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4 years ago

Is 2/2 greater than 5/6?

Mathematics

1 answer:

abruzzese [7]4 years ago

6 0

Answer:

Yes, 2/2 is greater than 5/6

Step-by-step explanation:

2/2 is a full number where as 5/6 is still a fraction. (If it where a full number it would be 6/6.)

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Solve the equation 2 sec² x = 3 - tan x for the domain 0° ≤ x ≤ 360°

vodka [1.7K]

$2 \sec^2 x = 3- \tan x \\\\\implies 2(1 +\tan^2 x) = 3- \tan x \\\\\implies 2 + 2 \tan^2 x +\tan x -3 =0\\\\\implies 2 \tan^2 x + \tan x -1 =0\\\\\implies 2u^2 + u -1 =0~~~ ;[\text{set} \tan x = u]\\\\\implies u = \dfrac{-1\pm \sqrt{1-4\cdot 2 \cdot (-1)}}{2(2)}\\\\\implies u =\dfrac{-1 \pm\sqrt{9}}{4}\\\\\implies u = \dfrac{-1 \pm 3}{4}\\\\\implies u = \dfrac{2}{4}=\dfrac 12~~ \text{or} ~~u =\dfrac{-4}{4} =-1\\\\$

$\implies \tan x = \dfrac 12 ~~ \text{or} ~~ \tan x =-1~~~ ;[\text{Substitute back u =tan x}]\\\\\text{Now,}~ \\\\\tan x = -1,\\\\\implies x = n\pi - \dfrac{\pi}4\\\\\\\text{For interval,}~ [0,2\pi) \\\\x = \dfrac{3\pi}4, \dfrac{7\pi}4\\\\\text{In degrees,}~ x = 135^{\circ}, x =315^{\circ}\\\\\tan x = \dfrac 12\\\\\implies x = n\pi + \tan^{-1} \left(\dfrac 12 \right)\\\\\text{For interval} ~[0,2\pi),\\\\$

$x=\tan^{-1} \left(\dfrac 12 \right), \left[\pi +\tan^{-1} \left( \dfrac 12 \right)\right]\\\\\text{in degrees,} ~~x=\tan^{-1} \left(\dfrac 12 \right), \left[180^{\circ} +\tan^{-1} \left( \dfrac 12 \right)\right]\\\\\\\\\text{Combine all solutions:}\\\\x=\dfrac{3\pi}4, \dfrac{7\pi}4, \tan^{-1} \left(\dfrac 12 \right), \left[\pi +\tan^{-1} \left( \dfrac 12 \right)\right]\\\\\\$

$\text{In degrees,}~ x = 135^{\circ},~315^{\circ},~\tan^{-1} \left(\dfrac 12 \right), \left[180^{\circ} +\tan^{-1} \left( \dfrac 12 \right)\right]$

4 0

2 years ago

What is the answer for this question please

Zigmanuir [339]

Answer:

Step-by-step explanation:

3 0

3 years ago

Read 2 more answers

I will pick the brainiest answer! Thanks! :)

umka21 [38]

Answer:

The first one: if 2/3 is 12 then 1/3 is 6. 3/3 is 18. SO Jane had 18 stuffed animals before the donation.

The second one: 25 students then 13 are men so 25-13 is 12. 12/25 as a percentage is 48%

Hope this helps!

7 0

3 years ago

Read 2 more answers

5/4 + 4(1/4x1/4)<br><br> Solve

vfiekz [6]

So for this we're going to use this rule: a/b x c/d = ac/bd

simplify 1 x 1 to 1

simplify 4 x 4 to 16

4 x 1/16 to 4/16

simplify 4/16 to 1/4

simplify to 6/4

Lastly simplify

Answer: 3/2

*In decimal form it would be 1.5

5 0

3 years ago

Solve 100 ÷ 5 × 4 + 4 3power

hram777 [196]

Answer:

144

Step-by-step explanation:

exponents first: $4^{3} = 64$

then division: 100/5 = 20

now we have: 20 x 4 + 64

then multiply: 20 x 4 = 80

then add: 80 + 64 = 144

8 0

3 years ago