A surveyor leaves her base camp and drives 42km on a bearing of 032degree she then drives 28km on a bearing of 154degree,how far is she from her camp base and what is her bearing from it

Answers

Answer 1

Answer:

The surveyor is 36.076 kilometers far from her camp and her bearing is 16.840° (standard form).

Step-by-step explanation:

The final position of the surveyor is represented by the following vectorial sum:

[tex]\vec r = \vec r_{1} + \vec r_{2} + \vec r_{3}[/tex] (1)

And this formula is expanded by definition of vectors in rectangular and polar form:

[tex](x,y) = r_{1}\cdot (\cos \theta_{1}, \sin \theta_{1}) + r_{2}\cdot (\cos \theta_{2}, \sin \theta_{2})[/tex] (1b)

Where:

[tex]x, y[/tex] - Resulting coordinates of the final position of the surveyor with respect to origin, in kilometers.

[tex]r_{1}, r_{2}[/tex] - Length of each vector, in kilometers.

[tex]\theta_{1}, \theta_{2}[/tex] - Bearing of each vector in standard position, in sexagesimal degrees.

If we know that [tex]r_{1} = 42\,km[/tex], [tex]r_{2} = 28\,km[/tex], [tex]\theta_{1} = 32^{\circ}[/tex] and [tex]\theta_{2} = 154^{\circ}[/tex], then the resulting coordinates of the final position of the surveyor is:

[tex](x,y) = (42\,km)\cdot (\cos 32^{\circ}, \sin 32^{\circ}) + (28\,km)\cdot (\cos 154^{\circ}, \sin 154^{\circ})[/tex]

[tex](x,y) = (35.618, 22.257) + (-25.166, 12.274)\,[km][/tex]

[tex](x,y) = (10.452, 34.531)\,[km][/tex]

According to this, the resulting vector is locating in the first quadrant. The bearing of the vector is determined by the following definition:

[tex]\theta = \tan^{-1} \frac{10.452\,km}{34.531\,km}[/tex]

[tex]\theta \approx 16.840^{\circ}[/tex]

And the distance from the camp is calculated by the Pythagorean Theorem:

[tex]r = \sqrt{(10.452\,km)^{2}+(34.531\,km)^{2}}[/tex]

[tex]r = 36.078\,km[/tex]

The surveyor is 36.076 kilometers far from her camp and her bearing is 16.840° (standard form).


Related Questions

Name the marked angle in 2 different ways

Answers

Answer:

∠DEB or ∠BED

Step-by-step explanation:

The letter of the angle always goes in the middle.

why does reflexive property exist

Answers

The reflexive property can be used to justify algebraic manipulations of equations.

Which of the following is equivalent to the expression below?
log_6^36+log_6^216

Answers

Step-by-step explanation:

log_6^36+log_6^216

= log_6^ (36 × 216)

= log_6^ (6² × 6³)

= log_6^ (6^5)

= 5

8 books cost 11.20. Find the cost of 5 books

Answers

First of all we have to find the cost of a book then multiply it by 5 :

$ 11.20 ÷ 8 = $ 1.4

$ 1.4 × 5 = $ 7

Thus 5 books have a cost of $ 7 .

Answer:

The cost of 5 books is $7

Step-by-step explanation:

If there are 8 books and you need to find the cost of 5, you need to first find the cost for one book.

If 8 books cost 11.20.

11.20 ÷ 8 = 1.40

1.40 is the cost of one book

1.40 x 5 = 7

So the cost of 5 books is $7

I tried my best to explain

What is the slope of the line

Answers

Answer:

[tex]\displaystyle m = -3[/tex]

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to Right

Algebra I

Reading a coordinate planeCoordinates (x, y)Slope Formula: [tex]\displaystyle m = \frac{y_2-y_1}{x_2-x_1}[/tex]

Step-by-step explanation:

Step 1: Define

Identify points from graph

Point (-1, 0)

Point (0, -3)

Step 2: Find slope m

Simply plug in the 2 coordinates into the slope formula to find slope m

Substitute in points [Slope Formula]:                                                              [tex]\displaystyle m = \frac{-3-0}{0--1}[/tex][Fraction] Subtract:                                                                                           [tex]\displaystyle m = \frac{-3}{1}[/tex][Fraction] Divide:                                                                                               [tex]\displaystyle m = -3[/tex]

Answer:

-3

Step-by-step explanation:

Determine the center and the diameter of the circle with the equation. x^2-6x+y^2+8y=24

Answers

Answer:

The center of the circle is (3, -4)

The diameter of the circle is 2

Step-by-step explanation:

The given equation of the circle is x² - 6·x + y² + 8·y = 24

The general form of the equation of a circle is x² + y² + 2·g·x + 2·f·y + c = 0

The center of the circle = (-g, -f)

The radius of the circle = √(g² + f² - c)

By comparing the given equation of the circle with the general form of the equation of a circle, we have;

2·g = -6, 2·f = 8, and c = 24

From 2·g = -6, we get;

∴ g = -6/2 = -3

g = -3

from 2·f = 8, we get;

∴ f = 8/2 = 4

f = 4

Therefore;

The center of the circle, (-g, -f) = (-(-3), -4) = (3, -4)

The center of the circle = (3, -4)

The radius of the circle, r = √(g² + f² - c) = √((-3)² + 4² - 24) = 1

The diameter of the circle, d = 2×r = 2 × 1 = 2

The diameter of the circle = 2.

Bab isn’t good with quick mafs

Answers

Answer:

153.86

Step-by-step explanation:

Formula area circle = πr²

Solve:

Area = 3.14* 7²

Area = 3.14 * 49

Area = 153.86

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

equivalent expression for 8 (y-7)

Answers

Answer:

8y - 56

Step-by-step explanation:

Answer:

multiply 8 by the numbers in brackets 8y-56

The given lengths are two sides of a right triangle. All three side lengths of the triangle are integers, and together they form a Pythagorean triple. Find the length of the third side, then indicate whether it is a leg or a hypotenuse.

Answers

Answer:

C) 92, leg

Step-by-step explanation:

a² + 28² = 96²     *the hypotenuse is always the longest side

a² + 784 = 9216

a² = 8432

a = √8432

'a' is approximately 92, and is a leg

PLEASE HELP AS SOON AS YOU CAN!!!!

Answers

Answer:

The answer is neptune

Step-by-step explanation:

Beccause -353 is less than -288

Va rog macar 1 si 2 hai va rog frumos

Answers

Answer:

can you translate to English

Step-by-step explanation:

Scarlett can bake 10 cookies with each scoop of flour. Write an equation that shows the relationship between the scoops of flour x and the cookies y. Write your answer as an equation with y first, followed by an equals sign.

Answers

y = 10x

Where y is equal to the amount of cookies and x is the scoops of flour.

what is the meaning of the quadratic formula. write it down?​

Answers

Answer:

Quadratic formula is the tool for solving for an unknown number (usually x)

Step-by-step explanation:

The formula is below

Answer:

Below.

Step-by-step explanation:

The formula, which gives the solutions of the equation, is

x = [-b ±√(b^2-4ac)]/2a.

- a, b and c are the coefficients of the quadratic equation

ax^2 + bx + c = 0.

4x +y = 10 graph the linear equation​

Answers

Graph not attached, linear equation: y=-4x+10

There is a jar of jellybeans on Mr. Schidrich's desk. 40% of the jellybeans are red. If
there are 55 jelly beans in the jar, how many are red??

Answers

Answer:

22 Red Jellybeans

Step-by-step explanation:

Out of the 55 jellybeans in the jar, 40% of them are red, which means you have to do 40% of 55 to see which ones are red. We know 10% of 55 is 5.5, then multiply 5.5 x 4 to get 22 is 40% of 50 hope this helped :)

Adam earns $18 an hour. If his wages for the
week amount to $810, how many hours did he
work for?

Answers

Answer:

45 hours

Step-by-step explanation:

if he makes 18 dollars per hour and he has 810 dollars all you have to do is divide 810/18 and you get 45

You purchase 75 shares of stock at $15 per share. The next day the stock drops 3%; however, a week later it increases in value by 7%. If you immediately sell your 75 shares, how much will you gain or lose (a) in dollar amount and (b) in percent?

Answers

Answer:

You have gained $43 and the value increased by 3.8%

Step-by-step explanation:

You would 75 times 15 = $1125

then you would do 1125 times 97% = 1091.25

now you would do 1091.25 times 107% = estimation of 1168

then you would do 1168/1125 which is estimated to 1.038 and you would convert that into a percentage = 103.8%

You would do 1168 - 1125 = $43 and 103.8 - 100 = 3.8%

Kadeesha has a point card for a movie theater.
She receives 50 rewards points just for signing up she earns 12.5 points for each visit to the movie theater she needs at least 210 points for a free movie ticket right and solve for an inequality the number of visits kadeesha can make to earn her first free movie ticket

Answers

Answer:

50 + 12.5 v ≥ 210

She needs at least 13 visits

Step-by-step explanation:

points for signing up + points per visit* number of visits ≥  210

50 + 12.5 v ≥ 210

Subtract 50 from each side

50 + 12.5 v -50 ≥ 210-50

12.5 v ≥ 160

Divide by 12.5

12.5 v/12.5 ≥ 160/12.5

v ≥ 12.8

She needs at least 13 visits

Answer:

Step-by-step explanation:

need help with thisss

Answers

9514 1404 393

Answer:

  cos(x) = 0.6

Step-by-step explanation:

First, we need to find UQ.

  UQ = UP·cos(y°) = UP·√(1 -sin²(y°)) = (26 cm)√(1 -25/169) = (26 cm)(12/13)

  UQ = 24 cm

Then TQ is ...

  TQ = 1/3UQ = 1/3(24 cm) = 8 cm

And cos(x°) is ...

  cos(x°) = √(1 -sin²(x)) = √(1 -64/100)

  cos(x°) = 6/10 = 3/5

  cos(x°) = 3/5 = 0.6

Demola is two years older than Deji and Tobi is half of Demola's age. The sum of their ages is 23. How old is Deji​

Answers

answer is in the picture

Liam is single. He has no children and an adjusted income of $26,700. Last year, his employer held $172 from each monthly paycheck. He used the standard deduction when filing. Find the amount of income tax due to the IRS or the amount overpaid.

A Liam owes the IRS $91

B The IRS owes Liam $91

C The IRS owes Liam $329

D Liam owes the IRS $329

Answers

Answer:

option B is the correct answer

Step-by-step explanation:

please make me as a brainlist answer

1 1/5+3 2/5
they both are mixed numers

Answers

Answer:

4 3/5

hope this helps

have a good day :)

Step-by-step explanation:

1+3=4

1/5+2/5=3/5

if a radio is bought for rs 1000 is sold for rs 1500 find what is the profit percentage?

Answers

Answer:

profit percentage is =(amount sold-amount bought)×100/amount bought

Answer:

profit: 1500-1000=500

profit percentage=x

now,

x % of 1000= 500

50% is the answer.

Triangle MNO has vertices M(6,5), N(2,2), and O(7,0). It's image has vertices M'(-6,5), N'(-2,2), and
O'(-7,0). Which line of reflection maps triangle MNO onto its image?
x = 1
y=1
x = 0
.y=0

Answers

Answer:

x=0

Step-by-step explanation:

because the y values are not changing and the x values are only changing from positive to negative.

A school librarian surveyed a random sample of $50$ students to find out which library resources students value most. The table below shows the results.

Library Resources Number of Students
Books 24
Study Areas 10
Classes 6
Movies 10

Which statements are best supported by the data?

Select all that apply.

A It is expected that $15\%$ to $25\%$ of all students will value movies the most.

B It is expected that $20\%$ to $30\%$ of all students will value books the most.

C In a group of $25$ students, it is expected that around $5$ students will value study areas the most.

D In a group of $100$ students, it is expected that around $6$ students will value classes the most.

E In a group of $200$ students, it is expected that $20$ students will value study areas the most, and $20$ students will value movies the most.

Answers

Answer:

E

Step-by-step explanation:

If you break each classification of what items metter most you get the following percentahes:

Books             48%

Study Areas     5%

Classes             6%

Movies             20%

A - you could make an argument that this MAY be an accurate reflection but the percentage does not bring 15% into the data so this seems like conjecture.

B - Data suggest a higher support for books at 48%

C - Data suggest 1 or two in a group of 25 would answer study areas

Please help!! Find the surface area of the cylinder as pictured below with a = 3 cm and b=
5 cm. Use 3.14 for r and round your answer to the nearest hundredth. Do not
include units in your answer.

Answers

156.12 if using pi

150.8 if using π

MARKING BRAINLIEST

HELP PLS

Answers

The Answer is:

C.) (x+2)(x+3)

Answer:

(x-2)(x+3)

Step-by-step explanation:

1. Start by setting up the synthetic division. The numbers 1, -4, -11, and 30 go on the inside on the division. To get the number on the outside, set x-5 equal to 0. solve and get 5.

2. bring the one down. multiply the one and the five and place the number you get underneath the -4 in the next column. From there, add the two numbers in the column.

3. After adding those two numbers, put the number you get (which should be 1) directly below the 5. Now multiply that number and the 5 again.

4. Repeat these steps until you fill the spaces under the next two columns. If you do it correctly, the number at the bottom of the very last column should be 0. This zero is known as the remainder. The remainder is not needed to complete this problem.

 Now that you have finished synthetic division, it is time to set up the new equation you got.

5. The 1 on the bottom left will be your [tex]x^{2}[/tex] value, the next 1 will be your x value, and the -6 will be your c. You should get the equation [tex]x^{2} + x -6[/tex]

6. From here, factor the polynomial. The factors must add up to the middle value (1) and multiple to c (-6). The factors -2 and 3 add up to 1 and multiply to -6

Therefore, your answer will be (x-2)(x+3)

9x10to the power of -9

Answers

-Answer :

[tex] \large \boxed{0.000000009}[/tex]

Solution :

Here we go :

[tex] \rightarrow9 \times 10 {}^{ - 9} [/tex]

[tex] \rightarrow \dfrac{9}{10 {}^{9} } [/tex]

[tex] \rightarrow \dfrac{9}{1000000000} [/tex]

[tex] \rightarrow0.000000009[/tex]

[tex] \bold{ \mathfrak{hope \: it \: helps \: you......}}[/tex]

Please give me the answer and show me how you solved it

Answers

Answer:

Option 1: -8c^8

Step-by-step explanation:

We multiply the numbers by the numbers, then the variables times the variables.

-2 times 4 gives us -8

c^3 times c^5 = c ^8. When multiplying a variable with exponents, you add the exponents.

You only multiply the exponents when it's something like (c^3)^5

how many and what type of solutions does 5x^2-2x+6 have

Answers

Answer:

two irrational solutions

Step-by-step explanation:

you can use the quadratic formula:  (b ± √b²- 4ac)÷2a

a = 5, b = -2, c = 6

= [2 ± √(-2²)-4(5)(6)] ÷ 2(5)

= (2 ± √4-120) / 10

two complex solutions:  (2+√-116)/10, (2-√-116)/10

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