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Schach [20]
3 years ago
10

A plane is an undefined term because it

Mathematics
1 answer:
horrorfan [7]3 years ago
5 0

A plane is an undefined term because:

Let us consider the options.

Option 1: can be named using three non collinear point.

This is not the correct answer because  a plane is a flat, two-dimensional surface that extends infinitely far. Therefore, it is undefined because it is a flat surface that extends indefinitely in all directions.

Option 2: is described generally, not using a formal definition.

This is not the correct answer because  a plane is a flat, two-dimensional surface that extends infinitely far. Therefore, it is undefined because it is a flat surface that extends indefinitely in all directions.

Option 3: is where other geometric shapes can be constructed.

This is not the correct answer because  a plane is a flat, two-dimensional surface that extends infinitely far. Therefore, it is undefined because it is a flat surface that extends indefinitely in all directions.

Option 4: is a flat surface that extends indefinitely in all directions.

This is the correct answer as plane is a flat surface that extends indefinitely in all directions.

Therefore, option 4 is the correct answer.

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What is the image of (1,0) after a counterclockwise rotation of 60 degrees?
Anestetic [448]

Answer:

\vec s = \left(\frac{1}{2},\frac{\sqrt{3}}{2}  \right)

Step-by-step explanation:

The coordinate has the following polar form:

\vec r = (1, 0^{\circ})

The image of the coordinate rotated counterclockwise 60° is:

\vec s = (1, 60^{\circ})

Its equivalent form in rectangular coordinates is:

\vec s = (1\cdot \cos 60^{\circ}, 1 \cdot \sin 60^{\circ})

\vec s = \left(\frac{1}{2},\frac{\sqrt{3}}{2}  \right)

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3 years ago
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6 0
3 years ago
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The table represents the temperature of a cup of coffee over time.
Harrizon [31]

Answer: first choice, exponential, because there is a relatively consistent multiplicative rate of change.

Explanation:

1) I have attached the figure with the data table that represents the temperature of a cup of coffee over time.

These are the data:

Time (min) ------ Temperature (°F)

0 ----------------------- 200

10 ---------------------- 180

20 --------------------- 163

30 --------------------- 146

40 ---------------------131

50 -------------------- 118

60 -------------------- 107

2) Since, the increase in time is constant, while the decrease in temperaute is not, you know that it is not linear.

3) The other two options involve exponential models.

The exponential models have a constant multiplicative rate of change, not additive. Therefore, the only feasible choice is the first one: temperature of a cup of coffee over time.

4) You can prove it:

i) Exponential models have the general form y = A [r]ˣ, where B is r is the multiplicative rate of change: any value is equal to the prior value multiplied by r:

y₁ = A [r]¹

y₂ = A[r]²

y₂ / y1 = r ← as you see this is the constant multiplicative rate of change.

ii) Test some data:

180 / 200 = 0.9

163 / 180 ≈ 0.906 ≈ 0.9

146 / 163 ≈ 0.896 ≈ 0.9

131 / 146 ≈ 0.897 ≈ 0.9

118 / 131 ≈ 0.901 ≈ 0.9

107 / 118 ≈ 0.907 ≈ 0.9

As you see all the data of the table have a relatively consistent multiplicative rate of change, which proves that the temperature follows an exponential decay; so the right choice is the first one.

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3 years ago
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