Amy is pulling a wagon with a force of 30 pounds up a hill at an angle of 25°. Give the force exerted on the wagon as a vector and as a linear combination of unit vectors i and j.

Answer:

Vector (ordered pair - rectangular form)

[tex]\vec F = (27.189,12.679)\,[lbf][/tex]

Vector (ordered pair - polar form)

[tex]\vec F = (30\,lbf, 25^{\circ})[/tex]

Sum of vectorial components (linear combination)

[tex]\vec F = 27.189\cdot \hat{i} + 12.679\cdot \hat{j}\,[N][/tex]

Step-by-step explanation:

From statement we know that force exerted on the wagon has a magnitude of 30 pounds-force and an angle of 25° above the horizontal, which corresponds to the +x semiaxis, whereas the vertical is represented by the +y semiaxis.

The force ([tex]\vec F[/tex]), in pounds-force, can be modelled in two forms:

Vector (ordered pair - rectangular form)

[tex]\vec F = \left(\|\vec F\|\cdot \cos \theta, \|\vec F\|\cdot \sin \theta\right)[/tex] (1)

Vector (ordered pair - polar form)

[tex]\vec F = \left(\|\vec F\|, \theta\right)[/tex]

Sum of vectorial components (linear combination)

[tex]\vec {F} = \left(\|\vec F\|\cdot \cos \theta\right)\cdot \hat{i} + \left(\|\vec F\|\cdot \sin \theta \right)\cdot \hat{j}[/tex] (2)

Where:

[tex]\|\vec F\|[/tex] - Norm of the vector force, in newtons.

[tex]\theta[/tex] - Direction of the vector force with regard to the horizontal, in sexagesimal degrees.

[tex]\hat{i}[/tex], [tex]\hat{j}[/tex] - Orthogonal axes, no unit.

If we know that [tex]\|\vec F\| = 30\,lbf[/tex] and [tex]\theta = 25^{\circ}[/tex], then the force exerted on the wagon is:

Vector (ordered pair - rectangular form)

[tex]\vec F= \left(30\cdot \cos 25^{\circ}, 30\cdot \sin 25^{\circ}\right)\,[lbf][/tex]

[tex]\vec F = (27.189,12.679)\,[lbf][/tex]

Vector (ordered pair - polar form)

[tex]\vec F = (30\,lbf, 25^{\circ})[/tex]

Sum of vectorial components (linear combination)

[tex]\vec F = (30\cdot \cos 25^{\circ})\cdot \hat{i} + (30\cdot \sin 25^{\circ})\cdot \hat{j}\,[N][/tex]

[tex]\vec F = 27.189\cdot \hat{i} + 12.679\cdot \hat{j}\,[N][/tex]

Hello! Would appreciate help!!

Find the value of x. Round to the
nearest tenth.

Help plzzzz I need the correct answers ASAP and that's my last marking period 4 and I'm in grade 12th

It's homework: Comprehension Questions - 3.1 Credit Basics:

Question 10: it's part 1 multiple choice questions and Part II: Analyze: Understanding Amortization

Janet just graduated from college, has a job she’s scheduled to begin in 3 months, and has decided to treat herself to 6 weeks of travel across South America before she buckles down and starts working full-time. To do the trip, she’s thinking of applying for a personal loan of $3500, and the bank she uses for her checking and savings account has offered her an interest rate of 24%. She has a goal of paying off the trip within two years, so she uses a Bankrate.com loan calculator and gets the following amortization schedule:


4) How many months does it take Janet to pay off her loan?


5) What is the total amount of interest Janet will pay at the end of the loan?

PLEASE HELP ASAP I have no idea how to solve this pls pls pls

a centre seat costs 25£ less than an aisle or window seat. A window or aisle seat costs a and a centre seat costs £271.complete the equation that describes this. how much does an aisle or window costs?​

What is the average rate of change of f(x)=x2+x−6 between x=1 and x=3 ?

A
5

B
–5

C
15

D
10

Mrs. McClure's famous peanut butter cookies call for 1 cup of peanut butter for every 1 2 of a cup of oil. Today, she wants to make a huge batch with 1 cup of oil. How much peanut butter should she use?

What are the measures of ∠1 and ∠2?

help asap pleaseeee !!!!!!

A small toy car costs $3. A large toy car costs 5 times as much as the small one.
Aaron wants to buy one of each. Which equation can he use to find the cost (a)
of the two cars?

the table describes some of the solutions of the inequality 3m>21. Which graph best describes the solutions of 3m>21?

Which expression shows the result of applying the distributive property to 9(2 + 5m)?
• 2 + 45m
O 18 + 45m
O 11 + 14m
18 + 5m

What is the volume of hemisphere with a radius of 8 ft rounded to the nearest tenth of cubic foot

What is the answer to this?-

What is the length of leg s of the triangle below?

= 1 cubic ft
What is the volume of the solid figure? Enter the answer in the box.

What percent of the data is between 30 and 50 on the number line?

its math algebra 1 i need help

what is the value of x?

Find the area of the figure.

anyone knowww thiusss ?




no scammers pleaseeee

h(x) = 18.75 - 4.53x What is the value of h(−11)?

Choose a number sentence is that illustrates distribute property of multiplication over addition 2×7+8 = 2+7×2+8

Janette measures the heights in inches of some of the flowers in her garden to see which ones are growing more. The heights are listed below. Which line plot represents the data correctly? 7 1 2 712 7 7 7 1 2 712 6 3 4 634 7 1 4 714 7 1 4 714 7 1 4 714 7 7 6 1 2 612 7 3 4 734 7 3 4 734 6 3 4 634 8 1 4 814 7 7 7 1 2 712 7 7 7 1 4 714 7 7 7 1 2 712 7 1 2 712

If Joe earns $38,000 a year: 
1. How much does he make a month?
2. If his budget per month is $3,200, can he afford that on his salary?

If /\PQR~/\SQT, find the value of x.

Convert 100° to radians. Will mark brainlist if correct

I need to turn this in ASAP please help!-

In the last three years, Frederico's basketball team won 50 more games than they lost. If they won 130 games, what was the ratio of wins to losses? Write the ratio in all three forms. 13/8, 13 to 8, 13:8 13/18. 13 to 18. 13:18 5/13, 5 to 13, 5:13 13/5. 13 to 5, 13:5​

Hi how’s your day ? Would you like to help me ?

The diameter of a circle measures 20 yd. What is the circumference of the circle?
Use 3.14 for it, and do not round your answer. Be sure to include the correct unit in your answer.
20 yd
yd

I need help!!!!!!!!!?