Please simplify: √4ab^3c^8

Why do all transformation preserve distance

yuradex [85]

Well, a distance-preserving transformation is called a rigid motion, and the name suggests that it <em>moves the points of the plane around in a rigid fashion.</em>

A transformation is distance-preserving if the distance between the images of any two points and the distance between the two original points are equal.

If that's confusing, I get it; basically if you transform something, the points from the transformation are image points. Take the distance from a pair of image points, and take the distance from a pair of original points, and they should be the same for a <em>rigid </em>motion.

I keep emphasizing this b/c not all transformations preserve distance; a dilation can grow or shrink things. But if you didn't go over dilations, don't say nothin XD

7 0

3 years ago

The curves r1(t) = 2t, t2, t4 and r2(t) = sin t, sin 5t, 2t intersect at the origin. Find their angle of intersection, θ, correc

masya89 [10]

Answer:

Therefore the angle of intersection is $\theta =79.48^\circ$

Step-by-step explanation:

Angle at the intersection point of two carve is the angle of the tangents at that point.

Given,

$r_1(t)=(2t,t^2,t^4)$

and $r_2(t)=(sin t , sin5t, 2t)$

To find the tangent of a carve , we have to differentiate the carve.

$r'_1(t)=(2,2t,4t^3)$

The tangent at (0,0,0) is [ since the intersection point is (0,0,0)]

$r'_1(0)=(2,0,0)$ [ putting t= 0]

$|r'_1(0)|=\sqrt{2^2+0^2+0^2} =2$

Again,

$r'_2(t)=(cos t ,5 cos5t, 2)$

The tangent at (0,0,0) is

$r'_2(0)=(1 ,5, 2)$ [ putting t= 0]

$|r'_1(0)|=\sqrt{1^2+5^2+2^2} =\sqrt{30}$

If θ is angle between tangent, then

$cos \theta =\frac{r'_1(0).r'_2(0)}{|r'_1(0)|.|r'_2(0)|}$

$\Rightarrow cos \theta =\frac{(2,0,0).(1,5,2)}{2.\sqrt{30} }$

$\Rightarrow cos \theta =\frac{2}{2\sqrt{30} }$

$\Rightarrow cos \theta =\frac{1}{\sqrt{30} }$

$\Rightarrow \theta =cos^{-1}\frac{1}{\sqrt{30} }$

$\Rightarrow \theta =79.48^\circ$

Therefore the angle of intersection is $\theta =79.48^\circ$ .

8 0

3 years ago

a dog food company sells its canned dog food to stores for $0.35 per can. one of the stores sells the can of dog food for $0.79.

iris [78.8K]

To answer your question its 27.65

6 0

3 years ago

A manager of a grocery store wants to determine if consumers are spending

ololo11 [35]

Answer:

1. The error in the assumption is taking the sample mean, $\bar x$ , as being equal to the population mean, μ

2. To correct the error, the manager will need to generate the confidence interval based on the population standard deviation on the acceptable values of the mean using the following relation;

$CI=\bar{x}\pm z\frac{\sigma}{\sqrt{n}}$

Step-by-step explanation:

We note that from the central limit theorem as the size of the sample, n, becomes more and more larger, the mean of the sample, $\bar x$ , approaches that of the population mean, μ, therefore as the grocery store manager uses the sample mean as the population mean's point estimate an error will be observed based on the size of the sample compared to the population, where the difference between the two means (the population mean and the sample mean) is $\left | \bar{x} - \mu \right |$

1. The error in the assumption is taking the sample mean, $\bar x$ , as being equal to the population mean, μ

2. To correct the error, the manager will need to generate the confidence interval based on the population standard deviation on the acceptable values of the mean using the following relation;

$CI=\bar{x}\pm z\frac{\sigma}{\sqrt{n}}$

Where:

σ = Population standard deviation = $30

z = z value at 95% confidence level = 1.96

$\bar x$ = Sample mean $160

n = Sample size = 10

Plugging in the values, we have;

$141.4 < $\bar x$ < $178.6

Hence the expected value of the mean should be between $141.4 and $178.6.

7 0

3 years ago

Theo can run 1/2 mile in 1/10 hour. If theo continues at this rate how far can he run in a hour?

kirill [66]

1/2 mile x 10 = 5 miles

5 0

3 years ago