N is the set of odd natural numbers greater than 11 and less than 21. Use set notation to write the elements of N. N

Mathematics

2 answers:

timurjin [86]3 years ago

5 0

<h3>Answer:</h3>

N is set of Odd Natural Number greater than 11 and less than 21.

$\sf N = \{x:x\:is\:an\:integer\:and\:11 < x < 21\}$

$\textsf{Integers = ...8, 9, 10,$\underbrace{\textsf{ 11, 12, 13, 14, 15, 16, 17, 18, 19, 20,}}_{\sf Required\:Integers}$ 21, 22...}$

⠀⠀⠀ $\rule{160}{0.8}$

☢ Odd Number : Those Integers (never a fraction) which leaves remainder after Dividing by 2 are called Odd Number.

⠀

✩ Odd Number between 11 to 21 :

$:\implies\textsf{13, 15, 17, 19}\\\\\\:\implies\textsf{N = \{13, 15, 17, 19\}}$

S_A_V [24]3 years ago

4 0

Answer:

N = {13, 15, 17, 19}

Step-by-step explanation:

The natural numbers greater than 11 and less than 21 are:

12, 13, 14, 15, 16, 17, 18, 19 and 20

Odd numbers are numbers that have remainders when divided by 2. Out of the numbers above, the numbers with remainders when divided by 2 are 13, 15, 17 and 19.

Since N is the set of odd natural numbers greater than 11 and less than 21,

N = {13, 15, 17, 19}

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Find the roots of h(t) = (139kt)^2 − 69t + 80

Sonbull [250]

Answer:

The positive value of $k$ will result in exactly one real root is approximately 0.028.

Step-by-step explanation:

Let $h(t) = 19321\cdot k^{2}\cdot t^{2}-69\cdot t +80$ , roots are those values of $t$ so that $h(t) = 0$ . That is:

$19321\cdot k^{2}\cdot t^{2}-69\cdot t + 80=0$ (1)

Roots are determined analytically by the Quadratic Formula:

$t = \frac{69\pm \sqrt{4761-6182720\cdot k^{2} }}{38642}$

$t = \frac{69}{38642} \pm \sqrt{\frac{4761}{1493204164}-\frac{80\cdot k^{2}}{19321} }$

The smaller root is $t = \frac{69}{38642} - \sqrt{\frac{4761}{1493204164}-\frac{80\cdot k^{2}}{19321} }$ , and the larger root is $t = \frac{69}{38642} + \sqrt{\frac{4761}{1493204164}-\frac{80\cdot k^{2}}{19321} }$ .

$h(t) = 19321\cdot k^{2}\cdot t^{2}-69\cdot t +80$ has one real root when $\frac{4761}{1493204164}-\frac{80\cdot k^{2}}{19321} = 0$ . Then, we solve the discriminant for $k$ :