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3 years ago

Find the midpoint of (-3,7) and (-9,1).

Mathematics

2 answers:

STatiana [176]3 years ago

5 0

(-6,4) is your mid point

Temka [501]3 years ago

3 0

Answer:

(-6, 4)

Step-by-step explanation:

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in exercises 15-20 find the vector component of u along a and the vecomponent of u orthogonal to a u=(2,1,1,2) a=(4,-4,2,-2)

Nimfa-mama [501]

Answer:

The component of $\vec u$ orthogonal to $\vec a$ is $\vec u_{\perp\,\vec a} = \left(\frac{9}{5},\frac{6}{5},\frac{9}{10},\frac{21}{10}\right)$ .

Step-by-step explanation:

Let $\vec u$ and $\vec a$ , from Linear Algebra we get that component of $\vec u$ parallel to $\vec a$ by using this formula:

$\vec u_{\parallel \,\vec a} = \frac{\vec u \bullet\vec a}{\|\vec a\|^{2}} \cdot \vec a$ (Eq. 1)

Where $\|\vec a\|$ is the norm of $\vec a$ , which is equal to $\|\vec a\| = \sqrt{\vec a\bullet \vec a}$ . (Eq. 2)

If we know that $\vec u =(2,1,1,2)$ and $\vec a=(4,-4,2,-2)$ , then we get that vector component of $\vec u$ parallel to $\vec a$ is:

$\vec u_{\parallel\,\vec a} = \left[\frac{(2)\cdot (4)+(1)\cdot (-4)+(1)\cdot (2)+(2)\cdot (-2)}{4^{2}+(-4)^{2}+2^{2}+(-2)^{2}} \right]\cdot (4,-4,2,-2)$

$\vec u_{\parallel\,\vec a} =\frac{1}{20}\cdot (4,-4,2,-2)$

$\vec u_{\parallel\,\vec a} =\left(\frac{1}{5},-\frac{1}{5},\frac{1}{10},-\frac{1}{10} \right)$

Lastly, we find the vector component of $\vec u$ orthogonal to $\vec a$ by applying this vector sum identity:

$\vec u_{\perp\,\vec a} = \vec u - \vec u_{\parallel\,\vec a}$ (Eq. 3)

If we get that $\vec u =(2,1,1,2)$ and $\vec u_{\parallel\,\vec a} =\left(\frac{1}{5},-\frac{1}{5},\frac{1}{10},-\frac{1}{10} \right)$ , the vector component of $\vec u$ is:

$\vec u_{\perp\,\vec a} = (2,1,1,2)-\left(\frac{1}{5},-\frac{1}{5},\frac{1}{10},-\frac{1}{10} \right)$

$\vec u_{\perp\,\vec a} = \left(\frac{9}{5},\frac{6}{5},\frac{9}{10},\frac{21}{10}\right)$

The component of $\vec u$ orthogonal to $\vec a$ is $\vec u_{\perp\,\vec a} = \left(\frac{9}{5},\frac{6}{5},\frac{9}{10},\frac{21}{10}\right)$ .

4 0

3 years ago

Which would not be a step in finding the area of a circle by cutting it

Mkey [24]

Answer:

D. Continue cutting smaller and smaller slices.

Step-by-step explanation:

While, in theory, this could be a step, it would be a pointless one. You would have to eventually rearrange the pieces, but now there would be more of them.

Hope this helps!

4 0

3 years ago

Please help ASAP! This is due by 2:15!! A store sold a case of candles for $17.85 that had been marked up by 110%. What was the

VMariaS [17]

Answer:

the original price would be <u>16.605.</u>

Step-by-step explanation:

4 0

3 years ago

A bag contains red and blue marbles, such that the probability of drawing a blue marble is 3/8. An experiment consists of drawin

lys-0071 [83]

Answer:

The probability of drawing exactly one blue marble is 15 over 32

Step-by-step explanation:

did test

5 0

3 years ago

Which of the following expressions is equivalent to xy^3?<br> (options in the pic)

Alex

Answer:

Step-by-step explanation:

${xy}^{3}$

means that xy is being multiplied with itself thrice.

Hence,

$xy \times xy \times xy$

5 0

3 years ago

Find the midpoint of (-3,7) and (-9,1).​

Find the midpoint of (-3,7) and (-9,1).