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3 years ago

Plzzzzz help me brainlest

Mathematics

1 answer:

velikii [3]3 years ago

4 0

Area ≈ 153.94 if the radius is 7

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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

Is this correct? the question is asking if the triangle would have a right, acute, or obtuse angle.

IgorLugansk [536]

Answer:

ut ok points from me so I took it from u

6 0

3 years ago

Need help ASAP DUE IN ONE DAY thanks

erastovalidia [21]

Answer:

(5k+14)(3k+8)

Step-by-step explanation:

7 0

3 years ago

Courtney is twice as old as Andre and three years older than Natalie. Courtney is half Shari's age. The difference between Shari

lesantik [10]

The question does not seem complete, but I'll represent the statement mathematically and look for their ages each. This is because the worst they can ask for is their ages.

Let C stand for Courtney's age, A for Andrei's age, N for Natalie's age and S for Shari's age. From the question we can deduce the following:

C = 2A

C = N + 3

C = S/2

S - N = C + A

S = 2C, N = C - 3 and A = C/2, therefore we have

2C - (C - 3) = C + C/2

C + 3 = C + C/2

C/2 = 3 and C = 6

A = C/2

A= 6/2

A = 3

N = C - 3

N = 6 - 3

N = 3

S = 2C

S = 2 x 6

S = 12.

C = 6, A = 3, N = 3 and S = 12

8 0

3 years ago

Can someone help? TvT please

zysi [14]

Answer:

I don't know bro actually which question ❓

7 0

3 years ago