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3 years ago

Explain why domain restrictions for inverse trigonometric functions are necessary

Mathematics

1 answer:

luda_lava [24]3 years ago

8 0

ANSWER

The domain of the trigonometric functions must be restricted in order to become invertible.

EXPLANATION

Trigonometric functions are periodic functions.

This functions are not invertible over the entire domain of the real numbers because they fail the horizontal line test.

However if we restrict the domain of trigonometric functions, they will now pass the horizontal line test and hence become invertible.

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In the figure, what is the area of the shaded region?

Hatshy [7]

Use Pythagoras theorem
${(6 + 3)}^{2} + {x}^{2} = {15}^{2} \\ {x}^{2} = 144 \\ x = 12$
Two triangles are similar
$\frac{6}{9} = \frac{y}{12} \\ y = 8$
(6+3)*12/2 - 6*8 /2 = 30

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4 years ago

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The common difference in an arithmetic sequence is –2 and the first term is 47. What is the 29th term?

BlackZzzverrR [31]

An arithmetic sequence is an ordered list of numbers where the next number is found by adding on to the last number (ex: 2,5,8,11... is a sequence where 3 is added on to find the next number).

The equation for an arithmetic sequence is
$A_{n}=A_{1}+(n-1)d$

$A_{n}$ is the "n-th" number in the sequence (ex: is the first term in the sequence)
d is the number you add (common difference) to find the next number
The first number in the sequence is 47 so $A_{1}=47$
d=-2 because the question gives you that

$A_{n}=A_{1}+(n-1)d$
 $A_{29}=47+(29-1)(-2)$
 $A_{29}=47+(28)(-2)$
 $A_{29}=47+-56$
 $A_{29}=-9$

The answer is A. -9.

 

The answer is C. 158

For the second one, it gives you $A_{1}=4$ and $A_{}=18$
You can use this to find d

 $A_{n}=A_{1}+(n-1)d$
 $A_{3}=4+(3-1)d$
 $18=4+(3-1)d$
 $18=4+2d$
 $14=2d$
 $7=d$

Now you can just solve using the equation normally.
 $A_{n}=A_{1}+(n-1)d$
 $A_{23}=4+(23-1)(7)$
 $A_{23}=4+(22)(7)$
 $A_{23}=4+154$
 $A_{23}=158$

The answer is C. 158

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3 years ago

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Apply the square root principle to solve (x-5)^2-40=0

Nitella [24]

Answer: {5 ± 2√10, 5 - 2√10}

Step-by-step explanation: First isolate the binomial squared by adding 40 to both sides to get (x - 5)² = 40.

Next, square root both sides to get x - 5 = ± √40.

Notice that root of 40 can be broken down to 2√10.

So we have x - 5 = ± 2√10.

To get x by itself, add 5 to both sides to get x = 5 ± 2√10.

So our answer is just {5 ± 2√10, 5 - 2√10}.

As a matter of form, the number will always come before the

radical term in your answer to these types of problems.

In other words, we use 5 ± 2√10 instead of ± 2√10 + 5.

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3 years ago

Helpppppp!!!!!!!! pleaseee!!!!!!!!!!

vovangra [49]

Adding all of the areas together:

5 x 6 = 30

4 x 6 = 24

3 x 6 = 18

4^2 + 3^2 = 16 + 9 = 25(square root) = 5

" " = 5

30 + 24 + 18 + 5 + 5 = 82 ft^2

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3 years ago

What kind of dimension does a point have?

Crazy boy [7]

Should be zero, I believe.

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3 years ago

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Explain why domain restrictions for inverse trigonometric functions are necessary​

Explain why domain restrictions for inverse trigonometric functions are necessary