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3 years ago

Evaluate (2/3) to the third power + 2 + 7/9

Mathematics

2 answers:

Gelneren [198K]3 years ago

8 0

(2/3) ^ 3 = (2*2*2) / (3*3*3) = 8 / 27
2 and 7/9 = (18 + 7)/9 = 25 /9

Add these two together
8/27 + 25/9 = 8/27 + 25*3/(9*3)
8/27 + 75/27 = 83/27 <<<< answer 1

The result
83 / 27 = 3 with a remainder of 2 = 3 2/27 <<<<< answer 2
83/ 27 = 3.074074 <<<<<<<< answer 3

Note
I don't know which answer to pick. I would suspect the first one, but it depends on what you have been told.

Jobisdone [24]3 years ago

5 0

We have 8/27 + 25/9 = 24/81 + 225/81 = 249/81 = 3.07;

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3 years ago

compute the projection of → a onto → b and the vector component of → a orthogonal to → b . give exact answers.

Nina [5.8K]

$\text { Saclar projection } \frac{1}{\sqrt{3}} \text { and Vector projection } \frac{1}{3}(\hat{i}+\hat{j}+\hat{k})$

We have been given two vectors $\vec{a}$ and $\vec{b}$ , we are to find out the scalar and vector projection of $\vec{b}$ onto $\vec{a}$

we have $\vec{a}=\hat{i}+\hat{j}+\hat{k}$ and $\vec{b}=\hat{i}-\hat{j}+\hat{k}$

The scalar projection of $\vec{b}$ onto $\vec{a}$ means the magnitude of the resolved component of $\vec{b}$ the direction of $\vec{a}$ and is given by

The scalar projection of $\vec{b}$ onto

$\vec{a}=\frac{\vec{b} \cdot \vec{a}}{|\vec{a}|}$

$\begin{aligned}&=\frac{(\hat{i}+\hat{j}+\hat{k}) \cdot(\hat{i}-\hat{j}+\hat{k})}{\sqrt{1^2+1^1+1^2}} \\&=\frac{1^2-1^2+1^2}{\sqrt{3}}=\frac{1}{\sqrt{3}}\end{aligned}$

The Vector projection of $\vec{b}$ onto $\vec{a}$ means the resolved component of $\vec{b}$ in the direction of $\vec{a}$ and is given by

The vector projection of $\vec{b}$ onto

$\vec{a}=\frac{\vec{b} \cdot \vec{a}}{|\vec{a}|^2} \cdot(\hat{i}+\hat{j}+\hat{k})$

$\begin{aligned}&=\frac{(\hat{i}+\hat{j}+\hat{k}) \cdot(\hat{i}-\hat{j}+\hat{k})}{\left(\sqrt{1^2+1^1+1^2}\right)^2} \cdot(\hat{i}+\hat{j}+\hat{k}) \\&=\frac{1^2-1^2+1^2}{3} \cdot(\hat{i}+\hat{j}+\hat{k})=\frac{1}{3}(\hat{i}+\hat{j}+\hat{k})\end{aligned}$

To learn more about scalar and vector projection visit:brainly.com/question/21925479

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1 year ago

A migrating bird flies 700 miles in 1414 hours. How many miles does it fly in 33 hours

Lisa [10]

In 1414 hours it covered 700 miles

In 1 hour it would have covered (700/1414) mile

In 33 hours it will then cover : 700/1414 * 33 = 16.34

So in 33 hours it will cover ≈ 16.34 miles.

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3 years ago

1. On Tuesday, Elena completed 20 items of her math homework in 36 minutes. At that same rate, how long will it take her to comp

zepelin [54]

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3 years ago

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Orlov [11]

I have no idea what this means im in 6th grade

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3 years ago