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3 years ago

Which is the graph of the linear inequality y < 3x + 1?

1 answer:

5 0

Start at +1 on the x axis and then use 3/1 for rise over run. So you will start at +1 and then from that point rise 3 run 1

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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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3 0

1 year ago

tammy is 14 years old. she has a younger sister and an older brother. her sister is 12. the mean of all their ages is 14. how ol

mafiozo [28]

Answer:

Step-by-step explanation:

To solve, we can use an equation finding the average of the siblings'ages.

$\frac{14 + 12 + x}{3} = 14 \\ \ 14 + 12 + x = 42 \\ x = 42 - 14 - 12 \\ x = 16$

7 0

3 years ago

Mr Todd buys 7 drinks at 48p each and 8 drinks at 52p each. What is the total cost of the 15 drinks?

Lesechka [4]

Answer:

80p

if you are adding 4p every time you add a drink you will be adding 7 drinks therefore you have to do (7x4p) this will equal 28p then you have to add 28p to 52p

Hope this helps

6 0

2 years ago

Barnard’s Star is approximately 35,133 billion miles from Earth. What is 35,133 billion in scientific notation?

julsineya [31]

C

Mark brainliest please

Hope this helps you

4 0

2 years ago

Year Cash Flow (A) Cash Flow (B)

jeka57 [31]

Answer:

2.46

3.63

195,929.85

236,551.79

35.39

34.31

Step-by-step explanation:

Explaining it is kind of akward, but I can explain if you want.

Not too sure about the last one, but the rest I feel good about

4 0

3 years ago