1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
kolbaska11 [484]
2 years ago
5

Use five different colors to paint the four rectangles A, B, C and D shown in the figure. No two rectangles sharing an edge can

be the same color. How many ways are there to color the rectangles?

Mathematics
1 answer:
GenaCL600 [577]2 years ago
8 0

There are 120 ways to color the 4 rectangles

<h3>How to determine the number of ways?</h3>

The given parameters are:

Paints, n = 5

Rectangles, = 4

The number of ways to color the rectangles is

Ways = ^nP_r

This gives

Ways = ^5P_4

Apply the permutation formula

Ways = \frac{5!}{1!}

Evaluate the expression

Ways = 120

Hence, there are 120 ways to color the 4 rectangles

Read more about permutation at:

brainly.com/question/1216161

#SPJ1

You might be interested in
(Do only the number line) just tell me what to write after the 0 I don't understand the number line
pantera1 [17]
One- twelfth for the first tiny line and the two-twelfth and so on until u reach 1
6 0
3 years ago
Read 2 more answers
A baseball team lost 4 more games than it won. If the team played 46 games, how many did it lose? How many did it win?
blsea [12.9K]
The team won 27 games and lost 19
4 0
3 years ago
If you could do this you’re the best and you’ll also get a lot of points thanks
Andre45 [30]

Answer:

take the answer on picture which I attached with your question

3 0
3 years ago
interpret r(t) as the position of a moving object at time t. Find the curvature of the path and determine thetangential and norm
Igoryamba

Answer:

The curvature is \kappa=1

The tangential component of acceleration is a_{\boldsymbol{T}}=0

The normal component of acceleration is a_{\boldsymbol{N}}=1 (2)^2=4

Step-by-step explanation:

To find the curvature of the path we are going to use this formula:

\kappa=\frac{||d\boldsymbol{T}/dt||}{ds/dt}

where

\boldsymbol{T}} is the unit tangent vector.

\frac{ds}{dt}=|| \boldsymbol{r}'(t)}|| is the speed of the object

We need to find \boldsymbol{r}'(t), we know that \boldsymbol{r}(t)=cos \:2t \:\boldsymbol{i}+sin \:2t \:\boldsymbol{j}+ \:\boldsymbol{k} so

\boldsymbol{r}'(t)=\frac{d}{dt}\left(cos\left(2t\right)\right)\:\boldsymbol{i}+\frac{d}{dt}\left(sin\left(2t\right)\right)\:\boldsymbol{j}+\frac{d}{dt}\left(1)\right\:\boldsymbol{k}\\\boldsymbol{r}'(t)=-2\sin \left(2t\right)\boldsymbol{i}+2\cos \left(2t\right)\boldsymbol{j}

Next , we find the magnitude of derivative of the position vector

|| \boldsymbol{r}'(t)}||=\sqrt{(-2\sin \left(2t\right))^2+(2\cos \left(2t\right))^2} \\|| \boldsymbol{r}'(t)}||=\sqrt{2^2\sin ^2\left(2t\right)+2^2\cos ^2\left(2t\right)}\\|| \boldsymbol{r}'(t)}||=\sqrt{4\left(\sin ^2\left(2t\right)+\cos ^2\left(2t\right)\right)}\\|| \boldsymbol{r}'(t)}||=\sqrt{4}\sqrt{\sin ^2\left(2t\right)+\cos ^2\left(2t\right)}\\\\\mathrm{Use\:the\:following\:identity}:\quad \cos ^2\left(x\right)+\sin ^2\left(x\right)=1\\\\|| \boldsymbol{r}'(t)}||=2\sqrt{1}=2

The unit tangent vector is defined by

\boldsymbol{T}}=\frac{\boldsymbol{r}'(t)}{||\boldsymbol{r}'(t)||}

\boldsymbol{T}}=\frac{-2\sin \left(2t\right)\boldsymbol{i}+2\cos \left(2t\right)\boldsymbol{j}}{2} =\sin \left(2t\right)+\cos \left(2t\right)

We need to find the derivative of unit tangent vector

\boldsymbol{T}'=\frac{d}{dt}(\sin \left(2t\right)\boldsymbol{i}+\cos \left(2t\right)\boldsymbol{j}) \\\boldsymbol{T}'=-2\cdot(\sin \left(2t\right)\boldsymbol{i}+\cos \left(2t\right)\boldsymbol{j})

And the magnitude of the derivative of unit tangent vector is

||\boldsymbol{T}'||=2\sqrt{\cos ^2\left(x\right)+\sin ^2\left(x\right)} =2

The curvature is

\kappa=\frac{||d\boldsymbol{T}/dt||}{ds/dt}=\frac{2}{2} =1

The tangential component of acceleration is given by the formula

a_{\boldsymbol{T}}=\frac{d^2s}{dt^2}

We know that \frac{ds}{dt}=|| \boldsymbol{r}'(t)}|| and ||\boldsymbol{r}'(t)}||=2

\frac{d}{dt}\left(2\right)\: = 0 so

a_{\boldsymbol{T}}=0

The normal component of acceleration is given by the formula

a_{\boldsymbol{N}}=\kappa (\frac{ds}{dt})^2

We know that \kappa=1 and \frac{ds}{dt}=2 so

a_{\boldsymbol{N}}=1 (2)^2=4

3 0
3 years ago
If the diameter of a circle is 20 cm, what is the area?
katovenus [111]

Answer:

A = 100 pi cm^2

Step-by-step explanation:

A = pi(r^2)

A = pi(10^2)

A = pi(100)

A = 314.16 '

Convert to pi units.

314.16 ---> 100pi cm^2

3 0
3 years ago
Read 2 more answers
Other questions:
  • What's the answer and how do you do it?
    5·2 answers
  • Simplify the expression (-4)(9)/(-6)<br><br>6<br><br>–36<br><br>36<br><br>–6
    15·1 answer
  • Scott and his family want to hike a trail that is 1,365 miles long. They will hike equal parts of the trail on 12 different hiki
    11·1 answer
  • HELPPPP PLEASEEEEeeeeee
    13·1 answer
  • How do you do two x to the second plus nine x minus five equal zero
    5·1 answer
  • The heights of baby giraffe are normally distributed with a mean of 63.6 inches and a standard deviation of 2.5 inches. If 100 b
    15·1 answer
  • Ordinary quarters and a fake quarter with two heads are placed in a hat. One-quarter is selected at random and tossed twice. If
    9·1 answer
  • -9 ( greater less than)<br> (&gt; with a line under it) <br> 2m + 2 - 3
    7·1 answer
  • Need help with y= <br><br> Thank you
    8·1 answer
  • What is 19.254 rounded to the nearest tenth and the nearest hundredth?
    5·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!