What is the solution to this system of equations?

Answer:

  caveat: your grader may expect <E, N> coordinates, reversed from these

  A. <N, E> = <-200, 346.410> (plane) and <25.712, 30.642> (wind)

  B. resultant <N, E> = <-174.288, 377.052>

  C. resultant = 415.385∠115°

Step-by-step explanation:

The necessary calculations for vector arithmetic are handily carried out by a suitable calculator. The attached shows a TI-84 work-alike, but there are many other possible choices.

The necessary calculations for doing this "by hand" (without a calculator that does vectors or complex numbers) are ...

  a∠b = a·cis(b) = (a·cos(b) +i·a·sin(b))

  a +i·b = √(a²+b²)∠arctan(b/a) . . . . . with attention to signs and quadrant

__

Ordinarily, bearings are measured clockwise from North, and angles in the x-y or complex plane are measured counterclockwise from +x (East). If you use bearing angles without any translation, the resulting (complex plane) coordinates from rectangular/polar conversion are ...

  (North + i·East)

Coordinates in this system can be added and subtracted in the usual way. When the result is converted back to a distance and direction, that direction can be considered to be a bearing angle. In short, we can use bearing angles in our math with no special treatment, provided we are consistent in that usage.

__

The airplane speed vector in <north, east> coordinates is ...

  400∠120° = 400cos(120°) +i·400·sin(120°) = <-200, 346.410>

Similarly, the wind speed vector is ...

  40∠50° = 40cos(50°) +i·40sin(50°) = <25.712, 30.642>

__

The sum of the vectors is found from the sum of their components:

  plane + wind = <-200 +25.712, 346.410 +30.642> = <-174.288, 377.052>

__

Converting this vector in linear form back to a magnitude and direction gives ...

  magnitude = √((-174.288)² +377.052²) = √172544.644542

  magnitude ≈ 415.385 . . . mph

  direction = arctan(-377.052/174.288) . . . . . 90° < θ < 180°

  direction ≈ 115°

_____

Additional comment

As we discussed above, the vector coordinates used here are <N, E> coordinates. If you translate the bearing angles to Cartesian plane angles (measured CCW from +x), the corresponding coordinates will be <E, N> coordinates. That is, rectangular coordinates will be reversed from those shown here. If you're filling in an answer box, you may want to be aware of that fact.

Answer:

18cm

Step-by-step explanation:

We have the length of the rectangle but we need to find the width which we'll call w. Area is a, l is length.

a = l * w

20 = 5 * w

divide both sides by 5 to cancel the multiplication by 5 on the right side

4 = w

The rectangle is going to have two sides that are the length of l, and two sides that are the the length of w. We're looking for the perimiter p.

p = 2l + 2w

p = (2 * 5) + (2 * 4)

p = 18

To find the slope:

 ⇒ must know the slope's formula

    ⇒ [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

        ⇒ [tex](x_{1} ,y_{1} )[/tex] and [tex](x_{2} ,y_{2} )[/tex] are any points on the line

           ⇒ we use (-1,2) and (0,5) since they are the only points that we

                know that are on the line

Let's solve:

  [tex]Slope = \frac{5-2}{0--1} =\frac{3}{1}[/tex]

Slope is 3

Hope that helps!

Answer:

question5=B that is the answer

The equation of the javelin path h(t) = -16t^2+68t+6.5 is a quadratic function

The javelin hits the ground after 4.344 seconds

The equation of the javelin path is given as:

h(t) = -16t^2+68t+6.5

When it hits the ground, h(t) = 0.

So, we have:

-16t^2+68t+6.5 = 0

Using a graphing calculator, we have:

t = 4.344 and t = -0.094

Time cannot be negative.

So, we have:

t = 4.344

Hence, the javelin hits the ground after 4.344 seconds

Read more about quadratic functions at:

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[tex]\qquad\qquad\huge\underline{{\sf Answer}}♨[/tex]

Let's solve ~

If it passes through x, then let's find x when y = 0

[tex]\qquad \tt \dashrightarrow \:0 = {x}^{2} - x - 6[/tex]

[tex]\qquad \tt \dashrightarrow \: {x}^{2} - 3x + 2x - 6 = 0[/tex]

[tex]\qquad \tt \dashrightarrow \:x(x - 3) + 2(x - 3) = 0[/tex]

[tex]\qquad \tt \dashrightarrow \:(x - 3) (x + 2) = 0[/tex]

So, required values of x are 3 and -2

Now, let's differentiate the equation to get slope slope for tangent ~

[tex]\qquad \tt \dashrightarrow \: m = \dfrac{d}{dx} ( {x}^{2} - x - 6)[/tex]

[tex]\qquad \tt \dashrightarrow \: m = 2 x - 1[/tex]

Now, plug in the values of x to find slopes of tangents

[tex]\qquad \tt \dashrightarrow \: m _1 = (2 \times 3) - 1[/tex]

[tex]\qquad \tt \dashrightarrow \: m_1 = 6 - 1[/tex]

[tex]\qquad \tt \dashrightarrow \: m _1 = 5[/tex]

and

[tex]\qquad \tt \dashrightarrow \:m_2 = (2 \times - 2) - 1[/tex]

[tex]\qquad \tt \dashrightarrow \:m_2 = - 4- 1[/tex]

[tex]\qquad \tt \dashrightarrow \:m_2 = - 5[/tex]

We know, tangent are normal are perpendicular. so let's find out slopes of normals m1' and m2'

[tex]\qquad \tt \dashrightarrow \:m _1\cdot m_1 ' = - 1[/tex]

[tex]\qquad \tt \dashrightarrow \:m _1' = \dfrac{- 1}{m_1}[/tex]

[tex]\qquad \tt \dashrightarrow \:m _1' = \dfrac{- 1}{ 5}[/tex]

and

[tex]\qquad \tt \dashrightarrow \:m _2\cdot m_2 ' = - 1[/tex]

[tex]\qquad \tt \dashrightarrow \:m _2' = \dfrac{- 1}{m_2}[/tex]

[tex]\qquad \tt \dashrightarrow \:m _2' = \dfrac{- 1}{ -5}[/tex]

[tex]\qquad \tt \dashrightarrow \:m _2' = \dfrac{1}{ 5}[/tex]

Now, write the equations of normals using point slope form :

Normal 1 : passing through (3 , 0), and slope = -1/5

[tex]\qquad \tt \dashrightarrow \:y - 0 = - \dfrac{1}{5} (x - 3)[/tex]

[tex]\qquad \tt \dashrightarrow \:5y = - (x - 3)[/tex]

[tex]\qquad \tt \dashrightarrow \:5y = - x + 3[/tex]

[tex]\qquad \tt \dashrightarrow \:x + 5y - 3 = 0[/tex]

and

Normal 2 : passing through (-2 , 0), and slope = 1/5

[tex]\qquad \tt \dashrightarrow \:y - 0 = \dfrac{1}{5} (x - ( - 2))[/tex]

[tex]\qquad \tt \dashrightarrow \:5y = x + 2[/tex]

[tex]\qquad \tt \dashrightarrow \ x - 5y + 2 = 0[/tex]

That's all for Aunty ~ hope it helps !

The chords in the circle L are illustrations of intersecting chords

The lengths that are even numbers are FJ and GJ

The length AD is given as:

AD = 10

From the circle, we have:

AD = AH + HK + KD

Where:

AH = 3 and KD = 2

So, we have:

10 = 3 + HK + 2

Solve for HK

HK = 5 ---- odd length

Next, we calculate length FH using the following intersecting chord theorem

FH * HB = AH * HD

This gives

(FJ + 3) * 3 = 3 * (2 + 5)

Divide by 3

FJ + 3 = 7

Subtract both sides by 3

FJ = 4 --- even length

Next, we calculate length KE using the following intersecting chord theorem

KE * KC = KD * KA

This gives

KE * 3.2 = 2 * (5 + 3)

Evaluate the product

KE * 3.2 = 16

Divide by 3.2

KE = 5 --- odd length

Next, we calculate length GJ using the following intersecting chord theorem

GJ * JE = FJ * JB

This gives

GJ * 4.5 = 4 * (6 + 3)

Evaluate the product

GJ * 4.5 = 36

Divide by 4.5

GJ = 8 --- even length

Hence, the lengths that are even numbers are FJ and GJ

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Answer:



These are the inequalities

A: [tex]W\geq -7[/tex]

B: [tex]W > -7[/tex]

C: [tex]W < -7[/tex]

D: [tex]W\leq -7[/tex]

I assume the "different" one is referring to the wording of the expression. B, C, and D are all similarly worded so I believe A is the "different" one.

Answer:

B

Step-by-step explanation:

the tangent- chord angle XYZ is half the measure of its intercepted arc XY

∠ XYZ = [tex]\frac{1}{2}[/tex] × 94° = 47°

Answer:

I think that the correct answer would be B. 47 degrees

Step-by-step explanation:

hope this helps

pls mark brainliest

Answer:

V = 682.66667

Step-by-step explanation:

Answer:

x=12

Step-by-step explanation:

The photo might help.

If anything is not understandable I'm here to help :)

Answer:

C

Step-by-step explanation:

because the nearest is to ones tenth hundred thousand

Answer:

Air that is moving primarily in a horizontal direction.

Answer:

Wind is the movement of air horizontally.

Answer:

A, D, E, F

Step-by-step explanation:

If you graph those four equations or plug in 0 as x, you would find that all of them are equal to -8

Answer:

The third angle is 104

Step-by-step explanation:

their for first angle is x and second angle of a triangle is 52 more than the first angle x×52 and again The third angle is two times the first and x=52×2×= 104

Answer:

$1.50

Step-by-step explanation:

4(1.50 + 3x) = 24

4(1.50 + 3x)  = 24/4                                                                                                                

_________

1.50 + 3x = 6.  subtract by 1.50 from both sides.

3x = 4.50

3x/3 = 4.50

          ____

             3

x = 1.50

                                                                      hope this helps!

The margin of error of the 90% confidence interval will be 0.024 and it increases when there's a higher confidence interval.

The margin of error of the 99% confidence interval will be:

= 1.645 × [✓0.36(1 - 0.36)/1006

= 0.024

The margin of error for a 99% confidence interval will be calculated thus:

= 2.576 × [✓0.36(1 - 0.36)/1006

= 0.03898

This implies that margin error increases when there's a higher confidence interval.

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Answer:

I think the answer is 6/40

Step-by-step explanation:

Answer:

8cm

Step-by-step explanation:

[tex]Here,\\\\Area(A)=64\pi cm^{2} \\Radius(r)=?\\\\As\:we\:have,\\\\\hookrightarrow Area=\pi r^{2} \\\\\hookrightarrow \frac{64\pi cm^{2} }{\pi } =r^{2} \\\hookrightarrow 64 cm^{2} =r^{2} \\\\\hookrightarrow \sqrt{64cm^{2} } =r\\\\\hookrightarrow 8cm=r\\\\\hookrightarrow r=8cm[/tex]

Answer:

[tex]\huge\boxed{\bf{radius_{circle} = 8cm}}[/tex]

Step-by-step explanation:

Given:-

To find:-

Ans:-

[tex]\sf \to Area_{circle} = \pi*r^2 [/tex]

[tex]\sf \to 64\cancel{\pi} cm^2 = \cancel{\pi}*r^2 [/tex]

[tex]\sf \to 64cm^2 = r^2 [/tex]

[tex]\sf \to r = \sqrt{64cm^2} [/tex]

[tex]\sf \to r = 8cm [/tex]

therefore [tex]\tt radius_{circle} [/tex] = 8cm

[tex]\: [/tex]

[tex]\huge\colorbox{skyblue}{BlackPain}[/tex]

Answer:

y is 12 degrees

x is 30 degrees

Step-by-step explanation:

If angle ABC is equal to angle MNC, that means 5y equals to 60 degrees. 60 divided by 5 equals 12. So, y equals 12 degrees

2x and 4x equals 180 degrees. So, 180 divided by 6 equals to 30. So x equals 30 degrees

Answer:

x = 30, y = 12

Step-by-step explanation:

2 similar equilateral triangles, each corner is 60 degrees.

2x = 60 degrees

divide by 2

x = 30 degrees

5y = 60 degrees

divide by 5

y = 12 degrees

This can be verified by checking 4x + 2x which gives you 180 degrees forming that straight line angle.

To calculate the area of a parallelogram

 ⇒ we must know the formula

     ⇒ Area = base * height

What are we given:

Thus:

   Area = 3ft * 4ft = 12 [tex]ft^2[/tex]

Hope that helps!

Step-by-step explanation:

16.

x = Xien's age

2 + x/2 = 11

x/2 = 9

x = 18

so, Xien is 18 years old.

17.

4x - 5 = 7

first dividing everything by 4 is not a mistake. I would have done it as second step simply to avoid dealing with the fractions. but it works either way.

so, his way :

4x/4 - 5/4 = 7/4

4x/4 = 12/4

x = 3

my way

4x - 5 = 7

4x = 12

x = 3

Answer:

see explanation

Step-by-step explanation:

the angles in a square are right .

the diagonals bisect the angles , then

∠ OKL = 45°

The diagonals are perpendicular to each other , then

∠ MOL = 90°

All sides are congruent , so

perimeter = 4 × NM = 4 × 8 = 32

Answer:

Perimeter: 32

measure of angle OKL: 45

measure of angle MOL: 90

Step-by-step explanation:

Things to remember:

- the side of the square are all equal

- vertical angles are congruent

 + ex. MON and KOL; MOL and NOK

- the entirety of the four angles in the center of the square equal 360 degrees

 + ex. MON + MOL + LOK + KON = 360 degrees

- corners of a square equal 90 degrees and since lines MK and LN cut the square in half we can assume that angles like OKL are also cut in half, making them 45 degrees

+ ex. angle NKL (90) = OKL (45) + OKN (45)

- The four triangles in the square are isosceles

If we have the angles of OML and MLO we can find MOL since the angles of a triangle equal 180

OML (45) + MLO (45) + MOL (x) = 180

90 + x = 180

x = 90

Answer:

xy=3_equation I

x+y=76/15 eq 2

Step-by-step explanation:

from eq

x=3/y

now put x=3/y in eq 2

3/y+y=76/15

(3+y^2) 15=76y

45+15y^2=76y

15y^2-76y+45=0

by using quardic equation

x=76+_root under 76^2-4×15×45/2×15

y= 5776+- 53.62/2×15

taking positive sign and taking negative sign

y=194.32

y=190.745

Answer:

$469887

Step-by-step explanation:

you should use compound interest formula which is

A=P(1+r/100) ^t

A = 242800 ( 1 + 0.045 ) ^ 15

when you punch this into a calculator you will get 469886.5771.....

when you round it off to a whole number the answer is $469887

Answer:

—8, —5, —2, 1, 4

Step-by-step explanation:

Check out the attached photo

The surface area of the shape is 400 square yards

The formula for calculating the surface area of the shape is given as:

Surface area = Area of square + area of triangle

Surface area = (15 * 20) + (0.5 * 10 * 20)
Surface area = 300 + 100
Surface area = 400 square yards

Hence the surface area of the shape is 400 square yards

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