Caroline leaves her apartment and walks 45° north of west for 1000 feet and then walks 200 feet due north to go to the grocery store. How far and at what north of west
quadrant is Caroline from being at her apartment?

Answers

Answer 1

Answer:

  1150 ft W 52° N

Step-by-step explanation:

There are several ways a problem like this can be solved. Perhaps the easiest is to make use of a suitable vector calculator.

Using West as the reference for angles measured clockwise (toward north), the final position is ...

  1000∠45° +200∠90° = 1150.149∠52.063°

__

You can also figure this using the Law of Cosines. It will tell you the resultant distance (c) in terms of the individual distances (a, b) and the angle between them (135°).

  c² = a² +b² -2ab·cos(C)

  c² = 1000² +200² -2·1000·200·cos(135°) ≈ 1,322,842.7

  c ≈ √1322842.7 ≈ 1150.149

The angle difference from 45°N can be found using the Law of Sines.

  sin(B)/b = sin(C)/c

  B = arcsin(b/c·sin(C)) = arcsin(200/1140.149·sin(135°)) ≈ 7.063°

This means Caroline's bearing from home is 45° +7.063° ≈ 52° north of west.

Caroline's final position is 1150 W 52° N in relation to her home.

Caroline Leaves Her Apartment And Walks 45 North Of West For 1000 Feet And Then Walks 200 Feet Due North

Related Questions

what is the answer? HELP MEEE

Answers

Answer: 126

Step-by-step explanation:

11+5=16

Step-by-step explanation:

square root of 121 is 11 and cube root of 125 is 5 i.e

11^2=121 and 5^3=125

3.(08.01 MC)
Find the length of the base of a square pyramid If the volume is 48 cubic inches and has a height of 9 inches.
O 4 inches
O 8 inches
O 16 inches
0
24 inches

Answers

Answer:

4 inches

Step-by-step explanation:

The formula is L=√((3×V)/h)

Find an irrational number between 6 and 28

Answers

Answer:

Step-by-step explanation:

All the whole numbers or integers between 6 and 28 are rational numbers because they can be expressed as improper fractions as for example 7 = 7/1 but the square root of 7 is an irrational number because it can't be expressed as a fraction.

Answer:

√101 (square root of 101)

Step-by-step explanation:

Irrational numbers are numbers that can't be written as fractions.

The square root of 101 is irrational because it is not a perfect square which means that it has an infinite amount of numbers after the decimal point. Because of this the square root of 101 cannot be expressed as a fraction.

Determine which postulate can be used to prove the triangles are congruent then identify the valid congruency statement (SELECT TWO ANSWERS)

Options:
A) AAS
B)ASA
C) HL
D) CDE ≅ FDE
E) DEC ≅ EDF
F) ECD ≅ DFE

Answers

Answer:

A) AAS

D) CDE ≅ FDE

Step-by-step explanation:

∠C ≅ ∠F              Given

∠DEC ≅ ∠EDF    Given

DE ≅ DE               Reflexive property

ΔCDE ≅ ΔFDE        AAs congruent

The selling price of an item is $550 it’s marked down by 20% but the sale price is still marked up from the cost of $400 find the markup from cost to sale price

Answers

The answer is $40

Solution: from the given information we can know the selling price now is $550(1-20%)= so the markup from cost to sale price is 440=40

Keiko measures the circumference of three fruits.
Complete the table to show Keiko's measurements, the actual measurements, the
difference between the measurement and the actual, and the percent error.
CLEAR
CHECK
6 cm
81 cm
10%
50%
20%
10 cm
Apple
Grapefruit
Watermelon
15 cm
24 cm
Keiko's measurement
DRAG AND DROP
AN ITEM HERE
DRAG AND DROP
AN ITEM HERE
30 cm
Actual measurement
90 cm
5 cm
Absolute difference
DRAG AND DROP
AN ITEM HERE
9 cm
Percent error
DRAG AND DROP
AN ITEM HERE
DRAG AND DROP
AN ITEM HERE
DRAG AND DROP
AN ITEM HERE
no

Answers

The absolute measurement specifies the magnitude of the difference

which may be positive or negative.

The completed table is presented as follows;

[tex]\begin{tabular}{|l|c|c|c|}&\textbf{Apple}&\textbf{Grapefruit}&\textbf{Watermelon}\\\textbf{Keiko's measurement}&15 cm&24 cm& \underline{81 cm}\\\textbf{Actual measurement}&\underline{10 cm}&30 cm&90 cm\\\textbf{Absolute difference}&5 cm&\underline{6 cm}&9 cm\\\textbf{Percent error}&\underline{50\%}&\underline{20\%}&\underline{10\%}\end{array}\right][/tex]

Reasons:

The formulas for the inputs in the table are;

Absolute difference = Keiko's measurement - Actual measurement

The difference between Keiko's measurement and the actual measurement can be positive or negative while the absolute difference is always positive

[tex]\displaystyle Percent \ error = \mathbf{\frac{Keiko's \ measurement - Actual \ measurement}{Actual \ measurement} \times 100}[/tex]

Therefore;

[tex]\displaystyle Percent \ error = \frac{ \mathbf{Absolute \ difference}}{Actual \ measurement} \times 100[/tex]

Which gives for Apple;

The actual measurement for Apple = 15 cm - 5 cm = 10 cm

[tex]\displaystyle Percent \ error \ for \ Apple = \frac{5 \, cm}{10 \, cm} \times 100 = \mathbf{50\%}[/tex]

Grapefruit column of the table;

Absolute difference for Grapefruit = |24 cm - 30 cm| = |-6 cm| = 6 cm

The absolute difference for Grapefruit = 6 cm

[tex]\displaystyle Percent \ error \ for \ Grapefruit = \mathbf{\frac{6 \, cm}{30 \, cm} \times 100} = 20\%[/tex]

Percent error for Grapefruit = 20%

Watermelon column of the table;

Keiko's measurement = Absolute difference + Actual measurement

Using the given options, we have, 90 - 9 = 81

Therefore, the difference = -9, while the absolute difference = 9

Keiko's measurement for Watermelon = 90 cm - 9 cm = 81 cm

[tex]\displaystyle Percent \ error \ for \ Grapefruit= \frac{9 \, cm}{90 \, cm} \times 100 = 10\%[/tex]

The completed table is as follows;

[tex]\begin{tabular}{|l|c|c|c|}&\textbf{Apple}&\textbf{Grapefruit}&\textbf{Watermelon}\\\textbf{Keiko's measurement}&15 cm&24 cm& \underline{81 cm}\\\textbf{Actual measurement}&\underline{10 cm}&30 cm&90 cm\\\textbf{Absolute difference}&5 cm&\underline{6 cm}&9 cm\\\textbf{Percent error}&\underline{50\%}&\underline{20\%}&\underline{10\%}\end{array}\right][/tex]

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Keith spent $8 on tomatoes. How many did he get? ​

Answers

Answer:

its got 6

Step-by-step explanation:

I REALLY DONT KNOW

Answer:

Step-by-step explanation:

Let t be the unit cost of the tomatoes:  e. g., t = $1.25/lb.

If Keith spent $8 on tomatoes, the number he bought would then be

   $8

------------- = 6.4 lb of tomatoes

$1.25/lb

Of course he couldn't buy 0.4 tomato, but this method of calculating how many tomatoes he could buy theoreticallyl is correct.

The general formula would be

   $8

------------   and the end result would be the number of pounds Keith could

  $t / lb                               buy for $8.

Can someone help me solve This. Use photo as context. In exponential growth functions , the base of the exponent must be greater than 1. How would the function change if the base of the exponent were 1? How would the exponent change if the base of the exponent were between 0 and 1?

Answers

Answer:

If the exponent was 1, the function would remain constant but if the function was between 0-1 it would decrease towards the x-axis.

HELP ORGENT
Tyrone has $95 to spend. He already bought pants for $22. How many $5 t-shirts can he buy if he wants to have at least $15 left over?

a. Write an inequality that demonstrates this situation

b. solve your inequality

c. Explain what your answer means to Tyrone

Answers

Answer:

it should be a.

Step-by-step explanation:

5x+2y=10

slope=________

y-intercept=_________

y=x

slope=________

y-intercept=_________

Answers

Answer:

A)  -5/2 and 5

B) 1 and 0

Step-by-step explanation:

y=mx+b is the standard form:  m is the slope and b is the y-intercept.

5x+2y=10

y = -(5/2)x + 5  [Rearrange to standard format]

slope__-5/2__  

y-intercept__5___

===========

y=x

Slope = 1

Y-intercept = 0

Solve for x: 2(7x – 6) = 30

Answers

Answer:

X=3

Step-by-step explanation:

2 times 7x = 14x

2 times -6 = -12

14x-12=30

(+12)

14x=42

(÷14)

X=3

Generate a frequency table for the following data: 3, 12, 25, 2, 3, 6, 17, 17, 15, 13, 20, 12, 21, 18, 19.
Use the ranges listed in the table:

Range Number of Values
1 – 5
6 – 10
11 – 15
16 – 20
21 – 25


What value should be placed in the second column for the range 11 – 15?

A: 4, B: 3, C: 5, D: 6

3

5

6

Answers

Answer:

4

Step-by-step explanation:

DeMarcus is organizing a group of friends to attend a concert.
The ticket pricing is shown in the table below. Use the information
to create a graph and answer the questions.
Miu
# OF TICKETS
2
3
5
7
TOTAL COST ($)
32
48
80
112
16
9
14
126
IDS
84
63
42
1. Rate of Change:
Equation:
2. What does the ordered pair (1, 16) represent in this situation?
212
1234
078410
3. Describe how you know that this is a proportional relationship:

Answers

Answer:

Give me some hint please

The rate of change is 16, the equation is y = 16x, the (1,16) represents that the cost of 1 ticket is $16 and by y = 16x it is clear that it is a direct proportion.

How to form an equation?

Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.

The table of tickets and their cost is given,

The graph of it has been plotted below,

The rate of change or slope = (48 - 32)/(3 - 2) = 16

The equation is y = mx + c where m is the slope and it is 16

So, y = 16x + c

Now substitute (2,32)

32 = 2(16) + c

c = 0

So the equation becomes y = 16x

Since y = kx is a direct proportional equation so it will be also direct proportionally.

In (1,6) , 1 = number of ticket , 16 = cost of ticket so it is $16.

Hence "The rate of change is 16, the equation is y = 16x, the (1,16) represents that the cost of 1 ticket is $16 and by y = 16x it is clear that it is a direct proportion".

For more about the equation,

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IM GIVING OUT BRIANLIEST

Answers

Answer:

3.78

Step-by-step explanation:

how many morerock cds than classical cds were sold

Answers

25 because im like that and smart

Given that XY is a line segment with the angle a = 51°, work out the value of
the angle marked b.
Y
b
a
X
The diagram is not drawn to scale.
ASP PLZ

Answers

Answer:

129º

Step-by-step explanation:

This is just a guess since you didn't include the diagram

b is supplemetary to a

therefor

b = 180 - a

b = 180 - 51

b = 129º

It would be 129 degrees

How do I rewrite the following expression is there a form 1/4 (4x+8) please help me it’s gonna help my grade

Answers

Answer:

You can expand this with this rule:

[tex]a(b+c)=ab+ac[/tex]

Similarly,

[tex]\frac{1}{4}(4x+8) =\frac{1}{4}*4x+\frac{1}{4}*8[/tex]

[tex]\frac{1}{4}*4x+\frac{1}{4}*8=x+2[/tex]

How to solve (8x-3)(5x+4)=0

Answers

Answer:

x= 3/8 = 0.375 , x= -4/5= -0.8

Step-by-step explanation:

8x-3=0

8x=3

8x/8 = 3/8

x= 3/8 converted to decimal will be =0.375

for 5x+4=0

5x= -4

5x/5 = -4/5

x= -4/5 = converted to decimal will be = -0.8

Answer:

x —4/5 or 3/8

Step-by-step explanation:

hope it helps u

plzz plzz plzz mark as brainliest

A flight from Boston to London only took 5 hours because of a strong tailwind. The flight back to Boston against the same wind took 6 hours. What was the speed of the wind if the speed of the plane in still air is 550 mph?

Answers

If the flight back to Boston against the same wind took 6 hours. The speed of the wind if the speed of the plane in still air is 550 mph is 50 mph.

How to find the speed of the plane?

Given data:

Boston to London = 5 hours

Flight back to Boston  = 6 hours

Still air = 550 mph

Using this formula

Speed (s) = Distance /Time

We need to formula an equation that will be used to find the speed

Equation: (550 + s)5 = (550 - s)6

So,

Let s represent the speed

(550 + s)5 = (550 - s)6

2750 +5s = 3300 - 6s

Collect like terms

6s +5s = 3300 - 2750

11s = 3300 - 2750

11s = 550

Divide both side by  11s

s= 550/11

s = 50mph

Therefore the speed of the plane is 50mph.

Learn more about speed here:https://brainly.com/question/28439044

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PLEASSSSSSE HELP, WILL GIVE BRAINLIEST


How many chromosomes would a diploid offspring have when the haploid sex cells contain 46 chromosomes?

23

46


58

92

Answers

Answer:

I think its 46 since the 2 speices need the same amount of chromosomes to make an offspring

Step-by-step explanation:

I need help :( I forgot how to do this

Answers

Answer:

[tex]A=\frac{1}{2}h(b_{1}+b_{2} ) | *2\\2A=h(b_{1}+b_{2} ) | : (b_{1}+b_{2} )\\\frac{2A}{(b_{1}+b_{2} )} = h[/tex]

I hope it's good.

Take care !

(3 x^-2 y^3)^3 Please help ASAP

Answers

Answer:

I don't understand what do you mean by (3 x^-2 y^3)^3

by itself?

If answered correct you will be MARKED BRAINLIEST

Answers

Answer:

a^18

Step-by-step explanation:

(a^2 x a^2 x a^2)^3

first, calculate the product inside the parentheses

(a^6)^3

simplify the expression

a^18

Enter an algebraic expression for the word expression. The quotient of -1 and y​

Answers

Answer:

Step-by-step explanation:

-1/y

What is the nth term rule of the lines
5, 8, 11, 14, 17....
Tn​

Answers

I think the answer is 3n+2.

Answer:

3n+2

Step-by-step explanation:

A digital music service sells 12 songs for $9. 96. At this rate, how many songs can you purchase for $4. 15?.

Answers

The amount of songs you can purchase for $4.15 is 5 songs as 1 song is $0.83 and 5 will be $4.15

Calculate the sum of each expression. Arrange the expressions in the order of their value from largest to smallest.

Answers

Answer:

Check attached

Step-by-step explanation:

[] The first one you add

    () -8 + 9 = 1

    () -2/5 + 1/5 = -1/5

    () 1/1 = 5/5, 5/5 - 1/5 = 4/5

[] The second one you subtract, the + and - become a -

    () 9 - 5 = 4

    () 2/5 - 3/5 = -1/5

    () 4 - 1/5 = 3 4/5

    () 3 * 5 = 15, 15 + 4 = 19/5

[] The third one you add

    () 2 + 2 = 4

    () 1/5 + 2/5 = 3/5

    () 4* 5 = 20, 20 + 3 = 23/5

Have a nice day!

     I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)

- Heather

Which expression below is equivalent?

A. 7x+x+8=16x

B. x+x+1+1=2x+2

C. 5(x+3)=5x+5

D. 9x−18=9(x+2)

Answers

Lets look at each one:

A. 7x+x+8=16x

This left side will be 8x + 8, so its wrong.

B. x+x+1+1=2x+2

This left side will be 2x + 2, it is right!

C. 5(x+3)=5x+5

This left side will be 5x+15, so its wrong.

D. 9x−18=9(x+2)

This left side will be 9(x-2), so its wrong.

Our answer is going to be B) x+x+1+1=2x+2

x + x = 2x

1 + 1 = 2

2x + 2

I hope this helps! :)


How would you best describe the angle pair
<3 and <8

Answers

Answer:

Vertical angles

help me pleaseeeeeeeee

Answers

Answer:

a) 84m

b) 86cm

Step-by-step explanation:

a) 8316/99=84

You take to whole and divide it by the length to get the width.

b) 288-58-58=172/2=86

You take the width and subtract it from the perimeter twice because there are two sides. then take that answer and divide it by two to get what your last two sides equal. This gives you the length.

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