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alexira [117]
3 years ago
13

Carlos drank 2740 mL of water after football practice. How many liters did he drink

Mathematics
2 answers:
natta225 [31]3 years ago
6 0

we know that

1\ L=1,000\ ml

so

by proportion

Find how many liters are 2,740\ ml

\frac{1}{1,000} \frac{L}{ml}=\frac{x}{2,740} \frac{L}{ml} \\\\1,000*x=2,740 \\\\ x= \frac{2,740}{1,000} \\\\ x=2.74 \ L

therefore

<u>the answer is</u>

2.74 \ liters

Bas_tet [7]3 years ago
4 0
2740/1000= 2.74

So the answer is 2.74 Liters
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Answer:

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(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

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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)

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3 years ago
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Gennadij [26K]
Let's go through this problem step by step while bearing in mind the concept of PEMDAS.

Step 1: (66.3-14.62)/0.6-0.2^{2}
Declaration of the expression. Nothing wrong here yet.

Step 2: (51.68)/0.6-0.2^{2}
Clarise evaluated what's inside the parenthesis first - which was the right thing to do! There are no mistakes in this step.

Step 3: (51.68)/0.4^{2}
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Step 4: (51.68)/0.16
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Step 5: 3.23 (Clarise's final answer)
In Clarise's final step, she manages to get the wrong answer! Dividing 51.68 by 0.16 would give us 323. This is another mistake of Clarise.

Looking at the choices, we can now identify what mistakes Clarise made:
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Robert is inspecting a shipment of 22 inch pipes. The length of the pipes may vary by 1%. What is the range of allowable lengths
Slav-nsk [51]

Answer:

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Step-by-step explanation:

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Now, 1% of 22 = \frac{1}{100}  \times 22 = 0.22

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⇒ 22 inch ± 1%  =  22.22 inch and 21.78 inch

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