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2 years ago

Why is 8.8 classified as a rational number?

1 answer:

4 0

A rational number can be expressed as the ratio of two integers.

$\frac{a}{b}$

Where a and b are integers and b is not equal to 0.

The rational number 8.8 can be expressed as two integers. Like $\frac{8.8}{1}$

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For what values of θ on the polar curve r=θ, with 0≤θ≤2π , are the tangent lines horizontal? Vertical?

Bond [772]

Given that $r=\theta$ , then $r'=1$

The slope of a tangent line in the polar coordinate is given by:

$m= \frac{r'\sin\theta+r\cos\theta}{r'\cos\theta-r\sin\theta}$

Thus, we have:

$m= \frac{\sin\theta+\theta\cos\theta}{\cos\theta-\theta\sin\theta}$

Part A:

For horizontal tangent lines, m = 0.

Thus, we have:

$\sin\theta+\theta\cos\theta=0 \\ \\ \theta\cos\theta=-\sin\theta \\ \\ \theta=- \frac{\sin\theta}{\cos\theta} =-\tan\theta$

Therefore, the <span>values of θ on the polar curve r = θ, with 0 ≤ θ ≤ 2π, such that the tangent lines are horizontal are:

</span><span>θ = 0

</span>θ = <span>2.02875783811043
</span>
θ = <span>4.91318043943488

Part B:

For vertical tangent lines, $\frac{1}{m} =0$

Thus, we have:

$\cos\theta-\theta\sin\theta=0 \\ \\ \Rightarrow\theta\sin\theta=\cos\theta \\ \\ \Rightarrow\theta= \frac{\cos\theta}{\sin\theta} =\sec\theta$

</span>Therefore, the <span>values of θ on the polar curve r = θ, with 0 ≤ θ ≤ 2π, such that the tangent lines are vertical are:

</span>θ = <span>4.91718592528713</span>

3 0

3 years ago

17 13/18 divided by 2 7/9

erik [133]

let's firstly convert the mixed fractions to improper fractions and then divide.

$\bf \stackrel{mixed}{17\frac{13}{18}}\implies \cfrac{17\cdot 18 +13}{18}\implies \stackrel{improper}{\cfrac{319}{18}}~\hfill \stackrel{mixed}{2\frac{7}{9}}\implies \cfrac{2\cdot 9+7}{9}\implies \stackrel{improper}{\cfrac{25}{9}} \\\\[-0.35em] ~\dotfill$

$\bf \cfrac{319}{18}\div \cfrac{25}{9}\implies \cfrac{319}{\underset{2}{~~\begin{matrix} 18 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}}\cdot \cfrac{\stackrel{1}{~~\begin{matrix} 9 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}}{25}\implies \cfrac{319}{50}\implies 6\frac{19}{50}$

7 0

2 years ago

Which stament is true

yanalaym [24]

Answer:

i think it A

Step-by-step explanation:

4 0

2 years ago

Read 2 more answers

‼️10 points‼️

Tamiku [17]

Answer:

<h3>The answer is option D.</h3>

Step-by-step explanation:

Equation of a line is y = mx + c

where

m is the slope

c is the y intercept

Slope of the line using points ( 5 , - 1) and

( - 5 , 2) is

m = 2+1/ -5-5 = - 3 / 10

Equation of the line using point ( 5 , - 1) is

y + 1 = -3/10(x - 5)

y = -3/10x + 3/2 - 1

The final answer is

Hope this helps you.

4 0

3 years ago

Subtract.

jeka94

(x+1)-(-2x-5)
=x+1+2x+5
=3x+6
=3(x+2)

7 0

2 years ago

Read 2 more answers