Help me three questions please really easy I promise answer

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: 8x + 5= 61

Step-by-step explanation: x represents the cost of one ticket for the show, 8 is the amount of tickets, 5 is the extra fee, 61 is the total.

Answer:

729 is a perfect square

Step-by-step explanation:

because 27 * 27 = 729

Answer:

3x²-1

Step-by-step explanation:

f(x) = x²

g(x) = 3x-1

[g·f](x)

g(f(x))

3(x²)-1

Answer:

sure

Step-by-step explanation:

Answer:

hello

Step-by-step explanation:

Answer:

11/200

Step-by-step explanation:

This is the correct answer boo

Answer: x=4

Step-by-step explanation:

Answer:

-15/16

Step-by-step explanation:

-5/8 ÷ 2/3

Copy dot flip

-5/8 * 3/2

Multiply the numerators

-5*3 = -15

Multiply the denominators

8*2 =16

Put the numerator over the denominator

-15/16

This is the step-by-step explanation

Answer:

The equation that models the relationship between Z and N is N = 56 Z

Step-by-step explanation:

The form of the linear equation is y = m x + b, where

∵ Mark reads 42 pages of a book every [tex]\frac{3}{4}[/tex] of an hour

→ Find his rate per hour by dividing the number of pages by its time

∴ His rate of reading = 42 ÷  [tex]\frac{3}{4}[/tex] = 42 ×  [tex]\frac{4}{3}[/tex] = 56 pages per hour

∵ His rate = 56 pages/hour

∴ m = 56

∵ Z represents the number of hours Mark reads

→ That means replace x in the form of the equation above with Z

∵ N represents the number of pages of the book he reads

→ That means replace y in the form of the equation above with N

∴ N = 56 Z + b

∵ There is no initial amount of reading

∴ b = 0

∴ N = 56 Z

The equation that models the relationship between Z and N is N = 56 Z

Answer:

1/15 kg

Step-by-step explanation:

Divide by 5 can be written as multiply by 1/5

1/3 * 1/5 = 1/15

Answer:

21

Step-by-step explanation:

Answer:

The width is 4 cm

The length is 12 cm.

Step-by-step explanation:

Area of a rectangle

Given a rectangle of width W and length L, its area is calculated as follows:

[tex]A=W\cdot L[/tex]

The area of the given rectangle is 48 cm^2, and the length is three times the width, thus:

L = 3W

Substituting into the formula of the area:

[tex]W\cdot L=48[/tex]

[tex]W\cdot 3W=48[/tex]

Simplifying:

[tex]3W^2=48[/tex]

Solving:

[tex]W^2=48/3=16[/tex]

[tex]W=\sqrt{16}=4[/tex]

The width is 4 cm. Find the length:

L=3W=3*4= 12

The length is 12 cm.

The image attached shows the rectangle on the centimeter grid

Answer:

0.350 km

Step-by-step explanation:

Hi there !

35000 cm = 35000/100 m = 350 m

350 m = 350/1000 km = 0.350 km

Good luck !

Answer:

7 3/4

Step-by-step explanation:

4 1/8 + 3 5/8

Add the whole numbers, 4 + 3 = 7.

Add the fractions, 1/8 + 5/8 = 6/8.

You get 7 6/8. Simplify 6/8 to get 3/4.

Your answer is 7 3/4.

Answer:

Hi ___

A ratio is created from two numbers it can also be a fraction.

To find a ratio you have to have 2 numbers

You can take these 2 numbers and divide them so they are a unit ratio

For example 3:6 can be reduced to 1:3

Step-by-step explanation:

Hope this helps please give brainliest

Answer:

ur nan

Step-by-step explanation:

Answer:

33mph

Step-by-step explanation:

because if u divide 99 by 3 that is the answer

Answer:

A. 40x + 10y + 10z = $160

B. 8 Roses, 2 lilies and 2 irises

C.

1. 20x + 5y + 5z = $80

2. 4x + y + z = $16

3. 8x + 2y + 2z = $32

Step-by-step explanation:

Cost for each flower = $160/5 = $32

So we have $32 for each bouquet consisting of 12 flowers each.

Roses = x = $2.50 each

lilies = y = $4 each

irises = z = $2 each

8x + 2y + 2z = $32

8($2.50) + 2($4) + 2($2) = $32

$20 + $8 + $4 = $32

$32 = $32

a. Maximum budget is $160

40x + 10y + 10z = $160

40($2.50) + 10($4) + 10($2) = $160

$100 + $40 + $20 = $160

$160 = $160

b. From above

8x + 2y + 2z = $32

8 Roses, 2 lilies and 2 irises

c. No. There are other solutions If total cost is not limited

1. 20x + 5y + 5z

20($2.50) + 5($4) + 5($2)

$50 + $20 + $10

= $80

2. 4x + y + z

4($2.50) + $4 + $2

$10 + $4 + $2

= $16

3. 8x + 2y + 2z

8($2.50) + 2($4) + 2($2)

$20 + $8 + $4

= $32

Answer:

392984

Step-by-step explanation:

Answer:

A is the answer

Step-by-step explanation:

According to BODMAS (or DMAS), first we add and then subtract

if both operations are of add, we add it at the same time

Answer:

The height of the plane is 405 meters

Step-by-step explanation:

Trigonometric Ratios

The situation can be represented as shown in the image below. The ground, the height H, and the direct distance to the plane to the shipwreck form a right triangle, where the trigonometric ratios stand.

Since the known distance is adjacent to the angle, and the required height is opposite to the given angle, we use the tangent ratio, defined as:

[tex]\displaystyle \tan\ x=\frac{\text{opposite leg}}{\text{adjacent leg}}[/tex]

[tex]\displaystyle \tan 5^\circ=\frac{H}{4629}[/tex]

We need to find H, so we solve for H:

[tex]H=4629\cdot\tan5^\circ[/tex]

H=405 m

The height of the plane is 405 meters

Answer: one angle would be 50 degrees while the other would be 130 degrees.

Step-by-step explanation:

Answer:

−n−323

Step-by-step explanation:

i'm sorry wheres the picture?

[tex]\large\underline{\bf \red{Step \:by\: Step \:Explanation:}}[/tex]

Given two equations are :

We may write them as ,

Multiplying equⁿ (i) by 2 :

⇒ 2(2x + y - 6 ) = 0.

⇒ 4x + 2y - 12 = 0 .....................(iii) .

Subtract equⁿ (ii) from equⁿ (iii) :-

⇒ 4x + 2y - 12 = 0

ㅤ- 4x + 3y - 8 = 0 [ Sign changes ]

__________________

⇒ 5y - 20 = 0.ㅤㅤㅤㅤㅤ

⇒ 5y = 20.

⇒ y = 20/5.

⇒ y = 4

Put this value in (i) to obtain x .

⇒ 2x + y - 6 = 0.

⇒ 2x +4 - 6 = 0.

⇒ 2x - 2 = 0.

⇒2x = 2 .

⇒ x = 2/2.

⇒ x = 1 .

Hence the value of x is 1 & y is 4.

[tex]\boxed{\purple{\bf\pink{\dag}\:Hence\:the\: correct\: option\:is\:[b]\:(1,4)}}[/tex]

Answer:

A

Step-by-step explanation:

By solving (x+6)(x-9), we get x^2 - 3x - 54. By looking at our y-intercept, we can see that only option A has the correct intercept.

Answer:

A

Step-by-step explanation: