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).
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?
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%
4x +y = 10 graph the linear equation
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
answer is in the picture
1 1/5+3 2/5
they both are mixed numers
Answer:
4 3/5
hope this helps
have a good day :)
Step-by-step explanation:
1+3=4
1/5+2/5=3/5
8 books cost 11.20. Find the cost of 5 books
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
Determine the center and the diameter of the circle with the equation. x^2-6x+y^2+8y=24
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.
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.
156.12 if using pi
150.8 if using π
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.
Please give me the answer and show me how you solved it
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
what is the meaning of the quadratic formula. write it down?
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.
PLEASE HELP AS SOON AS YOU CAN!!!!
Answer:
The answer is neptune
Step-by-step explanation:
Beccause -353 is less than -288
Adam earns $18 an hour. If his wages for the
week amount to $810, how many hours did he
work for?
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
Va rog macar 1 si 2 hai va rog frumos
Answer:
can you translate to English
Step-by-step explanation:
if a radio is bought for rs 1000 is sold for rs 1500 find what is the profit percentage?
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.
MARKING BRAINLIEST
HELP PLS
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)
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.
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
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.
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
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
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.
9x10to the power of -9
[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]
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
Answer:
option B is the correct answer
Step-by-step explanation:
please make me as a brainlist answer
Which of the following is equivalent to the expression below?
log_6^36+log_6^216
Step-by-step explanation:
log_6^36+log_6^216
= log_6^ (36 × 216)
= log_6^ (6² × 6³)
= log_6^ (6^5)
= 5
Name the marked angle in 2 different ways
Answer:
∠DEB or ∠BED
Step-by-step explanation:
The letter of the angle always goes in the middle.
need help with thisss
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
how many and what type of solutions does 5x^2-2x+6 have
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
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
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:
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??
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 :)
equivalent expression for 8 (y-7)
Answer:
8y - 56
Step-by-step explanation:
Answer:
multiply 8 by the numbers in brackets 8y-56
What is the slope of the line
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 RightAlgebra 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:
why does reflexive property exist
Bab isn’t good with quick mafs
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