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3 years ago

Selling price of a comic book: $1.70. Sales tax rate: 4%

Mathematics

1 answer:

poizon [28]3 years ago

7 0

Answer:

$1.77

Step-by-step explanation:

1.7 X .04 = .068 (this is your tax)

so then add it to the cost of the comic book:

1.7+.068=1.768

this is money so round to the nearest hundredth: $1.77

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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

The diameter of a circle has endpoints P(-12, -4) and Q(6, 12).

nexus9112 [7]

9514 1404 393

Answer:

(x +3)² +(y -4)² = 145

Step-by-step explanation:

The center of the circle is the midpoint of the given segment PQ. If we call that point A, then ...

A = (P +Q)/2

A = ((-12, -4) +(6, 12))/2 = (-12+6, -4+12)/2 = (-6, 8)/2

A = (-3, 4)

The equation of the circle for some radius r is ...

(x -(-3))² +(y -4)² = r² . . . . . . where (-3, 4) is the center of the circle

The value of r² can be found by substituting either of the points on the circle. If we use Q, then we have ...

(6 +3)² +(12 -4)² = r² = 9² +8²

r² = 81 +64 = 145

Then the equation of the circle is ...

(x +3)² +(y -4)² = 145

3 0

3 years ago

Please help will give brainliest

enyata [817]

Answer:

A IS THE ANSWER

Step-by-step explanation:

5 0

3 years ago

Please help me with this problem and if you can show your work

ella [17]

Answer:

2.9

just answering wrong because i need points sorry

7 0

3 years ago

Round the following 8.388 to 2 decimal places

Roman55 [17]

The answer will be 8.39 because the third number (8) is above 5 so you have to round up. Good luck!

3 0

3 years ago