Given that cos(theta) = 8/17 and that theta lies in Quadrant IV, what is the exact value of sin 2(theta)?

Answers

Answer 1

Answer:    [tex]-\frac{240}{289}[/tex]

=========================================================

Explanation:

Use the pythagorean trig identity [tex]\sin^2(\theta)+\cos^2(\theta) = 1[/tex] and plug in the fact that [tex]\cos(\theta) = \frac{8}{17}\\\\[/tex]

Isolating sine leads to [tex]\sin(\theta) = -\frac{15}{17}\\\\[/tex]. I'm skipping the steps here, but let me know if you need to see them.

The result is negative because we're in quadrant 4, when y < 0 so it's when sine is negative.

Therefore,

[tex]\sin(2\theta) = 2\sin(\theta)\cos(\theta)\\\\\sin(2\theta) = 2*\left(-\frac{15}{17}\right)*\left(\frac{8}{17}\right)\\\\\sin(2\theta) = -\frac{240}{289}\\\\[/tex]


Related Questions

What is the equation of a line that has a slope of One-half and passes through point (2, –3)?

Answers

Answer: y = one-half x minus 4

Step-by-step explanation:

y = 1/2 x + b

-3 = 1/2 (2) + b

-3 = 1 + b

-3 - 1 = b

-4 = b

which is bigger 25 fl oz or 1 pint

if you help it would be appreciated

#learning with brainly

Answers

Answer:

25 fl oz

Step-by-step explanation:

1 pint is equivalent to 16 fl oz, so we're left with 25 fl oz and 16 fl oz. As you can see, 25 is greater than 16, making 25 fl oz the correct answer.

25 fl oz is equal to 1.5625 pints. so 25 fl oz is bigger

3. Subtract
x)--5x2 + x-2
g(x) = -3x2 + 3x + 9 9

Answers

Step-by-step explanation:

For example: Subtract 4x - 10y + 15z from 5x + 8y - 20z.

Step 1: Arrange the polynomials in standard form. In this example, it is already arranged.

Step 2: Place them horizontally.

(4x - 10y + 15z) - (5x + 8y - 20z)

Step 3: Change the sign of the second polynomial through the parentheses.

4x - 10y + 15z - 5x - 8y + 20z

Step 4: Arrange the like terms together.

4x - 5x - 10y - 8y + 15z + 20z

Step 5: Solve the equation

-x - 18y + 35z

Therefore, when we subtract 4x - 10y + 15z from 5x + 8y - 20z = -x - 18y + 35z.

Find center and radius of this circle:
[tex](x-9)^2+(y+4)^2=25[/tex]

Answers

Answer:

Center: (9,-4)

Radius: 5

Step-by-step explanation:

Equation for a circle:

[tex](x-h)^2+(y-k)^2=r^2[/tex]

h=9

k=-4

r=5

center is (h,k)

to find the radius, get square root of 25

Answer:

Center is (9,-4)

Radius: 5

Step-by-step explanation:

h=9

k=-4

r=5

Distance between -3,-2 and 5,2

Answers

We can find the distance between two points by using distance formula,

[tex] \qquad \: D = \sf \red{\sqrt{ {(x_2 -x_1)}^{2} + {(y_2 -y_1)}^{2} }}[/tex]

Here,

x₁ = -3

x₂ = 5

y₁ = -2

y₂ = 2

Therefore,

[tex] : \implies \: D = \sf \red{\sqrt{ {(x_2 -x_1)}^{2} + {(y_2 -y_1)}^{2} }} \\ \\ : \implies \: D = \sf \sqrt{ {(5-( - 3))}^{2} + {(2 -( - 2))}^{2} }

\\ \\ : \implies \: D = \sf \sqrt{ {8}^{2} + {4}^{2} } \\ \\ : \implies \: D = \sqrt{64 + 16}

\\ \\ : \implies \: D = \sqrt{80} [/tex]

Hence the √80 = 8.94 approx is the distance between the two points (-3,-2) and (5,2).

To find :-

The distance between 2 points

Given :-

Here we have been provided 2 points

(-3, -2) and (5, 2)

Solution :-

[tex] (x_1,y_1) = (-3,-2) \\ (x_2,y_2) = (5,2) [/tex]

Formula to find distance is

[tex] = \sqrt{ {(x_2 - x_1)}^{2} + {(y_2 - y_1)}^{2} } [/tex]

[tex] = \sqrt{ {(5 - ( - 3))}^{2} + {(2 - ( - 2))}^{2} } \\ = \sqrt{ {(8)}^{2} + {(4)}^{2} } \\ = \sqrt{64 + 16} \\ = \sqrt{80} \\ = 4 \sqrt{5} [/tex]

Result :-

The distance between 2 points is 4√5.

[tex] \mathcal {BE \: \: BRAINLY} [/tex]

Fred is baking cookies for a school
bake sale. It takes
2/3 of a cup of
sugar to
make one batch of
cookies. How many cups
of sugar
does he need to double the
recipe?

Answers

Answer: Fred needs 4/3 a cup of sugar, which can be simplified into 1 1/3.

Step-by-step explanation:

If you do 2/3 times 2/1 (because double means twice the amount) you will get 4/3, which again, can be simplified into 1 1/3.

There are 114 cans of soup in a grocery store. The ratio of large cans of soup to small cans of soup is 12:7. A customer buys 2 large cans of soup. What is the new ratio of large cans of soup to small cans of soup in the grocery store? Choose all the correct answers. A. 3:5 B. 5:3 C. 8:5 D. 10:7 E. 35:21 F. 37:21

Answers

The ratio of the large cans to small cans shows the distribution of both cans

The new ratio of large cans of soup to small cans of soup in the grocery store is (b) 5 : 3 and (e) 35: 21

How to determine the ratio?

The given parameters are:

Ratio = 12 : 7

Rewrite as:

Large : Small= 12 : 7

The number of cans is given as:

Can = 114

So, the distribution of the cans are:

Large = 12/(12 + 7) * 114

Large = 72

Small = 7/(12 + 7) * 114

Small = 42

When 2 large cans are purchased, the remaining number of cans are:

Small = 42

Large = 70

Express as ratio

Large : Small = 70 : 42

Simplify

Large : Small = 35 : 21

Large : Small = 5 : 3

Hence, the new ratio  is (b) 5 : 3 and (e) 35: 21

Read more about ratio at:

https://brainly.com/question/16981404

PLEASE HELP howard has 3 times money as ronald if howard gives ronald $50, Ronald will then have 3 times as much as howard how much money in dollars will the two of them have together. Brainliest for answer​

Answers

Answer:

$100

Step-by-step explanation:

What we know,

Howard has 3 times more money than RonaldIf Howard gives Ronald $50, Ronald will then have 3 times more money than Howard

Let us assume that Ronald has $25, so Howard must have $75,

Now Howard gives $50 to Ronald, Now Ronald has $75,

Therefore our assumption is correct,

Therefore Ronald and Howard together will have $100.

Help solving this problem

Answers

Answer:

A=0.50

B=0.477

C=0.423<p<0.531

Step-by-step explanation:

sample size N :333

number of success X: 159

sample part of success x/n = 159/333

x=0.477 B

0.50 A Half a chance to flip a tail or head

part C:

[tex]0.477 plusminus 1.96 * \sqrt{ \frac{0.477 (1 - 0.477)}{333} } [/tex]

simplify

[tex]0.477 plusminus 1.96 * 0.0536[/tex]

expand

[tex]0.477 + 1.96 * 0.0536[/tex]

[tex]0.531[/tex]

expand minus

[tex]0.477 - 1.96 * 0.0536[/tex]

[tex]0.423[/tex]

finally answer part c

[tex]0.423 < p < 0.531[/tex]


55. Find the inverse function of [tex]g(x)=\log _{4}\left(x^{3}+2\right)[/tex] .

Answers

[tex]y= g(x) = \log_4 (x^3 +2)\\\\\text{Replace x with y and solve for y:}\\\\~~~~x=\log_4 (y^3 +2)\\\\\implies y^3 +2 = 4^x\\\\\implies y^3 =4^x-2\\ \\\implies y = \sqrt[3]{4^x -2}\\\\\implies f^{-1} (x) = \sqrt[3]{4^x -2}[/tex]

The sum of the first 10 terms of an arithmetic series is 100 and the sum of next 10 300 .Find the series.​

Answers

Let a be the first term in the sequence, and d the common difference between consecutive terms. If aₙ denotes the n-th term in the sequence, then

a₁ = a

a₂ = a₁ + d = a + d

a₃ = a₂ + d = a + 2d

a₄ = a₃ + d = a + 3d

and so on, up to the n-th term

aₙ = a + (n - 1) d

The sum of the first 10 terms is 100, and so

[tex]\displaystyle \sum_{n=1}^{10} a_n = 100 \\ \sum_{n=1}^{10} (a + (n-1)d) = 100 \\ (a-d) \sum_{n=1}^{10} 1 + d \sum_{n=1}^{10} n = 100 \\ 10a+45d = 100[/tex]

where we use the well-known sum formulas,

[tex]\displaystyle \sum_{n=1}^N 1 = 1 + 1 + 1 + \cdots + 1 = N[/tex]

[tex]\displaystyle \sum_{n=1}^N n = 1 + 2 + 3 + \cdots + N = \frac{N(N+1)}2[/tex]

The sum of the next 10 terms is 300, so

[tex]\displaystyle \sum_{n=11}^{20} a_n = 300 \\ (a-d) \sum_{n=11}^{20} 1 + d \sum_{n=11}^{20} n = 300 \\ (a-d) \left(\sum_{n=1}^{20} 1 - \sum_{n=1}^{10} 1\right) 1 + d \left(\sum_{n=1}^{20} n - \sum_{n=1}^{10} n\right) = 300 \\ 10a+145d = 300[/tex]

Solve for a and d. Eliminating a gives

(10a + 145d) - (10a + 45d) = 300 - 100

100d = 200

d = 2

and solving for a gives

10a + 145×2 = 300

10a = 10

a = 1

So, the given sequence is simply the sequence of positive odd integers,

{1, 3, 5, 7, 9, …}

given recursively by the relation

[tex]\begin{cases}a_1 = 1 \\ a_n = a_{n-1} + 2 & \text{for }n>1\end{cases}[/tex]

and explicitly by

[tex]a_n = 1 + 2(n-1) = 2n - 1[/tex]

for n ≥ 1.

whai is numarates what is ​

Answers

Answer:

Not a proper question. But I think it's a 5

[tex] \huge \pink{ \underline{ \overline{ \: 5 \: i \: think}}}[/tex]

Find the area (image attached) this is literally my 3 time asking

Answers

I'll help you!

Answer:

EXACT: 2.7√1.71 + 4.05 units²

APPROX: 3.5307 + 4.05 = 7.58 units²

Step-by-step explanation:

See the attached help image

Total A = 2 triangles + 1 trapezoid

Triangles

Find missing side:

2.7² + b² = 3²

b² = 3² - 2.7²

b = √1.71

Find area of triangles:

A = bh/2

A = b(2.7)/2

A = √1.71(2.7)/2
A = 1.35√1.71 units²

Trapezoid

A = (a + b)(h)/2

A = ((3-√1.71) + √1.71)(2.7)/2

A = (3)(2.7)/2

A = 4.05 units²

Total

2(1.35√1.71) + 1(4.05)

EXACT: 2.7√1.71 + 4.05 units²

APPROX: 3.5307 + 4.05 = 7.58 units²

50 POINTS!!! PLEASE HELP DUE SOON
A fireman needs to get water to a second-floor fire. His ladder is 30 ft long and he leans it against the vertical wall so that the top of the ladder is 27 ft above the ground.

(a) Use trigonometry to find the angle formed between the ground and the ladder. Round to the nearest tenth of a degree and show all your work.

(b) For safety reasons, the fireman wants the angle the ladder makes with the ground to be no more than 65°. Will the ladder be safe the way it is positioned? Explain.

Answers

Answer:

sorry I tried But Don't Know The Answer

Question 3 of 10
which choice is equivalent to the quotient
According to the property
below?
O A -5
B. 25
C5
OD. - 5
ES

Answers

Answer: D: Square Root Of 5

Step-by-step explanation: 30/6 is 5, now fill in the sqrt symbol. Hope this helped. (This problem was one of the simpler, friendlier numbers.)


Help please!! MY LIFE DEPENDS ON THIS

Answers

Answer:

D

Step-by-step explanation:

A total of 18 teams made 26 or more feild goals.

The answer is D
I took the test

Two of the angles in a triangle measure 17° and 153° What is the measure of the third angle?

Answers

Answer:

10

Step-by-step explanation:

153+17=170
180-170=10

Find the slope of the line containing the pair of points.
(5,1) and (-5, -9)
I really need this

Answers

Answer:

1

Step-by-step explanation:

[tex]my \: dear \: \\ to \: find \: the \: slope \: of \: a \: line \: use \: the \: formular \\ slope = \frac{y2 - y1}{x2 - x1} \\ from \: the \: question \: x1 = 5 \: \: y1 = 1\: \: x2 = - 5 \: \: y2 =- 9 \\ slope = \frac{ - 9 - 1}{ - 5 - 5} = \frac{ - 10}{ - 10} = 1 \\ therefore \: slope = 1 \\ hope \: this \: helps \\ stay \: focused \: with \: your \: studies[/tex]

also may i have help with this one

Answers

The answer should be 11 since adding all the x’s up before 13 equals 11

Jim is 8 ft 9 in tall. Jane is 23.5 in tall. How many times taller than Jane is​ Jim?

Answers

because 23.5 inches is 1.9 feet, Jim is 8 times taller than Jane :)

graph of F(x), shown below, has the same shape as the graph of G(x) = x4, but it is shifted 4 units to the right. What is its equation?F(x) = _____

Answers

Answer:

G(x) = (x-4)⁴

Step-by-step explanation:

The equation of the graph of f(x) which is formed by shifting 4 units to the right of g(x) is f(x) = (x - 4)⁴

What is Translation of Functions?

Translation of functions is defined as the when each point in the original graph is moved by a fixed units in the same direction.

There are horizontal translation and vertical translation of functions.

Given a function G(x).

G(x) = x⁴

A function F(x) is formed by shifting the graph of G(x) to the right by 4 units.

A function h(x) when shifted to the right by k units becomes h(x - c).

So the graph of G(x) when shifted to the right by 4 units becomes G(x - 4).

G(x - 4) = (x - 4)⁴

So, F(x) = (x - 4)⁴

Hence the function is F(x) = (x - 4)⁴.

Learn more about Translation of Functions here :

https://brainly.com/question/29198392

#SPJ7

What was likely the purpose of the Great Enclosure?
A. To keep slaves and workers from escaping
B. To protect Zimbabweans from outside invasion
C. To separate the wealthy from the poor in society
D. To enclose cattle and horses

Answers

The great enclosure was built to have a surplus population and its religious and administrative activities. There fore the answer would be B since they are trying to protect the population and there religion

Is 5,000 cm greater than 5m

Answers

yes it is! 5000 centimeters is greater than 5 meters.

Answer:

Yes

Step-by-step explanation:

5,000 cm = 50m

[tex]\frac{1m}{100cm} =5000cm[/tex]

[tex]\frac{1m(5000)}{100}[/tex]

[tex]\frac{5000m}{100}[/tex]

= 50 m

hope this helps :)

how to solve the answers​

Answers

Answer:

divide what is on the right hand side of the equal sign by what is next to x or y

Step-by-step explanation:

e.g.

2x=3

x=3/2

fraction:3/2

decimal: 1.5

Answer:

divide what is on the right hand side of the equal sign by what is next to x or y

Step-by-step explanation:

Two cables are securing a kayak to a roof rack. The forces are represented by vectors Vector u = LeftAngleBracket negative 5, 6, 3 RightAngleBracket. and Vector t = LeftAngleBracket negative 8, negative 2, 1 RightAngleBracket.. If both cables are replaced by a single cable, what vector would represent the cable?

LeftAngleBracket 3, 8, 2 RightAngleBracket.
LeftAngleBracket negative 13, 4, 4 RightAngleBracket.
LeftAngleBracket negative 3, negative 8, negative 2 RightAngleBracket.
LeftAngleBracket 13, negative 4, negative 4 RightAngleBracket.

Answers

Answer:

< –13, 4, 4 >

Step-by-step explanation:

Vector u = < –5, 6, 3 >

Vector t = < –8, –2, 1 >

  -5   6   3

+ -8  -2   1

 -13   4   4

Vector u + t = < –13, 4, 4 >

Answer:

B. <14,-3>

Step-by-step explanation:

What is 10,000 written as a power with a base of 10?

Enter your answer in the boxes.

Answers

Answer:

10 to the power of 4

Step-by-step explanation:

Please help this mad hard

Answers

Answer:

First Net

Step-by-step explanation:

The first net will be the answer because you can see that the figure has a square base. The first net has a square base as well. Now, the side of the figure has equal triangles, and so does the first net. The first net fits the figure best.

Hope this helps :)

A table showing Tickets Sold, Cost, and Total. The first row shows Child, with the entries, c, 3, and 3 c. The second row shows Adult, with entries, x, 5, 5 x. The last row shows Total, with all three entries blank.
Tickets to a baseball game cost $3 for a child’s ticket and $5 for an adult ticket. At the last game, $521 was collected when 139 people attended the game. Which value could replace x in the table so that a single-variable equation can be written and solved to determine the number of child’s tickets, c, sold?

Answers

Answer:

x = 52, c = 87

Step-by-step explanation:

Set up and then solve this system of equations:

3c + 5x = 521--->3c + 5x = 521

c + x = 139 --->3c + 3x = 417

-------------------

2x = 104

x = 52, c = 87

Answer: the answer is 139-c

What is the area of a circular cardboard piece needed for the base of a model of a volcano that is 20 centimeters tall and has a volume of 960 cubic centimeters?

Answers

Closer to 960 because of the 10 and 20

Answer:

144

Step-by-step explanation:

im right:D have  a good day or night

please help me with these questions , thank you​

Answers

Answer:

1. 4[tex]x^{3}[/tex] + 26x² + 4x - 48

2. 2[tex]x^{3}[/tex] - 23x² + 60x - 32

3. [tex]x^{5}[/tex] + 7[tex]x^{3}[/tex] - 4x + 2[tex]x^{4}[/tex] + 14x² - 8

4. 2[tex]x^{7}[/tex] + [tex]x^{6}[/tex] - 28[tex]x^{5}[/tex] + 3x + 12

Step-by-step explanation:

To multiply polynomials, simply distribute whatever's outside the largest set of parenthesis, then combine like terms.

1) Distribute the parenthesis (x + 6):

x(4x² + 2x - 8)  +  6(4x² + 2x - 8)

4[tex]x^{3}[/tex] + 2x² -8x  +  6(4x² + 2x -8)

4[tex]x^{3}[/tex] + 2x² -8x + 24x² + 12x - 48

Combine like terms:

4[tex]x^{3}[/tex] + 26x² + 4x - 48

2) Distribute the parenthesis (x - 8):

x(2x² - 7x + 4)  +  (-8)(2x² - 7x + 4)

2[tex]x^{3}[/tex] - 7x² + 4x  +  (-8)(2x² - 7x + 4)

2[tex]x^{3}[/tex] - 7x² + 4x  +  -16x² + 56x - 32

Combine like terms:

2[tex]x^{3}[/tex] - 23x² + 60x - 32

3) Distribute the parenthesis (x + 2):

x([tex]x^{4}[/tex] + 7x² - 4)  +  2([tex]x^{4}[/tex] + 7x² - 4)

[tex]x^{5}[/tex] + 7[tex]x^{3}[/tex] - 4x  +  2([tex]x^{4}[/tex] + 7x² - 4)

[tex]x^{5}[/tex] + 7[tex]x^{3}[/tex] - 4x + 2[tex]x^{4}[/tex] + 14x² - 8

No like terms to combine, so:

[tex]x^{5}[/tex] + 7[tex]x^{3}[/tex] - 4x + 2[tex]x^{4}[/tex] + 14x² - 8

4) Distribute the parenthesis (x + 4):

x(2[tex]x^{6}[/tex] - 7[tex]x^{5}[/tex] + 3)  +  4(2[tex]x^{6}[/tex] - 7[tex]x^{5}[/tex] + 3)

2[tex]x^{7}[/tex] - 7[tex]x^{6}[/tex] + 3x  +  4(2[tex]x^{6}[/tex] - 7[tex]x^{5}[/tex] + 3)

2[tex]x^{7}[/tex] - 7[tex]x^{6}[/tex] + 3x + 8  [tex]x^{6}[/tex] - 28[tex]x^{5}[/tex] + 12

Combine like terms:

2[tex]x^{7}[/tex] + [tex]x^{6}[/tex] - 28[tex]x^{5}[/tex] + 3x + 12

hope this helps!

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