if sin(32)=x , then sin(4) cos(4) cos(8) cos(16)=..............
Solve using double angle trigonometric functions​

Answers

Answer 1

If sin 32 is equal to x, then sin 4 · cos 4 · cos 8 · cos 16 is equal to x/8 by using double angle trigonometric functions.

How to simplify an expression by trigonometric expressions

Trigonometric expressions are formulas that utilize trigonometric functions. Trigonometric functions are a kind of trascendental functions, that is, functions that cannot be described in algebraic terms.

In this question we must simplify a given expression by using the following trigonometric formula:

sin 2x = 2 · cos x · cos x   (1)

Now we proceed to expand the expression given:

x = sin 32

x = 2 · sin 16 · cos 16

x = 4 · sin 8 · cos 8 · cos 16

x = 8 · sin 4 · cos 4 · cos 8 · cos 16

Thus,

sin 4 · cos 4 · cos 8 · cos 16 = x/8

If sin 32 is equal to x, then sin 4 · cos 4 · cos 8 · cos 16 is equal to x/8 by using double angle trigonometric functions. [tex]\blacksquare[/tex]

To learn more on trigonometric functions, we kindly invite to check this verified question: https://brainly.com/question/6904750


Related Questions

Can the numbers 24, 32, and 40 be the lengths of the three sides of a right triangle?

Answers

Answer:

no

Step-by-step explanation:

no

Yes

since the hypotenuese will be forty

24×24=576

32×32=1024

1024+576=1600

√40=1600 which makes YES be the correct answer

NEED HELP 100 POINTS TO ANSWER QUESTION PLEASE !!!!!!!!

Find the volume of the prism:



Question 5 options:

V = 125 in³


V = 100 in³


V = 120 in³


V = 105 in³

Answers

120 is the answer because 4*5 is 20 and then you multiply 20*6 and you get 120

2021 balls are arranged in a row and are numbered from 1 to 2021. Each ball is coloured in one of four
colours: green, red, yellow or blue. Among any five consecutive balls there is exactly one red, one yellow and one blue ball. After any red ball the next ball is yellow. The balls numbered 2, 20 and 202 are green. What colour is the ball numbered 2021?
(A) green
(B) red
(C) yellow
(D) blue
(E) not determined

Answers

Answer:

D) blue

Step-by-step explanation:

because the first ball has to be blue

the second ball is green

the third is red

and the fourth one is yellow

so u multiply 1(blue ball)× 2021=blue ball

Are the triangles similar? How do you know?

Answers

Answer:

They are similar because triangle AMY has sides double the size of CED. If you divide AMY's triangle sides by 2, you will have a triangle that is the exact size of CED. :)

Have an amazing day!!

Please rate and mark brainliest!!!

Answer:

The triangles are similar

Step-by-step explanation:

To tell whether the triangles are similar or not we can compare their side lengths

if the triangle are similar then their side lengths' will be proportional:

MY/CD = AY/ED

10/5 = 8/4 cross multiply expressions

40 = 40 as we can see from this result, the side lengths are proportional so we can say these triangles are similar

PLEASE HELP AS SOON AS POSSIBLE
6) The graphic shows the average number of points scored per game for
ten players in the NBA. What is the range value of the data set? A) 3.45 B) 3.5 C) 6.9 D) 7

Answers

Answer:

6.9

Step-by-step explanation:

I took the USATP hope it helps

There are only blue cubes, red cubes and yellow cubes in a box.
The table shows the probability of taking at random a blue cube from the box.
Colour
blue
red
yellow
Probability
0.4
The number of red cubes in the box is the same as the number
of yellow cubes in the box.
a) Complete the table.
(2)
There are 30 blue cubes in the box.
b) What is the total number of cubes in the box?

Answers

Answer:

a) 240 grams

b) 360 grams

c) 2 packs

Step-by-step explanation:

a) 1 biscuit = 4 grams of flour

60 biscuits = 240 grams of flour

Conclusion, 240 grams of flour is needed for 60 biscuits.

b) 240×3÷2 = 360 grams of butter

c) 360÷250

= 1.44

≈ 2 packs

Hope this helps =)

Can someone help me please

Answers

Answer:

Option A

Step-by-step explanation:

To simplify this fraction:

We subtract the powers:

[tex]\frac{6^{3} }{6^{6} } = 6^{3-6}[/tex]

[tex]6^{-3}[/tex] = [tex]\frac{1}{6^{3} }[/tex] = 1/216

These answers I wrote in the last line are options B,C and D.

Therefore Option A is not equivalent.

The answer is A, hope this helps!!

What is the volume of this container? (Image below)

Answers

Answer:

A. 56 in3

Step-by-step explanation:

Formula for Volume; LWH

L * W * H = 4* 4 * 2

16 * 2 = 32(3)

(second half of the container)

LWH = 3 * 4 * 2

12 * 2 = 24(3)

32 + 24 = 56(3)

Break into two cuboids

In cuboid

★V=LBH

Hence

#1

L=1B=2H=4

Volume:-

1(2)(4)=8in³

#2

L=4B=3H=4

Volume:-

4(3)(4)48in³

Total:

8+4856in³

The figure below is made up of unit cubes that each have a volume of 1 cubic centimeter.

A. 7
B. 9
C. 11
D. 13



HELP PLEASE​

Answers

Answer:

c. 11

Step-by-step explanation:

Bottom row: 6 cubes

middle row: 4 cubes

top row: 1 cube

11 cubes total.

The graph below shows the relationship between the number of oranges purchased and the cost. Which statement about the unit rate of the graph is true?
The unit rate is 1.


The unit rate is13

The unit rate is 3.


The unit rate is 9.

Answers

Answer: The unit rate is 1/3

Step-by-step explanation:

The slope of the line, which also represents the unit rate, is 1/3.

The height of a poplar tree in feet at age t years can be modeled by the function h(t)=6+3ln(t+1) . use the model to predict the number of years when the height will exceed 18 feet.

Answers

The function h(t)=6+3ln(t+1) is a logarithmic function

The height of the tree will exceed 18 feet after 53.6 years

How to determine the number of years?

The function is given as:

h(t)=6+3ln(t+1)

When the height is 18 feet, we have:

6+3ln(t+1) = 18

Subtract 6 from both sides

3ln(t+1) = 12

Divide both sides by 3

ln(t+1) = 4

Take the exponent of both sides

t + 1 = e^4

Evaluate the exponent

t + 1 = 54.6

Subtract 1 from both sides

t = 53.6

This means that the height of the tree will exceed 18 feet after 53.6 years

Read more about logarithmic functions at:

https://brainly.com/question/25953978


Calculate the zeros of the function f(x) = x2 – 12x + 35 by completing the square.

Answers

Answer:

x = 5, x = 7

Step-by-step explanation:

to find the zeros let f(x) = 0 , that is

x² - 12x + 35 = 0 ( subtract 35 from both sides )

x² - 12x = - 35

To complete the square

add ( half the coefficient of the x- term )² to both sides

x² + 2(- 6)x + 36 = - 35 + 36

(x - 6)² = 1 ( take the square root of both sides )

x - 6 = ± [tex]\sqrt{1}[/tex] = ± 1 ( add 6 to both sides )

x = 6 ± 1

then

x = 6 - 1 = 5

x = 6 + 1 = 7

Which quadratic function in vertex form has a vertex at (-2, 5) And passes through the point (2, -3)?

Answers

Answer:graph{-19/9(x+3)^2+5 [-10, 2, -20, 10]}

Step-by-step explanation:

y

=

19

9

(

x

+

3

)

2

+

5

Explanation:

If an equation representing a parabola is in vertex form such as

y

=

a

(

x

k

)

2

+

h

then its vertex will be at

(

k

,

h

)

. Therefore the equation for a parabola with a vertex at (-3, 5), will have the general form

y

=

a

(

x

+

3

)

2

+

5

If this parabola also passes through the point

(

0

,

14

)

then we can determine the

a

parameter.

14

=

a

(

0

+

3

)

2

+

5

9

a

=

19

a

=

19

9

So our equation in vertex form is

y

=

19

9

(

x

+

3

)

2

+

5

graph{-19/9(x+3)^2+5 [-10, 2, -20, 10]}

Is this triangle acute, right or obtuse?

Answers

Answer:

acute

Step-by-step explanation:

Check using the Pythagorean Theorem:

A^2 + B^2 ≟ C^2

9^2 + 115 ≟ 11^2

196 > 121,

so this triangle is acute because the sum of each leg squared is longer than the length of the hypotenuse squared.

A student is working on a project for which he records the revolutions per minute (rpm) for a small electric motor as he increases the voltage in a circuit. Here is the table showing the results:

Voltage
(volt) Motor Speed
(rpm)
0 0
1 25
2 50
3 75
4 100
Create a graph showing the relationship in the table. Think about the title, axis labels, and whether you need to connect the points with a line.

Answers

Answer:

See below ↓

Step-by-step explanation:

The relation is :

Let y = Motor Speed and x = Voltagey = 25x

Title : Variation of Motor Speed with Applied Voltage

x-axis label : Voltage (volt)

y-axis label : Motor speed (rpm)

As it constantly varies with a value of x and they are not isolated data points, they should be connected with a line.

[tex]\sqrt{x}-2=\sqrt{x-10}[/tex]

Answers

Answer:

Exact Form:

49/4

Decimal Form:

12.25

Mixed Number Form:

12 1/4

Step-by-step explanation:

Isolate the radical, then raise each side of the equation to the power of its index.

√x-2=√x-10

x-4√x+4=x-10

-4√x+4=-10

-4√x=-10-4

-4√x=-14

√x=7

-

2

x= 49

---

44

what is this pls help

Answers

-4.5 or -4.3 i’m not really sure i’m just estimating

I NEED HELP WITH THIS ALEKS TOPIC

Answers

subtraction/algebraic subtraction

What you have looks right, the reason for step 7 should just be algebraic subtraction since there is a DG on both sides that can be simplified out of the equation

I’m not sure what exact answer your question will allow, but it’ll be something along the lines of subtraction

Which answer choice correctly represents 0.513333… ?

Answers

Answer = 3rd picture

Find the Volume of 2 centimeter 2 centimeter 8 centimeters

Answers

Answer:

32 cm^3

Step-by-step explanation:

Hope it will help you

Answer:

32 cm^3

Step-by-step explanation:

V = L x W x H

V = 2 x 2 x 8

V = 4 x 8

V = 32

The answer would be 32cm^3

I hope it helps! Have a great day!

Your Murderer~

find the area of the circumference of a circle with diameter 7yd use the value 3.14 as pie

Answers

Given,

Diameter of the circle = 7 yd

Have to take the value of π as 3.14

[tex] \: [/tex]

To Find,

The area and the circumference of a circle.

[tex] \: [/tex]

Solution :

As, the diameter is 7 yd, therefore the radius will be 3.5 yd

First of all, we'll find the circumference of the circle :

[tex]\\{ \longrightarrow \qquad{ \underline {\boxed{ \pmb{ \mathfrak{ \: \: Circumference_{(circle)} = 2 \pi r}}}}}} \: \: \bigstar \\ \\[/tex]

Now, we'll substitute the required values in the formula :

[tex]\\ { \longrightarrow \qquad{ \sf{ \: \: Circumference_{(circle)} = 2 \times 3.14 \times 3.5}}} \: \: \\ \\[/tex]

[tex] { \longrightarrow \qquad{ \sf{ \: \: Circumference_{(circle)} = 3.14 \times 7}}} \: \: \\ \\[/tex]

[tex] { \longrightarrow \qquad{ \sf{ \pmb{ \: Circumference_{(circle)} = 21.98}}}} \: \: \\ \\[/tex]

Therefore,

The circumference of the circle is 21.98 yd

[tex] \: [/tex]

Now, we'll find the area of the circle :

[tex]\\{ \longrightarrow \qquad{ \underline {\boxed{ \pmb{ \mathfrak{ \: \: Area_{(circle)} = \pi r^2}}}}}} \: \: \bigstar \\ \\[/tex]

[tex]{ \longrightarrow \qquad{ {{ { \sf{ \: \: Area_{(circle)} = 3.14 \times { \times (3.5)}^{2} }}}}}} \: \: \\ \\[/tex]

[tex]{ \longrightarrow \qquad{ {{ { \sf{ \: \: Area_{(circle)} = 3.14 \times { \times 3.5 \times 3.5 }}}}}}} \: \: \\ \\[/tex]

[tex]{ \longrightarrow \qquad{ {{ { \sf{ \: \: Area_{(circle)} = 3.14 \times 12 .25 }}}}}} \: \: \\ \\[/tex]

[tex]{ \longrightarrow \qquad{ {{\pmb { \sf{ \: \: Area_{(circle)} = 38.465 }}}}}} \: \: \\ \\[/tex]

Therefore,

The area of the circle is 38.46 yd² approximately

what geometric figure have 5-12 sides

Answers

A dodecagon is a twelve-sided polygon that's equally spaced around a circle and with all sides, the same length.

solve kx + 7 = 4 for x

Answers

Answer:

are we looking for x if we are its

Step-by-step explanation:

x= -3/k

Answer:

 x = -3/k

Step-by-step explanation:

Solve kx+7=4 for x

kx+7=4

kx =4 - 7

kx = -3

A rectangle that measures 1 foot by 5 feet.
What is the perimeter of the rectangle?

5 feet
6 feet
12 feet
36 feet

Answers

Answer:

C. 12 feet

Step-by-step explanation:

If a rectangle measures 1 foot by 5 feet, that means that one side is 1 foot and one side is 5 feet. Since a rectangle has two sets of parallel sides, the other sides of the rectangle will also measure 1 foot by 5 feet.

Adding all of the side lengths will give us the perimeter.

1 + 5 + 1 + 5 = 12

hope this helps :)

Prove the identity.
(1 - sin’x) cscx = cosx cotx
=
Note that each Statement must be based on
the right of the Rule.
rules:
algebra, reciprocal, quotient, pythagorean, odd/even

Answers

[tex]\textit{Pythagorean Identities} \\\\ sin^2(\theta)+cos^2(\theta)=1\implies cos^2(\theta)=1-sin^2(\theta) \\\\[-0.35em] \rule{34em}{0.25pt}\\\\\ [1-sin^2(x)]csc(x)~~ = ~~cos(x)cot(x) \\\\[-0.35em] ~\dotfill\\\\\ [1-sin^2(x)]csc(x)\implies cos^2(x)csc(x)\implies cos^2(x)\cdot \cfrac{1}{sin(x)} \\\\\\ cos(x)\cdot \cfrac{cos(x)}{sin(x)}\implies cos(x)cot(x)[/tex]

Find the solutions to the rational equation:
x+2 2x-4
3
2
(2 pts)
A
X = 2
B
x = 6
с
x = -2
D
x = 4

Answers

Answer:

D

Step-by-step explanation:

[tex]\frac{x+2}{3}[/tex] = [tex]\frac{2x-4}{2}[/tex] ( cross- multiply )

3(2x - 4) = 2(x + 2) ← distribute parenthesis on both sides

6x - 12 = 2x + 4 ( subtract 2x from both sides )

4x - 12 = 4 ( add 12 to both sides )

4x = 16 ( divide both sides by 4 )

x = 4

Question : -

[tex] \longrightarrow \frac{x + 2}{3} = \frac{2x - 4}{2} [/tex]

What to Find : -

In this question we have to find the value of x .

Let's Get start Solving : -

[tex]\longrightarrow \frac{x + 2}{3} = \frac{2x - 4}{2} [/tex]

So , by cross multiplying :

[tex] \longrightarrow \: 2(x + 2) = 3(2x - 4)[/tex]

Now , calculation left hand side as well as right hand side :

[tex]\longrightarrow \: 2x + 4 = 6x - 12[/tex]

Now , transposing 6x to left hand side and 4 to right hand side :

[tex]\longrightarrow \: 2x - 6x = - 12 - 4[/tex]

Now , solving left hand side and right hand side :

[tex]\longrightarrow \: - 4x = - 16[/tex]

As negative sign is present on both the side , so it will cancel out :

[tex]\longrightarrow \: \cancel - 4x = \cancel- 16[/tex]

Now we have :

[tex]\longrightarrow \: 4x = 16[/tex]

Now we are transposing 4 to right side and it will change into division from multiplication :

[tex]\longrightarrow \: x = \cancel \frac{16}{4} [/tex]

So we get :

[tex]\longrightarrow \: \green{ \boxed{ \bold x = 4}}[/tex]

Therefore value of x is 4 .

Verification : -

We are verifying our answer by putting value of x in given question :

[tex]\longrightarrow \frac{4 + 2}{3} = \frac{2(4) - 4}{2} \: [/tex]

Solving ,

[tex]\longrightarrow \: \frac{6}{3} = \frac{8 - 4}{2} [/tex]

Now subtracting 8 and 4 :

[tex]\longrightarrow \: \frac{6}{3} = \frac{4}{2} [/tex]

Now , dividing 6 by 3 and 4 by 2 :

[tex]\longrightarrow \cancel{\frac{6}{3} } = \cancel{\frac{4}{2} }[/tex]

We get :

[tex]\longrightarrow \: \bold{2 = 2}[/tex]

That means ,

[tex]\longrightarrow L.H.S = R.H.S[/tex]

Hence Verified .

Therefore our answer is correct .

#[tex] \sf{Keep \: Learning}[/tex]

Ver en español
What is the surface area of this cone?

Use ​ ≈ 3.14 and round your answer to the nearest hundredth.

15 mm
12 mm

square millimeters

Answers

[tex]\bold{ANSWER:}[/tex]
396 square millimeters

[tex]\bold{EXPLANATIONS:}[/tex]

Question 4 of 30
An IV piggyback (IVPB) of 10,000 units/100 mL is to be given over 45 minutes. The pump should
programmed to deliver _mL/hr.(round to the nearest whole number)
Continue

Answers

Ratios are written as fractions or in the form a:b.  The  pump should be programmed to deliver 133mL/hr

Ratios and proportion

Ratios are written as fractions or in the form a:b.

According to the question, An IV piggyback (IVPB) of 10,000 units/100 mL is to be given over 45 minutes.

We are to determine the number of mL to be given in 60 minutes (1 hr)

100mL = 45 minutes

x mL = 60 minutes

Take the ratio

100/x = 45/60

Cross multiply

45x = 6000

x = 6000/45
x = 133mL/hr

Hence the  pump should be programmed to deliver 133mL/hr

Learn more on ratio and proportion here: https://brainly.com/question/2914376

9. Determine if x + 1 is a factor of x ^ 4 - 4x ^ 2 - 4x - 1 Justify your answer.

Answers

Answer:

No

Step-by-step explanation:

x + 1 is not a factor of the polynomial because the remainder is 2 and not 0


Increase £139 by 28%
Give your answer rounded to 2 DP

Answers

Answer:

£177.92

Step-by-step explanation:

To increase something by 28% would be to multiply the original value by 1.28:

So to increase £139 by 28%, we do:

£139 × 1.28 = £177.92

So this is our final answer

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