

Answer:

I think it is 648³ in. I think for the second one it is 372³ in.

Step-by-step explanation:

                               HOPE THIS HELPS U!!!!!!!!! :) :) :) :) :)

                                SORRY IF IT'S WRONG. :) :) :) :) :)

Answer:

Translation (3 right)

then a rotation 90 degrees clockwise

Or

Rotation of 90 degrees clockwise

Then translation (3 right)

Either one

Answer:

21708

Step-by-step explanation

Ok I am not so sure about this one, since this was a LOT of counting, and unless you want to see 5 pages of calculations, I'm just going to go on a limb and say trust me. However, if you really want to see for yourself, I'll give you a hint. For the first 1***1 numbers, the sum is 1440. For the 2***2 numbers, the sum is 1683. Try to calculate this to 9***9 to find the answer! Again, not sure about my answer if it's wrong, sorry!

Answer:

y = 4x...

Step-by-step explanation:

Answer:

61 degrees

Step-by-step explanation: