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Contact [7]
3 years ago
13

Lim as x approaches 2pi/3 from the right of csc x, solve by substituting csc with sin

Mathematics
1 answer:
Zielflug [23.3K]3 years ago
5 0
\bf csc(\theta)=\cfrac{1}{sin(\theta)}
\\\\
-------------------------------\\\\
\lim\limits_{x\to \frac{2\pi }{3}^+}~csc(x)\implies \lim\limits_{x\to \frac{2\pi }{3}^+}~\cfrac{1}{sin(x)}\implies \cfrac{1}{sin\left( \frac{2\pi }{3} \right)}\implies \cfrac{1}{\frac{\sqrt{3}}{2}}\implies \cfrac{\frac{1}{1}}{\frac{\sqrt{3}}{2}}

\bf -------------------------------\\\\
\cfrac{\frac{a}{b}}{\frac{c}{{{ d}}}}\implies \cfrac{a}{b}\cdot \cfrac{{{ d}}}{c}\qquad thus\\\\
-------------------------------\\\\
\cfrac{1}{1}\cdot \cfrac{2}{\sqrt{3}}\implies \cfrac{1\cdot 2}{1\cdot \sqrt{3}}\implies \cfrac{2}{\sqrt{3}}
\\\\\\
\textit{and now, rationalizing the denominator, we get}\implies \cfrac{2\sqrt{3}}{3}
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8x(12+7-9)-(4+10) what’s the answer
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Equation- 8x(12+7-9)-(4+10)

Answer- 80x−14

6 0
2 years ago
$5 PAYPAL + BRAINLIEST TO ANSWER THS
expeople1 [14]

Answer:

Quadratic Equation:

3x^2=2x +5

\text{Standard Form: } 3x^2-2x-5=0

From the standard form of a Quadratic Function, we get:

a=3,\:b=-2,\:c=-5

Discriminant:

\Delta=\left(-2\right)^2-4\cdot \:3\left(-5\right)

\Delta=\left(-2\right)^2+4\cdot \:3\cdot \:5

\Delta=64

From the discriminant, we conclude that the equation will have two real solutions.

State that:

b^2-4ac

b^2-4ac =0:\text{The equation has 1 real solution}

b^2-4ac >0:\text{The equation has 2 real solutions}

By the way, solving the equation given:

$x=\frac{2\pm\sqrt{64}}{2\cdot \:3}$

$x=\frac{2\pm\sqrt{64}}{6}$

$x=\frac{2\pm8}{6}$

$x_{1} =\frac{10}{6}=\frac{5}{3}  $

$x_{2}=\frac{-6}{6} =-1$

5 0
3 years ago
Pls help oooooooooooooopoo
grigory [225]

9514 1404 393

Answer:

  140°

Step-by-step explanation:

Angles 1 and 3 are "corresponding" angles, so are congruent.

  ∠1 = ∠3

  20x +60 = 30x +20

  40 = 10x . . . . . . . . . . . . subtract 20x+20

  4 = x . . . . . . . . . . . . . . divide by 10

  ∠1 = 20x +60 = 20(4) +60 = 80 +60

  ∠1 = 140°

3 0
3 years ago
Read 2 more answers
You and your best friend are meeting at
chubhunter [2.5K]

Answer:

  10.6 miles

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  d² = 8² +7²

  d² = 64 +49 = 113

  d = √113 ≈ 10.6

You and your friend are about 10.6 miles from each other.

4 0
2 years ago
PLEASE PLEASE HELP ME OUT! But i ask that you explain how you got your answer and not just give the answer.
rjkz [21]

ok so first we would do the function d(x) = 3(8)+2

which when solved turns out to be 26

we would then do the function h(x) = 2(26) +7

which when solved turns out to be 59

so he would need 59 dollars for the donuts

6 0
3 years ago
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