MATHEMATICS COLLEGE

Please help! Thank you!
Please help! Thank you! - 1

Answers

Answer 1
Answer:

The exact values of α and β as follows: α = 2π/3 and β = 7π/6. To find the exact value of the given trigonometric expressions, we need to use the Laws of Sines and Cosines.

What is Law of Sines?

The Law of Sines is a mathematical equation used to calculate the angles or sides of a triangle when two angles and one side are known. It states that the ratio of the sine of an angle to the length of the opposite side is constant.

The Law of Sines states that the ratio of a side to the sine of its opposite angle is equal for all sides and angles of a triangle. The Law of Cosines states that the square of a side of a triangle is equal to the sum of the squares of the other two sides minus twice the product of those sides multiplied by the cosine of the included angle.

We begin by finding the exact value of tan α. Using the Law of Sines, we can find the measure of α by solving the equation: tan α = 3/4 = sin α/cos α. This can be rearranged to find cos α = 4/3, and then we can use the inverse of cosine to find the exact value of α.

Using the Law of Cosines, we can find the exact value of β by solving the equation: -15/17 = (cos β)2 = (1 - sin2 β). This can be rearranged to find sin β = -4/5, and then we can use the inverse of sine to find the exact value of β.

Finally, using the given conditions, we can find the exact values of α and β as follows: α = 2π/3 and β = 7π/6.

For more questions related to cosines

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Students are asked to memorize a list of 100 words. The students are given periodic quizzes to see how many words they have memorized. The function L gives the number of words memorized at time t. The rate of change of the number of words memorized is proportional to the number of words left to be memorized. 1. Which of the following differential equations could be used to model this situation, where k is a positive constant?
A. dL/dt = kL
B. dL/dt = 100 - kL
C. dL/dt = k(100 - L)
D. dL/dt = kL - 100

Answers

Answer:

C. dL/dt = k(100 - L)

Step-by-step explanation:

We have a list containing 100 words.

L = number of words memorized at time t.

At any time t, the number of words left to be memorized is 100-L.

Therefore:

(dL)/(dt)\propto 100-L\n $Introducing k, a constant of proportion$\n(dL)/(dt)= k(100-L)

The correct option is C.

How did you get the answer

Answers

Answer:

when you solve a questions

Step-by-step explanation:

You get the answer when you solve a questions correctly

please mark brainlest i had never got brainlest

Answer:

by getting the information for  a text ot story

Step-by-step explanation:

Q1: A group of 50 biomedical students recorded their pulses rates by counting the number of beats for 60 seconds. (15)80

48

88

70

84

82

66

84

82

64

44

72

90

70

86

104

58

84

72

60

90

108

62

52

72

86

66

104

78

82

96

54

68

76

72

88

102

74

68

74

78

66

72

90

62

100

92

84

76

72



(a) Construct frequency distribution.

(b) Compute mode, median and mean of the frequency distribution.

(c) The lower and upper quartile of the frequency distribution.

Answers

Answer:

The answers are in the explanation.

Step-by-step explanation:

a)

X1 -Absolute frecuency -cumulative absolute frequency -Relative frecuency

44                 1                                      1                                              0.021

48                 1                                     2                                              0.021

52                 1                                     3                                              0.021

54                 1                                     4                                              0.021

58                 1                                     5                                              0.021

60                 1                                     6                                              0.021

62                 2                                    7                                              0.042

64                 1                                     8                                              0.021

66                 3                                    12                                              0.063

68                 2                                    14                                             0.042

70                 2                                    16                                             0.042

72                 6                                    22                                              0.126

74                 2                                    24                                             0.042

76                 2                                    26                                             0.042

78                 2                                    28                                             0.042

80                 1                                     29                                             0.021

82                 3                                    32                                              0.063

84                 4                                    36                                             0.084

86                 2                                    38                                             0.042

88                 2                                    40                                             0.042

90                 3                                    43                                              0.063

92                 1                                     44                                             0.021

96                 1                                     45                                             0.021

100                 1                                     46                                             0.021

102                 1                                     47                                             0.021

104                 2                                    49                                             0.042

108                 1                                     50                                             0.021

Total:             50                                   50                                                1

  • b) Mean: is the number average = 3806/48 = 78.12
  • Median: is the number or average number of half = 76
  • Mode: Is the number that appears most frequently = 72

  • c) Lower quartile: 67
  • Upper quartile: 84

What Ln(z) is answer????!!

Answers

Write z in exponential form:

z=1-i=\sqrt2 e^(-i\frac\pi4)

Then taking the logarithm, we get

\mathrm{Ln}(z)=\ln(\sqrt2) + \ln e^(-i\frac\pi4) = \boxed{\ln(\sqrt2)-\frac\pi4i}

so a is the correct answer.

Please help me with some math im stuck

Answers

y = - 40

- 40 since theres no letters it gonna be -40.

Suppose you wanted to estimate the difference between two population means correct to within 4.8 at the 92% confidence level. If prior information suggests that both population variances are approximately equal to 12 and you want to select independent random samples of equal size from the populations, how large should the sample sizes be?Critical Value: 1.75
The sample sizes should be: n1=___n2=_____?

Answers

Answer: n_1=n_2=4

Step-by-step explanation:

Given : Margin of error : E= 4.8

Confidence level : 92%

Significance level : 1-0.92=0.08

\sigma_1^2=\sigma_1^2\approx12

Two-tailed critical value :-

z_(\alpha/2)=z_(0.08/2)=z_(0.04)=1.75

If we want to select independent random samples of equal size from the populations,

Formula for the sample size :

n_1=n_2=((z_(\alpha/2))/(E))^2(\sigma_1^2+\sigma_2^2)

Then buy using given values , we have

n_1=n_2=((1.75)/(4.8))^2(12+12)

Simplify ,

n_1=n_2=((1.75)/(4.8))^2(12+12)=3.190\approx4  [Round to the next integer.]

Hence, the The sample sizes should be: n_1=n_2=4
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