Ask question

Ask question

All categories

3 years ago

6

A two-dimensional vector has an x-component of 10.3~\text{meters}10.3 meters and a y-component of 4.30~\text{meters}4.30 meters.

Calculate the angle (in degrees) that this two-dimensional vector makes with the positive x-axis.

1 answer:

Georgia [21]3 years ago

4 0

9514 1404 393

Answer:

23°

Step-by-step explanation:

The angle a vector makes relative to the +x axis is found as ...

α = arctan(y/x) = arctan(4.30/10.3) ≈ 22.66°

The angle is about 23°.

__

<em>Additional comment</em>

This vector resides in the first quadrant, so no adjustment of the angle is needed. In other quadrants, 180° may need to be added or subtracted from the angle given by the arctan function to arrive at the correct value. (Some calculators and spreadsheets have an ATAN2(x, y) function that takes signs into account.)

You might be interested in

An ellipse has a center at the origin, a vertex along the major axis at (20, 0), and a focus at (16, 0). the equation of the ell

olga_2 [115]

If the center is at (0, 0) and the vertex is at (20, 0), then the distance, a, is the length from the center to the vertex, 20. The distance from the center to the focus is c. The distance from the center to the focus is 16, so c = 16. The formula we use to find the focus is $c^2=a^2-b^2$ . We have our c value and our a value, so we will sub in those to find b. $16^2=20^2-b^2$ and 256 = 400 - b^2. -b^2 = -144, so b = 12. There you go!

5 0

3 years ago

Read 2 more answers

I NEED HELP FOR THIS QUESTION PLSSS

defon

Answer: 132 degrees

5 0

2 years ago

Read 2 more answers

A toy is shaped as a triangular prism. The toy has a

Anettt [7]

Answer:

$\huge\boxed{\sf h = 6.75 \ in.}$

Step-by-step explanation:

<u>Given Data:</u>

Base area = $A_{B}$ = 108 in.²

Volume = V = 729 in.³

<u>Required:</u>

Height = h = ?

<u>Formula:</u>

$V=A_{B}h$

<u>Solution:</u>

For h, rearranging formula:

$\displaystyle h = \frac{V}{A_{B}} \\\\h =\frac{729 \ in.^3}{108 \ in.^2} \\\\h = 6.75 \ in.\\\\\rule[225]{225}{2}$

4 0

2 years ago

On her math test, Anna got I 32 questions out of 36 | questions correct. About | what percent of the questions did Anna get corr

Scilla [17]

Answer:

%88.88... and on and on

Formula Nonsense: percentage = b/l then *100 add % sign

so P= 32/36 so 0.888....*100= 88.88... so she made 88%

6 0

2 years ago

You decide to enter in a rowing competition. To train, you go to the boat house and begin rolling down stream. You row for the s

fredd [130]

Answer:

Time spent rowing down stream $=100\ seconds$

Speed of boat in still water $=14\ ms^{-1}$

Step-by-step explanation:

Let speed of boat in still water be $= x\ ms^{-1}$

Speed of current $= 10\ ms^{-1}$

Speed of boat down stream = $\textrm{Speed of boat in still water +Speed of current}= (x+10)\ ms^{-1}$

Distance rowed down stream = 2400 m

Time spent rowing down stream = $\frac{Distance}{Speed}=\frac{2400}{x+10}\ s$ = $\frac{Distance}{Speed}=\frac{2400}{x+10}\ s$

Speed of boat up stream = $\textrm{Speed of boat in still water -Speed of current}= (x-10)\ ms^{-1}$

Distance rowed up stream = $\frac{1}{6} \textrm{ of distance rowed downstream}=\frac{1}{6}\times 2400 = 400\ m$

Time spent rowing up stream = $\frac{Distance}{Speed}=\frac{400}{x-10}\ s$

We know that,

$\textrm{Time spent rowing down stream =Time spent rowing up stream}$

So,

$\frac{2400}{x+10}=\frac{400}{x-10}$

Cross multiplying

$2400(x-10)=400(x+10)$

Dividing both sides by $400$

$\frac{2400(x-10)}{400}=\frac{400(x+10)}{400}$

$6(x-10)=x+10$

$6x-60=x+10$

Adding 60 to both sides.

$6x-60+60=x+10+60$

$6x=x+70$

Subtracting both sides by $x$

$6x-x=x+70-x$

$5x=70$

Dividing both sides by 5.

$\frac{5x}{5}=\frac{70}{5}$

∴ $x=14$

Speed of boat in still water $=14\ ms^-1$

Time spent rowing down stream = $\frac{2400}{14+10}=\frac{2400}{24}=100\ s$

3 0

2 years ago