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erastova [34]
2 years ago
13

Solve for t, 0 ≤ t < 2π 24sin^2(t) = 6tan(t)cos(t) Thank you!

Mathematics
1 answer:
Rama09 [41]2 years ago
6 0

Answer:

  t ∈ {0, 0.252680, 2.888912, 3.141593}

Step-by-step explanation:

Simplify and factor.

  4sin(t)^2 -sin(t) = 0 . . . . use tan=sin/cos, subtract 6sin(t), divide by 6

  sin(t)(4sin(t) -1) = 0 . . . . factor

Solutions make the factors zero.

  sin(t) = 0   ⇒   t = 0, π

  4sin(t) -1 = 0   ⇒   t = arcsin(1/4), π-arcsin(1/4) ≈ 0.252680, 2.888912

  t ∈ {0, 0.252680, 2.888912, 3.141593}

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Find the equation of a line perpendicular to -4x+y=10 that passes through the point (-4,9)
Oliga [24]

Answer:

y=-1/4x+8

Step-by-step explanation:

To find the equation of a line that is perpendicular to a line, you would take the opposite reciprocal of the slope.

Before that, we need to change the equation into slope-intercept form.

-4x+y=10

y=4x+10

The opposite reciprocal of the slope is -1/4.

Now, let's use the point-slope formula to find our equation of the line that passes through (-4,9).

y-y1=m(x-x1)

y-9=-1/4(x-(-4))

y-9=-1/4x-1

y=-1/4x+8

4 0
2 years ago
A store asked 250 of its customers whether or not they were satisfied with the service. The responses were also classified accor
anyanavicka [17]

Answer:

Correct option: e) a two-way table.

Step-by-step explanation:

In this case the store wants to see whether there is a relationship between the satisfaction level of the customer and their gender.

In statistics when there is a need to analyze or derive a relation between two categorical variables one should use a two-way table.

Categorical variables are qualitative variables that take on specific values that are usually labels. For example, grades obtained in an exam, gender, etc.

In this case the two categorical variables are: Gender and Satisfaction level.

To study the relation between the gender of a customer and their satisfaction level use a two-way table.

 

3 0
2 years ago
Solve for the following equation<br><br> 9/4x + 1/3 = 5/2x
marshall27 [118]

Answer:

3/4

Step-by-step explanation:

plug values in for x till you get it right

7 0
2 years ago
The inner core of Earth begins about 3200 miles below the surface of Earth and has a volume of about 581,000,000 pi cubic miles.
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7 0
2 years ago
The board of a large company is made up of 7 women and 9 men. 6 of them will go as a delegation to a national conference.
Burka [1]

Answer:

a) 5765760

b) 60480

c) 5705280

Step-by-step explanation:

Assuming that order is not important:

Number of women = 7

Number of men = 9

Members of the delegation = 6

a) How many delegations are possible?

n=\frac{16!}{(16-6)!}=16*15*14*13*12*11\\ n= 5765760

b) How many of these delegations have all men?

n_{men} = \frac{9!}{(9-6)!}=9*8*7*6*5*4  \\n_{men} = 60480

c) How many of these delegations have at least one woman?

n_{women >0}=n-n_{men}\\n_{women >0} =5765760-60480\\n_{women >0} =5705280

4 0
3 years ago
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