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3 years ago

Does a point have no dimension?

1 answer:

nataly862011 [7]3 years ago

4 0

A single point has no dimension.

A line of multiple points will have a length.
Points that creates a plane has two dimensions. length and width
Points that creates a solid shape has three dimensions. length, width, and height

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which of the functions have a range of real numbers greater than or equal to 1 or less than or equal to-1

lilavasa [31]

The question is incomplete. Here is the complete question:

Which of the functions have a range of all real numbers greater than or equal to 1 or less than or equal to -1? check all that apply.

A. $y=\sec x$

B. $y= \tan x$

C. $y= \cot x$

D. $y= \csc x$

Answer:

A. $y=\sec x$

D. $y=\csc x$

Step-by-step explanation:

Given:

The range is greater than or equal to 1 or less than or equal to -1.

The given choices are:

Choice A: $y=\sec x$

We know that, the $\sec x=\frac{1}{\cos x}$

The range of $\cos x$ is from -1 to 1 given as [-1, 1]. So,

$|\cos x|\leq 1\\\textrm{Taking reciprocal, the inequality sign changes}\\\frac{1}{|\cos x|}\geq 1\\|\sec x|\geq 1$

Therefore, on removing the absolute sign, we rewrite the secant function as:

$\sec x\leq -1\ or\ \sec x\geq 1\\$

Therefore, the range of $y=\sec x$ is all real numbers greater than or equal to 1 or less than or equal to-1.

Choice B: $y= \tan x$

We know that, the range of tangent function is all real numbers. So, choice B is incorrect.

Choice C: $y= \cot x$

We know that, the range of cotangent function is all real numbers. So, choice C is incorrect.

Choice D: $y=\csc x$

We know that, the $\csc x=\frac{1}{\sin x}$

The range of $\sin x$ is from -1 to 1 given as [-1, 1]. So,

$|\sin x|\leq 1\\\textrm{Taking reciprocal, the inequality sign changes}\\\frac{1}{|\sin x|}\geq 1\\|\csc x|\geq 1$

Therefore, on removing the absolute sign, we rewrite the cosecant function as:

$\csc x\leq -1\ or\ \csc x\geq 1\\$

Therefore, the range of $y=\csc x$ is all real numbers greater than or equal to 1 or less than or equal to-1.

6 0

3 years ago

What is 400 in expanded form (Warfare you get brainliest)

MAXImum [283]

Hey there, Lets solve your question together

Question - What is 400 in Expanded form ?

We know that expanded form is a spread out way to write a number by showing the value of each individual digit that contributes to make the full number.

Lets use an example to show expanded form

Number - 4,265

= 4 x 1,000 + 2 x 100 + 6 x 10 + 5 x 1

Now lets solve for the number 400 in expanded form.

The number "4" is in the hundreds place

The number "0" is in the tenths place

The number "0" is in the One's place

Therefore 400 in expanded form is 400+00+0.

 Hope this helps

5 0

3 years ago

Read 2 more answers

A cone is 10 inches tall and has a radius of 3 inches. What is the cone's volume?

Mandarinka [93]

The Answer is 94.2 cubic inches

7 0

2 years ago

Insert parenthesis to make the following true. 8 + 9x3 - 1 = 50

Serjik [45]

Answer:

(8+9) 3 - 1 = 50