Solve the following step by step

Answer:

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

Step-by-step explanation:

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

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

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

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

[tex]\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)[/tex]

[tex]\vec u_{\parallel\,\vec a} =\frac{1}{20}\cdot (4,-4,2,-2)[/tex]

[tex]\vec u_{\parallel\,\vec a} =\left(\frac{1}{5},-\frac{1}{5},\frac{1}{10},-\frac{1}{10} \right)[/tex]

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

[tex]\vec u_{\perp\,\vec a} = \vec u - \vec u_{\parallel\,\vec a}[/tex] (Eq. 3)

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

[tex]\vec u_{\perp\,\vec a} = (2,1,1,2)-\left(\frac{1}{5},-\frac{1}{5},\frac{1}{10},-\frac{1}{10} \right)[/tex]

[tex]\vec u_{\perp\,\vec a} = \left(\frac{9}{5},\frac{6}{5},\frac{9}{10},\frac{21}{10}\right)[/tex]

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

Answer:

I'm pretty sure it's 10/4 but I'm not totally sure

Answer:

on Khan the answer is B,C,E

Step-by-step explanation:

mark above answer BRILLIANT

Answer:

18 = 3 × 6

Step-by-step explanation:

Answer:3rd one

Step-by-step explanation:

Answer:6 apples cost exactly the same as 9 oranges. 10 apples and 10 oranges cost $7.50. Find the cost of 1 apple and the cost of 1 orange.

Step-by-step explanation:

Answer: 754

Step 1: Multiply 82 x 3.

82 x 3 = 246.

Step 2: Subtract 246, because he sold this much cookies.

1,000 - 246 = 754

Answer = 754.

Hope this helps you!

Answer:

First we need to multiply 3x82. 3x82=246  now we need to subtract 246 from 1,000. 1,000-246=754

Step-by-step explanation:

Answer:

the dollar for 9 interstate is 16 rupees is and interest rate for 88 percentage is is 14 rupees

Answer:

17:420

Step-by-step explanation:

17 seconds : 7 minutes

7 minutes = 420 seconds

17:420

The ratio of time measurements in two different units is 1/30.

Ratio is the quantitative relation between two amounts showing the number of times one value contains or is contained within the other.

Given are the time measurements in two different units.

Converting 2 minutes into seconds -

2 min = 2 x 60 = 120 seconds

Now, 4 seconds to 120 seconds can be written as fraction below -

x/y = 4/120 = 1/30

Then, the ratio will be -

x : y = 1 : 30

Therefore, the ratio of time measurements in two different units is 1:30

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#SPJ2

Answer:

y = 2

Step-by-step explanation:

....................

Answer:

1.9

Step-by-step explanation:

1.9 is the answer because if you add 1.2+0.7=1.9

Answer:

$609.50

Step-by-step explanation:

A = P(1 + r/n)^nt

   = 500(1 + [tex]\frac{.04}{2}[/tex])^2(5)

   = 500(1.02)¹⁰

    = 500(1.218994)

    = 609.497

Round answer up to $609.50

Answer:

b

Step-by-step explanation:

divide both sides by 2pi

Answer:

A/4r²=π

Step-by-step explanation:

A=4πr²

Divide each side by 4r²

A/4r²=4πr² /4r²

A/4r²=π

Answer: The slope is 500 and the y intercept is 0.

Step-by-step explanation:

To find the slope we need to find the rise and divide it by the run. The y intercept will be when x is equal to 0. And when x is 0 y is also zero because it cuts through the origin meaning that the y-intercept is  0.

The line rises up by 1000 and run by 2 to the right.

Slope :  1000/2 = 500

The slope is 500.

Answer:

C. Angle I and Angle H

Step-by-step explanation:

The congruncy lines on either side of the triangle show that.

An isosceles triangle has two congruent angles.

The two angles that must be congruent are: [tex]\mathbf{\angle I \cong \angle H}[/tex]

From the figure, we observe that side lengths HJ and HI are congruent.

The above highlight means that: the angles at the other points of HJ and HI.

The common point of HJ and HI is H, while the other points are J and I

So, the angles at J and I are congruent.

Hence, the correct option is (c)

Read more about isosceles angles at:

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Answer:

the answer is 48/100 im pretty sure .

Step-by-step explanation:

Answer:

12/25

Step-by-step explanation:

first you take your decimal and because it is a decmial the decimal is in a fraction, 48/100 don't pay attention to any 0's behind any other number.

once you have 48/100 divide the numerator(the top of the fraction) and the denominator(the bottom of the fraction) and divide it by 4

Answer:

1 hope this helps

Step-by-step explanation:

Answer:

19

Step-by-step explanation:

ANSWER:

1.3/2

2.4/27

3.2/25

4.3/25

5.4

Answer:

1.3/2

2.4/27

3.2/25

4.3/25

Step-by-step explanation:

Answer:

A.) bus only = 23

B.) LRT only = 34

C.) Jeep only = 9

D.) 5

Step-by-step explanation:

Let :

B = bus ; J = Jeep ; L = LRT

KINDLY CHECK ATTACHED PICTURE FOR DETAILED EXPLANATION

A set is a group of related item.

Let:

[tex]Total =120[/tex]

[tex]B = 68 \to Bus[/tex]

[tex]L = 78 \to LRT[/tex]

[tex]J =33 \to Jeep[/tex]

[tex]n(B\ n\ L) = 40[/tex]

[tex]n(B\ n\ J) = 20[/tex]

[tex]n(L\ n\ J) = 19[/tex]

[tex]All = 15[/tex]

(a) Bus only

This is calculated using:

[tex]B\ only = B - n(B\ n\ L) - n(B\ n\ J) + All[/tex]

So, we have:

[tex]B\ only = 68 - 40 - 20 + 15[/tex]

[tex]B\ only = 23[/tex]

(b) LRT only

This is calculated using:

[tex]L\ only = L - n(B\ n\ L) - n(L\ n\ J) + All[/tex]

So,

[tex]L\ only = 78 - 40 - 19 + 15[/tex]

[tex]L\ only = 34[/tex]

(c) Jeep only

This is calculated using:

[tex]J\ only = J - n(B\ n\ J) - n(L\ n\ J) + All[/tex]

So, we have:

[tex]J\ only = 33 - 20 - 19 + 15[/tex]

[tex]J\ only = 9[/tex]

(d) None

Let x represents those that took none of the means of transport.

So, we have:

[tex]Total = B\ only + J\ only + L\ only + [n(B\ n\ L) -All] +[n(B\ n\ J) -All] +[n(L\ n\ J) -All] + All + x[/tex]

This gives

[tex]120= 34 + 23 + 9 + [40 -15] +[20 -15] +[19 -15] + 15 + x[/tex]

[tex]120= 115 + x[/tex]

Collect like terms

[tex]x = 120 - 115[/tex]

[tex]x = 5[/tex]

See attachment for the Venn diagram of the set.

Read more about sets at:

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Answer:

c

Step-by-step explanation:

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Answer:

Step-by-step explanation:

ok so lets assume that line PQ and RS and QR and PS are parallel lines cut by a transeversal. To prove this you can do it in a couple of different ways the one way i know is that if you assume these are parralel then you can uses the alternate interior anges to prove that measure of QSP and SQR then by logic you know that PQS + SQR = RSQ+QSP which symplifies to PQR = RSQ

Answer:

There are a variety of possible answers, including the following:

4 and 4     (4 + 4 = 8........4 - 4 = 0.......... 6 > 0)

6 and 2     (6 + 2 = 8........6 - 2 = 4.......... 6 > 4)

5 and 3     (5 + 3 = 8.........5 - 3 = 2.......... 6 > 2)

And for the subtraction, each can be reversed (2 - 6 ...... 3 -5 ...... etc.)

Answer:

2 and 3 is the answer we know it right

Answer:

A. 217

Step-by-step explanation:

3,472/16 = 217

Answer:

idk

Step-by-step explanation:

Answer:

If you talking about iready. It's the first pink one.

Step-by-step explanation: