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3 years ago

What is the solution to this system of linear equations? x + y = 4 x − y = 6 A: (4, 6) B: (6, 4) C: (5, −1) D: (−1, 5)

Mathematics

1 answer:

zhuklara [117]3 years ago

4 0

Answer:

Step-by-step explanation:

Given the 2 equations

x + y = 4 → (1)

x - y = 6 → (2)

Add the 2 equations term by term to eliminate y, that is

2x = 10 ( divide both sides by 2 )

x = 5

Substitute x = 5 into either of the 2 equations and evaluate for y

Substituting into (1)

5 + y = 4 ( subtract 5 from both sides )

y = - 1

solution is (5, - 1 ) → C

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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

I need all help possible.

Leviafan [203]

So there are 52 horses
12 of them are white
how many are black?
52 - 12 = 40
there are 40 black horses
12 white horses to 40 black horses
12:40
12/40

Hope this helps :)

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3 years ago

Find a number that is 5 times as much as 4 divided by 2

barxatty [35]

10....

4 x 5 ÷ 2 is 10

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Blizzard [7]

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