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3 years ago

Evaluate (2 * x - 4) for x = 2

Mathematics

1 answer:

Arturiano [62]3 years ago

7 0

Answer:

Step-by-step explanation:

The expression we are given is (2 * x - 4).

We need to find the value of expression when x = 2.

Let's substitute 2 in as x.

Now our expression is (2 * 2 - 4).

First, let's multiply our 2 with our substituted 2.

1. 2 * 2 = 4

We're left with (4 - 4).

Finally, let's evaluate this expression.

2. (4 - 4) = 0.

Our answer is 0.

So (2 * x - 4) when x = 2 is 0.

Feel free to give brainliest.

Have a great day!

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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

Please help me on this! will give u brainliest tyy.

Y_Kistochka [10]

Answer:

A. The balloon is at its initial height

B. The boxer is 0 pounds from her starter weight

C. The company's size is smaller

Step-by-step explanation:

For A, -30+30 is equal to 0 so its gonna be the same height it was before.

For B, Gaining 7 pounds and losing 7 pounds means you are neither bitter or smaller. (-7+7=0)

For C, Losing 15 employees and gaining none means that there are less than there were previous meaning the company is now smaller.

Hope this helps.

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2 years ago

In the Gospels 8 8 40 But now you are seeking to kill me, while I am a man who has spoken to you of the truth which he heard fro

Alecsey [184]

Step-by-step explanation:

Jesus is God! God is shown to us in 3 forms, God, the Holy Spirit, and Jesus (human)! there aren't 3 Gods, just 1 with three different forms! ask me any questions!

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2 years ago

!! PLEASE HELP QUICKLY 20 POINTS !! Evaluate 4 - 0.25g + 0.5h when g=10 and h=5

Sonja [21]

Step-by-step explanation:

4- 0.25 + 0.5h

0.25g= 2.5

4- 2.5 = 1.5

0.5h = 2.5

4- 2.5 + 2.5

addition is first

2.5+2.5 = 5

4-5 =-1

I honestly don't know if that's right but I tried aha x

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3 years ago

Eight people, female and male, were surveyed about their choice of car color, green or blue. The table shows the choices they ma

Rom4ik [11]

The two-way table correctly compares the categorical data would be the second choice or letter B:

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I hope my answer has come to your help. God bless and have a nice day ahead!

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3 years ago

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