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3 years ago

How do I find a parallel equation?

1 answer:

6 0

Parallel are two equations that have the same slope but different y intercepts.

If the y intercepts are also the same, it is just the same line.

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HELP PLS IM TIMED What is the result of 96 divided by 6? Use the model to find the answer.

jeka94

Answer:

Step-by-step explanation:

9 divided by 6 is 1 but leaves 3 leaving 36 divide that by 6 so 16

6 0

2 years ago

Read 2 more answers

Find x, if the distance end points is (x,1) and (4,4) with the total distance is the square root of 10.

Alex Ar [27]

Okay, take a look at diagram 1 (I know it's rubbish I did it on paint :D), this shows all the information you've given in the question. The two coordinates and the distance between them.

Now if we draw additional lines on this diagram, we can make a right-angled triangle (this is on diagram 2). We can also work out the lengths of the additional sides because we know both coordinates at the end-points of the additional lines.

Finally because this is a right-angled triangle, Pythagoras' theorem must apply to its sides meaning
$( \sqrt{10} )^2 = (x-4)^2 + 3^2$
$10 = (x-4)^2 + 9$
$(x-4)^2 = 1 \Rightarrow x-4 = 1$
therefore x=5.

3 0

2 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

"Four more than a number is at least 22"

Reika [66]

Answer:

4 + x < 22

that's what the equation is

Step-by-step explanation:

a number just means a variable ex: x, y

at least is this : <

so 4 + x < 22

5 0

2 years ago

Read 2 more answers

Fill in the Blanks:

Damm [24]

Answer:

Unlike fractions: Fractions with different denominators are called, unlike fractions.

In case of two equivalent fractions, the product of the numerator of one fraction and denominator of the second fraction is equal to the product of the denominator of the first fraction and numerator of the second fraction.

A fraction is said to be in form if its numerator and denominator are 5. To add or subtract like fractions, we add or subtract the keeping the same.

Step-by-step explanation:

4 POINT I DONT NO

6 0

2 years ago

How do I find a parallel equation?​

How do I find a parallel equation?