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Precalc Quiz 23-25 > Study > Flashcards

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1
Q

Solve 25^x = 125

A
  1. (5^2)^x = 5^3
  2. 5^2x = 5^3
  3. ln(5^2x) = ln(5^3)
  4. 2x = 3
  5. x = 3/2
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2
Q

Solve 9^x = 3^x+1

A
  1. (3^2)^x = 3^x+1
  2. ln(3^2x) = ln(3^x+1)
  3. 2x = x+1
  4. x = 1
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3
Q

Solve 5^2x-3 = 3^x+1

A
  1. ln(5^2x-3) = ln(3^x+1)
  2. (2x-3)ln(5) = (x+1)ln(3)
  3. 2xln(5)-3ln(5) = xln(3)+ln(3)
  4. 2xln(5)-xln(3) = 3ln(5) + ln(3)
  5. x(2ln(5)-ln(3)) = 3ln(5)+ln(3)
  6. x = 3ln(5)+ln(3) / 2ln(5)-ln(3)
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4
Q

Solve 3^x - 8•3^-x = 2

A
  1. (3^x)^2 - 8 = 2•3^x 3^- x cancels
  2. Let u = 3^x
  3. (u^2) - 8 = 2u
  4. u^2 -2u-8 = 0
  5. (u-4)(u+2)
  6. 3^x = 4 or x = log3(4)
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5
Q

Solve log2(x-3) + log2(x-4) = 1

A
  1. log2[(x-3)(x-4)] = 1
  2. (x-3)(x-4) = 2
  3. x^2-7x+12=2
  4. (x-5)(x-2)
  5. x = 5
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6
Q

Solve log2(x+4) - log2(x+3) = 1

A
  1. log2[x+4/x+3] = 1
  2. x+4/x+3 = 2
  3. x+4 = 2x+6
  4. x = -2
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7
Q

How to get rid of this log?

log2(4x) = 3

A

With the base (2) to the x.

2^log2(4x) = 2^3

4x = 8

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8
Q

Solve 5(.7)^x + 3 < 18

A
  1. 5(.7)^x < 15
  2. .7^x < 3
  3. ln(.7^x) < ln(3)
  4. xln(.7) < ln(3)
  5. x > ln(3) / ln(.7)
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9
Q

Solve log(2x-5) <= 1

A
  1. 2x-5 > 0 so x > 5/2
  2. 2x-5 <= 10 so x <= 15/2
  3. (5/2, 5/12)
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10
Q

Write in long form:

ln[(x+5) / (x-1)√x+4]

A

4ln(x+5) - ln(x-1) - 1/2ln(x+4)

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11
Q

What does log3(1/27) equal?

A

-3

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12
Q

What does log64(4) equal?

A

1/3

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13
Q

If an inequality is decreasing on both sides, then

A

The inequality is flipped

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14
Q

Condensed form of:

9/2log(x)-log(3y)+log(2z)

A

log √x^9•2z / 3y

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15
Q

log2(x) = -3 equals

A

1/8

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16
Q

log3(x) = -1 equals

A

1/3

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17
Q

10^3x+5 = 11

A

ln(11)-5ln(10) / 3ln(10)

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18
Q

Two rays form an

A

Angle

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19
Q

Forms an angle

A

Two rays

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20
Q

Angle starts at and ends at

A

Initial side and terminal side

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21
Q

Initial side and terminal side

A

Sides that an angle starts and ends from

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22
Q

A counterclockwise angle is

A

Positive

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23
Q

Which angle is positive?

A

Counterclockwise

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24
Q

A clockwise angle is

A

Negative

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25
Negative angle
Counterclockwise
26
Two angles with same initial and terminal sides
Coterminal
27
Coterminal
Two angles with same initial and terminal sides
28
An angle lies in a quadrant if its terminal side is
In that quadrant
29
If a terminal side is in a quadrant then so is
The angle
30
An acute angle
Has measure between 0 and 90
31
Has measure between 0 and 90
Acute angle
32
An obtuse angle has measure
90 and 180
33
Measure 90 and 180
Obtuse angle
34
A straight angle has measure
180
35
Has measure 180
Straight angle
36
Angle who’s vertex is center of a circle
Central angle
37
Central angle
Angle who’s vertex is center of a circle
38
Circumference of unit circle
2π or 360
39
2π or 360
Circumference of unit circle
40
Degrees to radians
π/180
41
π/180
Degrees to radians
42
Radians to degrees
180/π
43
180/π
Radians to degrees
44
Find the angle θ with 0 < θ < 2π which is coterminal with 19π/4
1. 19π/4 - 2(2π) 2. 19π/4 - 4π 3. 3π/4
45
The length S of an arc subtended by an angle of θ radius in a circle of radius r is
S = rθ
46
S = rθ
The length S of an arc subtended by an angle of θ radius in a circle of radius r is
47
Linear velocity is
Distance over time: v = S/t
48
v = S/t
Linear velocity
49
Angular velocity is
Displacement over time: ω = θ/t
50
ω = θ/t
Angular velocity
51
Revolutions / min is
Multiplied by 2π
52
csc θ =
hypotenuse / opposite
53
hypotenuse / opposite
csc θ
54
sec θ =
hypotenuse / adjacent
55
hypotenuse / adjacent
sec θ
56
cot θ
adjacent / opposite
57
adjacent / opposite
cot θ
58
Two triangles that contain θ are
Similar
59
Similar triangles
Contain angle measure of θ
60
tan θ relationship to sin θ and cos θ
tan θ = sin θ/cos θ
61
If sin θ = a/c then sin^2 θ =
a^2/b^2
62
Pythagorean identitity
sin^2 θ + cos^2 θ = 1
63
sin^2 θ + cos^2 θ = 1
Pythagorean identitity
64
Solve: (2/5)^2 + cos^2 θ = 1
1. 4/25 + cos^2 θ= 1 2. cos^2 θ = 21/25 3. cos θ = √21/5
65
Cofunction identities
sin θ = cos(π/2 - θ) tan θ = cot(π/2 - θ) sec θ = csc(π/2 - θ) and other way around
66
sin θ = cos(π/2 - θ) tan θ = cot(π/2 - θ) sec θ = csc(π/2 - θ) and other way around
Cofunction identities

Precalc Quiz 23-25 (1 decks)

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