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3 years ago

Analyze the set below and complete the instructions that follow.

Mathematics

1 answer:

IrinaVladis [17]3 years ago

7 0

Answer:

Step-by-step explanation:

Given: the set is defined as $C=\left \{ x|x$

To find: Set builder form of the complement of the set C.

Solution:

A set is a well-defined collection of objects. Set-builder form is used to denote the elements of the set. This form can also be used to express sets using an interval or an equation.

Complement of set A refers to elements not in A.

For $C=\left \{ x|x$ ,

$C^c=\left \{ x|x\geq -42 \right \}$

Option C is correct.

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find the values of the six trigonometric functions for angle theta in standard position if a point with the coordinates (1, -8)

frutty [35]

Answer:

cosФ = $\frac{1}{\sqrt{65}}$ , sinФ = $-\frac{8}{\sqrt{65}}$ , tanФ = -8, secФ = $\sqrt{65}$ , cscФ = $-\frac{\sqrt{65}}{8}$ , cotФ = $-\frac{1}{8}$

Step-by-step explanation:

If a point (x, y) lies on the terminal side of angle Ф in standard position, then the six trigonometry functions are:

cosФ = $\frac{x}{r}$
sinФ = $\frac{y}{r}$
tanФ = $\frac{y}{x}$
secФ = $\frac{r}{x}$
cscФ = $\frac{r}{y}$
cotФ = $\frac{x}{y}$

Where r = $\sqrt{x^{2}+y^{2} }$ (the length of the terminal side from the origin to point (x, y)

You should find the quadrant of (x, y) to adjust the sign of each function

∵ Point (1, -8) lies on the terminal side of angle Ф in standard position

∵ x is positive and y is negative

→ That means the point lies on the 4th quadrant

∴ Angle Ф is on the 4th quadrant

∵ In the 4th quadrant cosФ and secФ only have positive values

∴ sinФ, secФ, tanФ, and cotФ have negative values

→ let us find r

∵ r = $\sqrt{x^{2}+y^{2} }$

∵ x = 1 and y = -8

∴ r = $\sqrt{x} \sqrt{(1)^{2}+(-8)^{2}}=\sqrt{1+64}=\sqrt{65}$

→ Use the rules above to find the six trigonometric functions of Ф

∵ cosФ = $\frac{x}{r}$

∴ cosФ = $\frac{1}{\sqrt{65}}$

∵ sinФ = $\frac{y}{r}$

∴ sinФ = $-\frac{8}{\sqrt{65}}$

∵ tanФ = $\frac{y}{x}$

∴ tanФ = $-\frac{8}{1}$ = -8

∵ secФ = $\frac{r}{x}$

∴ secФ = $\frac{\sqrt{65}}{1}$ = $\sqrt{65}$

∵ cscФ = $\frac{r}{y}$

∴ cscФ = $-\frac{\sqrt{65}}{8}$

∵ cotФ = $\frac{x}{y}$

∴ cotФ = $-\frac{1}{8}$

8 0

3 years ago

Is the expression completely factored: (5 - x)(6 - 5x)

Naya [18.7K]

Answer:

5x² - 31x + 30

Step-by-step explanation:

(5 - x)(6 - 5x)

= 30 - 25x - 6x + 5x²

= 30 - 31x + 5x²

= 5x² - 31x + 30

7 0

3 years ago

PLZ SOMEONE HELP ME I NEED HELP PLEASEE

dezoksy [38]

Answer:

about 35 years rounding its 36

Step-by-step explanation:

i converted evrything to positive and did 1371 minus 1296 to get 75 and i divided that by 2.0834

4 0

3 years ago

Read 2 more answers

What are the answers for both of these what are zeros help

Archy [21]

Graph 5- e)
graph 6- b)

4 0

3 years ago

93÷3= using subtraction to solve

m_a_m_a [10]

Answer:

=31 *The answer shouldn't have a remainder.*

Explanation:

Divide by the numbers.

$93/3=31$

$93/31=3$

Multiply by the numbers.

$31*3=93$

$3*31=93$

Hope this helps!

Thanks!

Have a great day!

6 0

3 years ago