Linearise cos^5(x). Help asap please
detailed answer (so much details are needed)
the answer should be:
\(\frac{1}{16} *(cos5x +5cos3x+10cosx)\)

The values of a, b, and n are: a = (3/4)^(1/7),  b = (3/4)^(1/7) and n = 8/3.

We know that the general formula for the binomial expansion of (a + b)ⁿ is:

(a + b)ⁿ = nC₀aⁿb⁰ + nC₁aⁿ⁻¹b¹ + nC₂aⁿ⁻²b² + ... + nCₖaⁿ⁻ᵏbᵏ + ... + nCₙa⁰bⁿ

where;

nCk = n! / (k!(n-k)!)

where;

We are given that the second, third, and fourth terms in the expansion are 12, 60, and 160 respectively. Therefore, we have:

nC₁aⁿ⁻¹b¹ = 12

nC₂aⁿ⁻²b² = 60

nC₃aⁿ⁻³b³ = 160

We can solve for a and b by dividing the second equation by the first and the third equation by the second. This gives:

nC₂/nC₁ = (n-1)a/b = 5 ...(1)

nC₃/nC₂ = (n-2)a/b = 8/3 ...(2)

Now, we can solve for a and b by solving the system of equations (1) and (2) simultaneously.

We can start by multiplying equation (1) by b and equation (2) by 3b, which gives:

(n-1)a = 5b ...(3)

(n-2)a = 8b ...(4)

Subtracting equation (4) from equation (3), we get:

a = 13b

Substituting this into equation (4), we get:

11b = 8b/n

Solving for n, we get:

n = 8/3

Substituting this value of n into equation (1), we get:

5 = (8/3 - 1)a/b = 5a/b

Therefore, a = b.

Substituting a = b into any of the equations for the terms in the expansion, we get:

nC₁aⁿ⁻¹b¹ = n(a + b)ⁿ⁻¹ = 12

Substituting n = 8/3, a = b, and simplifying, we get:

2a⁷ = 12/8

Solving for a, we get:

a = (3/4)^(1/7)

Therefore, the values of a, b, and n are:

a = (3/4)^(1/7)

b = (3/4)^(1/7)

n = 8/3

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Answer:

3 feet

Step-by-step explanation:

To solve this problem, we can use the Pythagorean theorem. Let's call the distance from the tent pole to the rope x. We can set up the following equation:

x^2 + 12^2 = 15^2

Solving for x, we get:

x = sqrt(15^2 - 12^2)

x = sqrt(9)

x = 3

Therefore, the distance from the tent pole to the rope is 3 feet.

Answer:

If I'm correct the answer is 4

Step-by-step explanation:

Not 100% sure if I'm correct but if Debra's garden is 12 feet in length and 10 feet in width then you would multiply 10 × 12 that would be 120. Then divide 120 to 30 and you get your answer, 4. ( not 100% sure )

Store revenue will be maximised, if they charge 7 dollars for each movie rental.

The entire amount of money received by an organisation's operations over a predetermined period of time is the basic definition of revenue.

A company's revenue is its total revenue before any expenses are subtracted. According to the definition, revenue is the total sum of money obtained through conducting commercial activities like sales.

Let store charge x $ for each movie.

No.of rented movies per weak = 108-9x(x-z)

Total revenue = x*[108-9(x-2)]

= x*[108-9x+18]

= x*[126-9x]

= 126x-9x^2

Total revenue will be maximised when dT/dx = 0

dT/dx = 126-9*2x

= 126-18x = 0

18x = 126

x = 7$

Store revenue will be maximised, if they charge 7 dollars for each movie rental.

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Answer: the Second one

Step-by-step explanation:

Hope this helps you

The domain and the range of the function f(x) = 1/4x - 2 is the all set of real values

The domain of the function is the set of input values of the graph

The range of a function is the set of output values of the graph.

This in other words mean the range of a function is the set of y values of the graph.

The function is given as

f(x) = 1/4x - 2

Next, we plot the graph of the function (see attachment)

From the graph, we can see that the graph is a linear graph

This means that the function has a domain and a range of all set of real values

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Answer:

A

Step-by-step explanation: 20 x 3.28 is 65.6 round it up its 66

An equation for the total cars and trucks for dealership A is: x + y = 164.

An equation for the total cars and trucks for dealership B is: 2x + 0.5y = 229.

The number of cars that dealership A sold is: 98 cars.

The number of trucks that dealership B sold is: 66 trucks.

In order to write a system of linear equations to describe this situation, we would assign variables to the number of cars sold and number of trucks sold, and then translate the word problem into an algebraic equation as follows:

Since the first dealership sold a total of 164 cars and trucks, a linear equation to model this situation is given by;

x + y = 164.

Additionally, the second dealership sold twice as many cars and half as many trucks as the first dealership, with a total of 229 cars and trucks;

2x + 0.5y = 229.

By solving the systems of linear equations simultaneously, we have:

2x + 0.5(164 - x) = 229

1.5x + 82 = 229

x = 98 cars.

For the y-value, we have;

2(98) + 0.5y = 229

0.5y = 229 - 196

y = 33/0.5

y = 66 trucks.

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Answer:

Step-by-step explanation:

Let's solve your inequality step-by-step.

y - 6 > 2y - 4

y - 2y > -4 + 6

-y > 2

now divide by -1 and inequality sign changes

-y/-1 < 2/-1

y < -2

Answer:It would be 40•.25=10

Step-by-step explanation: which means 40-10=30 so it’d be .25 and you’d move the decimal over 2 spots so it’d be 25% off

The equivalent expression of 6⁵ is 6² × 6³.

The equivalent expression of 5⁻² × 5⁵ × 5  is 5⁴.

Two algebraic expressions are said to be equivalent if their values obtained by substituting the values of the variables are same.

Equivalent expressions are expressions that work the same even though they look different.

Therefore, let's find the expression, equivalent to 6⁵,

Using law of indices,

\(A^{x} X A^{y} = A^{x +y }\)

Hence,

6² × 6³ = 6²⁺³ = 6⁵

5⁻² × 5⁵ × 5 = 5⁻²⁺⁵⁺¹ = 5⁴

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Answer:

Step-by-step explanation:

Each mechanic worked a total of 12.5 hours each.

Step-by-step explanation:

The amplitude is 2. Amplitude means height from the x-axis to the crest/trough.

The period is 2pi. It is from crest to crest (next crest) or trough to trough (next trough).

Note that crest are the highest points of a wave, and that troughs are the lowest points of a wave. (we are talking about transverse waves, but this is more of a physics thing).

Function of graph:
By playing around in a graphing calculator, I got the equation to be

2 (cos (x + pi/2)).

the 2 changes the amplitude, and the + pi/2 shifts the graph by pi/2 to the left.

Answer:

\(y = - 9x \\ theny = 2x + 33 \\ - 9x = 2x + 33 \\ - 9x - 2x = 33 \\ - 11x = 33 \\ x = \frac{ - 33}{11} = - 3 \\ x = - 3 \\

then\\ y=-9×-3=21\\ thank \: you\)

Answer:

Step-by-step explanation:

4.

Given:

10:s

6:y

8:13

Solve:

8/13 = 10/s

s = 65/4 or 16.25 cm

8/13 = 6/y

y = 39/4 or 9.75 cm

5.

Given:

70ft:88ft

o/90ft

n/53ft

Solve:

70/88 = o/90

o = 1575/22 or 71.59 ft

70/88 = n/53

n = 1855/44 or 42.16 ft

6.

Given:

5.7in:9.1in

9.6in:e

11.2in:t

Solve:

5.7/9.1 = 9.6/e

e = 15.33 in

5.7/9.1 = 11.2/t

t = 17.88 in

7.

Given:

74m:48m

43m:u

64m:y

Solve:

74/48 = 43/u

u = 1032/37 or 27.89 m

74/48 = 64/y

y = 1536/37 or 41.51 m

8.

Given:

16cm:o

11.8cm:101 (I can't see if that is a 101 or 10.1 but I can do it both ways)

6.2cm:t

Solve:

11.8cm/101 = 16cm/o

o = 136.95

or

11.8cm/10.1 = 16cm/o

o = 13.69

11.8cm/101 = 6.2cm/t

t = 53.07

or

11.8cm/10.1 = 6.2cm/t

t = 5.3

9.

Given:

AB:AC

AE:AD

EB:DC

ABE:ACD are right angles

DC = P

We know that:

13ft:30ft

AE:AD are unknown

8ft:DC

We are looking for P?

Solve:

13ft/30ft = 8ft/P

P = 240/13 or 18.46

Answer:

\(0, \dfrac{\pi}{6}, \dfrac{5\pi}{6}, \pi\)

Step-by-step explanation:

Given the equation:

\(sin(x)-2sin(x) tan(x)=0\)

To find:

The solutions of given equation in the range [0, 2\(\pi\)) i.e. 0 can be in the answer but \(2\pi\) can not be there in the answer.

Solution:

Taking \(tan(x)\) common, we get:

\(tan(x) (1-2sin(x))=0\)

The solutions can be given as:

\(tan(x) = 0\) OR \(1-2sin(x) = 0\)

Let us solve both the equations one by one:

First equation:

\(tan(x) = 0\\ \Rightarrow x=0, \pi\)

Second equation:

\(1-2sin(x) = 0\\\Rightarrow 2sinx=1\\\Rightarrow sinx=\dfrac{1}{2}\\\Rightarrow x = \dfrac{\pi}{6}, \dfrac{5\pi}{6}\)

Therefore, the answers as a comma separated list are:

\(0, \dfrac{\pi}{6}, \dfrac{5\pi}{6}, \pi\)

Answer:

thats right

Step-by-step explanation:

Answer:

rhombus

Step-by-step explanation:

Answer:

rhombus

Step-by-step explanation:

A rhombus has four congruent sides, and does not necessarily have to have right angles. (A square is considered a rhombus and has four right angles, so that is the only exception). So, your answer would be rhombus!

Hope this helped! ;)

Answer:

y = 2x+4

Step-by-step explanation:

When we substitute the value of x in y =2x+4. The output of function is exactly like in the table shown.

x = 1 —> y = 2(1)+4 = 6

x = 3 —> y = 2(3)+4 = 10

x = 5 —> y = 2(5)+4 = 14

x = 7 —> y = 2(7)+4 = 18

x = 9 —> y = 2(9)+4 = 22

Since the output is exactly like in the table. Therefore, y = 2x+4 represents the following table.

The value of f(5) is positive

At f(x) = 0, the value of x is 1

For the interval f(x) ≤ 0, the values of x are [-2, 1]

From the question, we have the following parameters that can be used in our computation:

The graph

On the graph, we have

f(5) = 1

This means that f(5) is positive

Also, we have

When f(x) = 0, the value of x is 1

For the interval f(x) ≤ 0, we have the values of x to be

-2 ≤ x ≤ 1

When represented as an interval, we have

[-2, 1]

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Answer:

18 ft

Step-by-step explanation:

G = 21

E = g - 3

E = 21 - 3

E = 18

Answer:

Ella threw the ball 18 feet

Answer:

Step-by-step explanation:

a. Variables:

D0 = Demand for nurses in 2000 = 2,000,000

S0 = Supply of nurses in 2000 = 1,890,000

D2020 = Projected demand for nurses in 2020 = 2,810,414

S2020 = Projected supply of nurses in 2020 = 2,001,998

Equations:

For 2000: D0 = S0

For 2020: D2020 = S2020

b. Using substitution, we can set the two equations equal to each other:

D0 = S0

2,000,000 = 1,890,000 + m(S0 - 1,890,000) (where m is the rate of increase in supply)

m = 0.063

Now we can use this value of m to find out during which year the supply of nurses was equal to the demand:

2,000,000 = 1,890,000 + 0.063(S - 1,890,000)

S = 2,013,008

Therefore, the supply of nurses was equal to the demand in the year 2013.

Answer:

\(\sqrt{384}\)

Step-by-step explanation:

\(\sqrt{384}\) is equivalent  to \(\sqrt[8]{6}\)

An equivalent expression to the given expression \(8\sqrt{6}\) is  \(\sqrt{384}\)

"It is a mathematical statement which consists of numbers, variables and some mathematical operations."

"The expressions that work the same even though they look different."

For given question,

We have been given an expression \(8\sqrt{6}\)

We know, for a positive real number a, \(\sqrt{a^2}=a\)

So, we can write 8 as \(8=\sqrt{8^2}\)

So, given expression becomes \(\sqrt{8^2}\sqrt{6}\)

We know, for any positive real numbers m, n, \(\sqrt{m} \sqrt{n}=\sqrt{mn}\)

\(\sqrt{8^2}\sqrt{6}\)

= \(\sqrt{8^2\times 6}\)

= \(\sqrt{64\times 6}\)

= \(\sqrt{384}\)

So, an expression \(8\sqrt{6}\) is equivalent to expression \(\sqrt{384}\)

Therefore, an equivalent expression to the given expression \(8\sqrt{6}\) is  \(\sqrt{384}\)

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Take into account that the median of a data set is given by the element of the set that is at the center of the ordered list of elements. If there is no possible to determine a central element in the list, then, you take two elements of the center and calculate the average value in between such elements.

Then, first order the elements, as follow:

1 , 2 , 3 , 4 , 4 , 5 , 7 , 8 , 9 , 12​

THe number of elements is 10, then, you conisder the two elements at the center of the list, that is, the 5th and 6th elements:

1 , 2 , 3 , 4 , 4 , 5 , 7 , 8 , 9 , 12​

and calculate the average in between these numbers:

median = (4 + 5)2 = 9/2 = 4.5

Hence, the median of the given data set id 4.5

Answer:

He bought 14 pens

Step-by-step explanation:

1.50 x 14 = 21 + 29.75= 50.75

Answer:

723 -> 01011010011

Step-by-step explanation:

Answer:

11,15,19,23,27,31,35,39,43,47,51,55,59,63,67,71,75,79,83,87,91,95,99,103,107,111,115

Step-by-step explanation:

I think this is what you wanted