MATHEMATICS COLLEGE

How do you solve the equation 2cos^2 - cosx = 0 for all solutions?

Answers

Answer 1

Answer:

Answer:

π/2 and π/3

Step-by-step explanation:

Given the equation 2cos²x - cosx = 0, to find the solution to the equation, we will follow the following step.

let P = cosx

The equation becomes 2P²-P = 0

P(2P-1) = 0

P = 0 and 2P-1 = 0

P= 0 and P = 1/2

Since P = cosx

cosx = 0 and cos(x) = 1/2

If cos(x) = 0

x = cos⁻¹0

x = 90⁰

x = π/2

If cos(x) = 1/2

x = cos⁻¹1/2

x = 60⁰

x = π/3

Hence the solutions to the equation are π/2 and π/3.

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The residents of a certain dormitory have collected the following data: People who live in the dorm can be classified as either involved in a relationship or uninvolved. Among involved people, 10 percent experience a breakup of their relationship every month. Among uninvolved people, 15 percent will enter into a relationship every month. What is the steady-state fraction of residents who are uninvolved

Answers

Answer:

The steady state proportion for the U (uninvolved) fraction is 0.4.

Step-by-step explanation:

This can be modeled as a Markov chain, with two states:

U: uninvolved

M: matched

The transitions probability matrix is:

$\begin{pmatrix} &U&M\nU&0.85&0.15\nM&0.10&0.90\end{pmatrix}$

The steady state is that satisfies this product of matrixs:

$[\pi] \cdot [P]=[\pi]$

being π the matrix of steady-state proportions and P the transition matrix.

If we multiply, we have:

$(\pi_U,\pi_M)*\begin{pmatrix}0.85&0.15\n0.10&0.90\end{pmatrix}=(\pi_U,\pi_M)$

Now we have to solve this equations

$0.85\pi_U+0.10\pi_M=\pi_U\n\n0.15\pi_U+0.90\pi_M=\pi_M$

We choose one of the equations and solve:

$0.85\pi_U+0.10\pi_M=\pi_U\n\n\pi_M=((1-0.85)/0.10)\pi_U=1.5\pi_U\n\n\n\pi_M+\pi_U=1\n\n1.5\pi_U+\pi_U=1\n\n\pi_U=1/2.5=0.4 \n\n \pi_M=1.5\pi_U=1.5*0.4=0.6$

Then, the steady state proportion for the U (uninvolved) fraction is 0.4.

Camden is making accessories for the soccer team. He uses 513.72 inches of fabric on headbands for 34 players and 2 coaches. He also uses 299.54 inches of fabric on wristbands for just the players. How much fabric was used on a headband and wristband for each player?

Answers

23.91941176470588 inches not including the coaches and 22.59055555555556 including the coaches

Hope this helps!

What is 0945987123987634678 divided by 67899876543444445678

Answers

Answer:35652846437467

Step-by-step explanation:simple math

Step-by-step explanation:

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Consider the following 8 numbers, where one labelled x is unknown. 26, 33, 46, x , 9, 7, 10, 11 Given that the range of the numbers is 60, work out 2 values of x .

Answers

Answer: Then the two possible values of x are 53 and -14

Step-by-step explanation:

When we have a set of numbers

{a, b, c, d, e}

The range will be equal to the difference between the larger number and the smaller number.

In our case, the set is:

{26, 33, 46, x, 9, 7, 10, 11}

First, we need to see than largest and smallest numbers in the set (ignoring x)

The largest is 46

the smallest is 7.

Now, if we considerate that x is the smallest number in the set, we will have that:

46 - x = 60

x = 46 - 60 = -14

If x is the largest number on the set, we have that:

x - 7 = 60

x = 60 - 7 = 53

Then the two possible values of x are 53 and -14

A survey of 800 students yielded the following information: 519 were seniors, 430 were commuters, and 300 of the seniors were commuters. How many of the 800 surveyed students were seniors or were commuters?

Answers

Answer:

The number is $(S \ u \ C ) = 649$

Step-by-step explanation:

From the question we are told that

The sample size is n = 800

The number of seniors is S = 519

The number of commuters is C = 430

The number of of seniors that are commuters is $(S\ n \ C )= 300$

Generally the number of 800 surveyed students who were seniors or were commuters is mathematically evaluated as

$(S \ u \ C ) = S + C - ( S \ n \ C )$

=> $(S \ u \ C ) = 519 + 430 - 300$

=> $(S \ u \ C ) = 649$

An angelfish was 1 1/2 inches long when it was bought. Now it is 2 1/3 inches long.a. How much has the angelfish grown?

b. An inch is 1/12 of a foot. How much has the angelfish grown in feet?

40 points!