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2 years ago

5

The half-life of a radioactive kind of rhythium is 1 year. If you start with 64 grams of it, how much will be left after 3 years

1 answer:

finlep [7]2 years ago

5 0

Answer:

Step-by-step explanation:

64×0.5³ = 8 grams

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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

State the degree for the polynomial:

Ivahew [28]

Answer:

4

Step-by-step explanation:

the degree of the polynomial is the highest degree of any of the terms.

7 0

2 years ago

Read 2 more answers

Need Help Badly!!!!!! The dot plot below shows the number of books 26 students read in a month: Dot plot labeled Number of Books

algol13

The dot plot below shows the number of books 26 students read in a month:

<span>Is the median or the mean a better center for this data and why? help plz

</span>

7 0

3 years ago

A regular octagon has a radius of 6 ft and a side length of

Svetlanka [38]

Answer:

<h2>Area of the regular octagon is approximately 102ft²</h2>

Step-by-step explanation:

Given the radius and length of a side of regular octagon as shown;

radius = 6ft and length of side = 4.6ft

Area of a regular octagon is expressed as $A = 2(1+\sqrt{2} )a^{2}$ where a is the length of one side. Given a = 4.6ft

Area = $A = 2(1+\sqrt{2} )(4.6)^{2}\\$

$= 2(1+\sqrt{2} )*21.16\\= (2+2\sqrt{2})*21.16\\ = 4.83*21.16\\= 102.20ft^{2} \\$

Area of the regular octagon is approximately 102ft²

3 0

3 years ago

A milligram is what fraction of a kilogram

pishuonlain [190]

The answer is 1/1000000

4 0

3 years ago