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BARSIC [14]
3 years ago
13

Consider the spiral given by c(t) = (e2t cos(2t), e2t sin(2t)). Show that the angle between c and c' is constant. c'(t) = _____L

et θ be the angle between c and c'. Using the dot product rule we have the following. c(t) · c'(t) = c(t) · c'(t) cos(θ) 2e4t =________ cos(θ)

Mathematics
1 answer:
Tcecarenko [31]3 years ago
8 0

Answer:

angle is 45° which is constant

Step-by-step explanation:

We use formula for two vectors <u>a </u>and <u>b</u>    to calculate angle θ between them by formula

cos θ =  <u>a .</u> <u>b</u>  / magnitude of <u>a </u>  ×  magnitude of <u>b</u>

<u>Please see the attached file</u>

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In a data set, the proportion of items that are in a particular category is called the.
Neporo4naja [7]

In a data set, the proportion of items that are in a particular category is called the Relative Frequency

<h3>What is Relative Frequency ?</h3>

Frequency mean how often an event can occur , an relative frequency means how many times that event will occur with respect to the total number of events.

For determining Relative frequency , we need to know the frequency for a particular event and the total number of event.

The proportion of items that are in a particular category is called the <u>Relative Frequency</u>.

To know more about Relative Frequency

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8 0
2 years ago
Kevlar epoxy is a material used on the NASA space shuttles. Strands of this epoxy were tested at the 90% breaking strength. The
Ratling [72]

Answer:

range = 7.87

X = 62.12, X²= 164.3516

mean = 1.2424

variance = 1.779

standard deviation = 1.33379

coefficient of variation = 107.3559%

Step-by-step explanation:

a.) The range =

highest number - lowest number

= 7.89 - 0.02

= 7.87

b.) from the attachment I solved for X and X²

∑X = 62.12

∑X² = 164.3516

c.)

the mean = ∑x/n

n = 50

= 62.12/50

= 1.2424

variance =

σ² = [∑x²-(∑x)²/n] / n-1

= [164.3516 - (62.12)²/50] / 50-1

= 164.3516 - 77.17788/49

= 87.173712/49

= 1.779

standard deviation = √σ

= √1.779

= 1.33379

d. coefficient of variation

= σ/mean * 100

= 1.33379/1.2424 * 100

= 107.3559

This number tells us that the the standard deviation of the time to failure is larger than the average time. option 3 is the correc4 answer here

6 0
3 years ago
Select the scenarios that correctly represent the given graph.
bogdanovich [222]
We have to write down some values that we can see from the graph. At x=0, the value is 100. At x=1, the y-value is 150 and at x=2 the graph has a value of a little over 200. We see also that this is an exponential graph, so we might assume that there is a specific ratio from each x-value to the next. We get that this ratio is 150/100=1.5. Hence, the quantity increases by 1.5 or 150% every time we add 1 to the x-coordinate. The 2 first sentences are correct. If an amount increases by 50% after a year, at the end of the year there is 150% of it (we need to add the initial capital which is 100%). Thus the graph here has as x-axis years and as y-axis money. The same concept holds for the 2nd sentence. The 3rd sentence is wrong because the value here is not multiplied but added. This would produce a linear graph. Sentence 4 has the wrong ratio; if that was true, then at x=1 we would have 200 oranges, not 150. For the same reason option 5 is wrong; 150*100=15000, not 150.
6 0
3 years ago
Please help me because I don't understand how to do it.:)
nadezda [96]

Answer:

231.7  cm^2

Step-by-step explanation:

We can find the area  by adding the area of the rectangle to the area of the 2 triangles.

The rectangle is

7+7+7 by 9

21 by 9

A = length * width

A = 21*9

A = 189

The triangles are identical so we find the area of one of them and multiply by 2

The base is 7 and the height is 6.1

A = 1/2 b*h

but since we have 2 of them

2A = 2*1/2 b*h

2A = b*h

2A = (7* 6.1)

     = 42.7


Add the rectangles area to the area of the two triangles

189 + 42.7

231.7  cm^2

6 0
4 years ago
Describe a point. what could you use as a model of a point ?
NNADVOKAT [17]

A point is an exact location.
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It has no area or volume.
It has no mass, shape, or other physical properties.

As a model ...

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     It looks like this  ==> ·

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-- You could use the tiny dot that the point of
a very sharp pencil makes on paper.

-- You could use the point of a pin.

-- You could use the tiny hole that the point of
a pin makes in a sheet of paper.

These are all bigger than a real point.  They all have a little bit of size,
length, width, height, and you can see them.  But they get the idea across.
(They 'make the point'.)
6 0
3 years ago
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