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algol13
3 years ago
10

Find the equation of the line passing through (1,3) and perpendicular to y=-4/3-2​

Mathematics
1 answer:
Effectus [21]3 years ago
3 0

Answer:

x=1

Step-by-step explanation:

Find the negative reciprocal of the slope of the original line and use the point-slope formula.

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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

#SPJ4

3 0
1 year ago
Faucet A flows at a rate of 100 liters per 5 minutes and Faucet B flows at a rate of 100 liters per 4 minutes into an empty pool
Dmitriy789 [7]

Answer:

It will take both faucets 200 minutes to fill a pool with 9,000 liters of water

Step-by-step explanation:

Here, we want to know the time it will take for both faucets to fill a pool with 9,000 liters of water

What we need here is to have a joint rate for both faucets;

For the first faucet, we have a rate of 100 liters per 5 minutes so this means in a minute;

100/5 = 20 liters per minute

For the second faucet, the per minute rate will be 100/4 = 25 liters per minute

So therefore, the joint rate will be;

25 liters per minute + 20 liters per minute = 45 liters per minute

So the time needed to fill 9,000 liters of water in a pool will be ;

9000 liters/ 45 liters per minute = 200 minutes

8 0
3 years ago
It takes 99 apples to make 9 pies. How many apples would it take to 4 pies? (Hint simplify your ratio first)
kolbaska11 [484]

Answer:

it would take 36 apples to make 4 pies.

Step-by-step explanation:

9 x 4 = 36

4+4+4+4+4+4+4+4+4= 36


4 0
3 years ago
What is the smallest integer greater than the square root of 148?
grin007 [14]
A.) 13. all you have to do is plug it into google
8 0
3 years ago
Read 2 more answers
Complete this statement using &gt;, &lt;, or =<br><br> 0.248_____0.259
andreyandreev [35.5K]

Answer:

Here the most appropriate answer is '>'

Thus it will be 0.248<u> > </u>0.259

8 0
3 years ago
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