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
OlgaM077 [116]
3 years ago
14

find thge length of the line segment with endpoints (7,2) and (-4,2), and explain how you arrived at your solution.

Mathematics
1 answer:
nirvana33 [79]3 years ago
8 0
Since they have same y (2), it means this is a straight line.  what you need to do is just find the distance between -4 and 7. distance between -4 and 7 is 7-(-4)= 11

You might be interested in
-4 1/5+3 2/3+ -1 2/5
Paul [167]

Answer:

-1.9

Step-by-step explanation:

I rounded it to the tenth

8 0
3 years ago
Read 2 more answers
Find the product and express it in scientific notation.
Tresset [83]

Answer:

b

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
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
Gloria, Teresa, and Rebecca went to an office supply store. Gloria bought 8 pencils, 4 markers, and 6 erasers. Her total was
Korvikt [17]
The answer is $20.00
3 0
2 years ago
Is -4/-19 equivalent to -4/19
Kazeer [188]

Answer:

No

Step-by-step explanation: The first one is positive and the second one is negative

4 0
2 years ago
Read 2 more answers
Other questions:
  • <img src="https://tex.z-dn.net/?f=%20%5Cbinom%7B%20-%2036%7D%7B%20-%204%7D%20" id="TexFormula1" title=" \binom{ - 36}{ - 4} " al
    15·2 answers
  • Is 4,234 rounded to the nearest ten thousand 0?
    8·2 answers
  • In this given graph, f(x) is a polynomial modeling the Pi-guy, the math superhero, flying around. Write an equation in terms of
    8·1 answer
  • For 7/20 what is an equivalent fraction with a denominator of 100
    15·2 answers
  • I'm really confused I'm not that good in math
    6·1 answer
  • Does anyone know how to do this? please help me
    13·2 answers
  • What is the scale factor of this dilation
    11·1 answer
  • (CO 4) In a sample of 15 stuffed animals, you find that they weigh an average of 8.56 ounces with a standard deviation of 0.09 o
    6·1 answer
  • Select all names that apply to the number 3/7
    13·1 answer
  • Can you help me i will mark brainliest
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!