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3 years ago

Select the correct answer from each drop-down menu.

Mathematics

1 answer:

pentagon [3]3 years ago

5 0

Answer 98

Step-by-step explanation:

first you add 7 then live

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

vodka [1.7K]

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

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

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

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

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2 years ago

A business owner wants to have the front window of her store painted and is considering two

Aleks [24]

Denise would have to take seven hours to charge the same amount of money as tiana. furthermore, it would cost the same amount as that is what the prompt is asking for.

to get the answer:
i subtracted $19 from $292 to eliminate the
fee element because if you were to divide
$292 by $39 without the step, the hours would be incorrect and the price would be greater.

after subtracting i got $273

from there i divided $273 by $39 and got 7 (the amount of hours it would take)

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3 years ago

Solve for b: 2(b + 3) = b – 4

Reil [10]

Answer:

b = -10

Step-by-step explanation:

2(b + 3) = b – 4

2b + 6 = b - 4

-b -b

b + 6 = -4

-6 -6

b = -10

8 0

3 years ago

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If the area of sector AOC is 12π cm² and the measure of the radius is 6 cm, what is the measure of the central angle in radians?

ella [17]

Answer:

Step-by-step explanation:

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3 years ago

Find the coordinates of the points of intersection of the graphs with coordinate axes:

Rashid [163]

I only know the y intercept which is 0,3

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3 years ago