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Precalc Quiz 23-25 > Study > Flashcards

Study Flashcards

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
Q

Negative angle

A

Counterclockwise

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26
Q

Two angles with same initial and terminal sides

A

Coterminal

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27
Q

Coterminal

A

Two angles with same initial and terminal sides

28
Q

An angle lies in a quadrant if its terminal side is

A

In that quadrant

29
Q

If a terminal side is in a quadrant then so is

A

The angle

30
Q

An acute angle

A

Has measure between 0 and 90

31
Q

Has measure between 0 and 90

A

Acute angle

32
Q

An obtuse angle has measure

A

90 and 180

33
Q

Measure 90 and 180

A

Obtuse angle

34
Q

A straight angle has measure

A

180

35
Q

Has measure 180

A

Straight angle

36
Q

Angle who’s vertex is center of a circle

A

Central angle

37
Q

Central angle

A

Angle who’s vertex is center of a circle

38
Q

Circumference of unit circle

A

2π or 360

39
Q

2π or 360

A

Circumference of unit circle

40
Q

Degrees to radians

A

π/180

41
Q

π/180

A

Degrees to radians

42
Q

Radians to degrees

A

180/π

43
Q

180/π

A

Radians to degrees

44
Q

Find the angle θ with 0 < θ < 2π
which is coterminal with

19π/4

A
  1. 19π/4 - 2(2π)
  2. 19π/4 - 4π
  3. 3π/4
45
Q

The length S of an arc subtended by an angle of θ radius in a circle of radius r is

A

S = rθ

46
Q

S = rθ

A

The length S of an arc subtended by an angle of θ radius in a circle of radius r is

47
Q

Linear velocity is

A

Distance over time:

v = S/t

48
Q

v = S/t

A

Linear velocity

49
Q

Angular velocity is

A

Displacement over time:

ω = θ/t

50
Q

ω = θ/t

A

Angular velocity

51
Q

Revolutions / min is

A

Multiplied by 2π

52
Q

csc θ =

A

hypotenuse / opposite

53
Q

hypotenuse / opposite

A

csc θ

54
Q

sec θ =

A

hypotenuse / adjacent

55
Q

hypotenuse / adjacent

A

sec θ

56
Q

cot θ

A

adjacent / opposite

57
Q

adjacent / opposite

A

cot θ

58
Q

Two triangles that contain θ are

A

Similar

59
Q

Similar triangles

A

Contain angle measure of θ

60
Q

tan θ relationship to sin θ and cos θ

A

tan θ = sin θ/cos θ

61
Q

If sin θ = a/c then sin^2 θ =

A

a^2/b^2

62
Q

Pythagorean identitity

A

sin^2 θ + cos^2 θ = 1

63
Q

sin^2 θ + cos^2 θ = 1

A

Pythagorean identitity

64
Q

Solve:

(2/5)^2 + cos^2 θ = 1

A
  1. 4/25 + cos^2 θ= 1
  2. cos^2 θ = 21/25
  3. cos θ = √21/5
65
Q

Cofunction identities

A

sin θ = cos(π/2 - θ)

tan θ = cot(π/2 - θ)

sec θ = csc(π/2 - θ)

and other way around

66
Q

sin θ = cos(π/2 - θ)

tan θ = cot(π/2 - θ)

sec θ = csc(π/2 - θ)

and other way around

A

Cofunction identities

Precalc Quiz 23-25 (1 decks)

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