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tester [92]
3 years ago
15

Fitness Classes cost £6 per person. The table shows the number of people who go to the classes on Thursday, Friday and Saturday.

Mathematics
1 answer:
Pachacha [2.7K]3 years ago
7 0

Answer:

£216

Step-by-step explanation:

  • Cost = £6 per person
  • Teacher earns = 90% of total

<u>Total number of people:</u>

  • 13 + 11 + 16 = £40

<u>Total paymen</u>t:

  • 40*6= £240

<u>Teacher earns in total per given week:</u>

  • 240*90/100 = £216

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Answer:

d = 15.8 m

Step-by-step explanation:

Apply the Pythagorean Theorem to find the length of the diagonal.  The correct equation for this particular rectangle is

d = √(9² + 13²) = √250 = √25·√10 = 5√10

To the nearest tenth, this comes to d = 15.8 m

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In this survey, 77 people prefer basketball. In a survey done a couple months later, only 70
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Suppose that v is an eigenvector of matrix A with eigenvalue λA, and it is also an eigenvector of matrix B with eigenvalue λB. (
galben [10]

Answer:

(a) Yes, λ_{A}+λ_{B}

(b) Yes, λ_{A}λ_{B}

Step-by-step explanation:

First, lets understand what are eigenvectors and eigenvalues?

Note: I am using the notation λ_{A} to denote Lambda(A) sign.

v is an eigenvector of matrix A with eigenvalue λ_{A}

v is also eigenvector of matrix B with eigenvalue λ_{B}

So we can write this in equation form as

Av=λ_{A}v

So what does this equation say?

When you multiply any vector by A they do change their direction. any vector  that is in the same direction as of Av, then this v  is called the eigenvector of A. Av is λ_{A} times the original v. The number λ_{A} is the eigenvalue of A.

λ_{A} this number is very important and tells us what is happening when we multiply Av. Is it shrinking or expanding or reversed or something else?

It tells us everything we need to know!

Bonus:

By the way you can find out the eigenvalue of Av by using the following equation:

det(A-λI)=0

where I is identity matrix of the size of same as A.

Now lets come to the solution!

(a) Show that v is an eigenvector of A + B and find its associated eigenvalue.

The eigenvalues of A and B are λ_{A} and λ_{B}, then

(A+B)(v)=Av+Bv=(λ_{A})v + (λ_{B})v=(λ_{A}+λ_{B})(v)

so,  (A+B)(v)=(λ_{A}+λ_{B})(v)

which means that v is also an eigenvector of A+B and the associated eigenvalues are λ_{A}+λ_{B}

(b) Show that v is an eigenvector of AB and find its associated eigenvalue.

The eigenvalues of A and B are λ_{A} and λ_{B}, then

(AB)(v)=A(Bv)=A(λ_{B})=λ_{B}(Av)=λ_{B}λ_{A}(v)=λ_{A}λ_{B}(v)

so,  

(AB)(v)=λ_{A}λ_{B}(v)

which means that v is also an eigenvector of AB and the associated eigenvalues are λ_{A}λ_{B}

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2 years ago
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2 years ago
Find the critical numbers of the function. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE
Furkat [3]

Answer:

x = -6 and x = 4

Step-by-step explanation:

In math, the critical points of a function are the points where the derivative equals zero.

So, first we will find the derivative of the function. The derivative is:

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Now, we are going to make the derivative equal zero and find the answers of the equation.

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So we have that the critical points are the answers to this equation:

x+6= 0 \\x= - 6

and

x-4=0\\x=4

Thus, the critical points are x=-6 and x=4

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3 years ago
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