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Andru [333]
3 years ago
13

Given sin A =11\61 and that angle A is in Quadrant I find the exact value of tan A in simplest radical form using a rational den

ominator
Mathematics
1 answer:
Amiraneli [1.4K]3 years ago
3 0

Answer:

Therefore,

\tan A=\dfrac{11}{60}

Step-by-step explanation:

Given:

\sin A=\dfrac{11}{61}

A is in I Quadrant

To Find:

\tan A = ?

Solution:

Using Identity

\sin^{2}A+\cos^{2}A=1

Now Substitute Sin A we get

(\dfrac{11}{61})^{2}+\cos^{2}A=1\\\\\cos^{2}A=1-\dfrac{121}{3721}=\dfrac{3600}{3721}\\\\\cos A=\pm\sqrt{\dfrac{3600}{3721}}\\\\\cos A=\dfrac{60}{61}

As 'A' is in First Quadrant Cos A is Positive

Now Tan identity we have

\tan A=\dfrac{\sin A}{\cos A}

Now Substitute Sin A and Cos A  we get

\tan A=\dfrac{\dfrac{11}{61}}{\dfrac{60}{61}}\\\\\tan A=\dfrac{11}{60}

Therefore,

\tan A=\dfrac{11}{60}

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Micah went to the mall with $50 to spend. After spending $8.75 on lunch, he
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Answer:

Step-by-step explanation:

Since he spends 8.75 on lunch, we subtract that from the total, 50 dollars. When we subtract that, we get 41.25 left. The variable is not clear for the sweatshirt cost and how much money you can spend on it, so I will call it x. Since 41.25 is the total amount you can spend on a sweatshirt, anything exactly that amount or less is okay. So, our answer is x is less than or equal to 41.25. (Less than or equal to is the < with a slash underneath)

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2 years ago
F(x)=-5x+8<br><br> What value of x would make f(x)=23?<br><br><br> Need Answers ASAP
EastWind [94]

Answer:

-3

Step-by-step explanation:

23=-5x+8

23-8=-5x

15=-5x

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3 years ago
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to start to solve the system of equations below, which number would you multiply in the equation -2x-5y=-1? The two equations ar
Leviafan [203]

Answer:

  The first equation can be multiplied by 2.

Step-by-step explanation:

The x-coefficients are -2 and 4. If the first one of these is multiplied by 2, it will be the opposite of the second of these. That is 2·(-2) = -4. When -4 and 4 are added, the result is 0, so the x-variable will be eliminated.

To solve these equations by "elimination", you look for simple relationships between the coefficients that will let you combine them to get zero.

_____

Here's the rest of the solution.

  2(-2x-5y) +(4x+2y) = 2(-1) +(8) . . . . after multiplying the first equation by 2 and adding the second equation

  -4x -10y +4x +2y = -2 +8 . . . . . the result of eliminating parentheses

  -8y = 6 . . . . . the result of collecting terms

  y = -6/8 = -3/4 . . . . divide by the y-coefficient

Since all of the coefficients in the second equation are even, a factor of 2 can be removed, and the equation written as ...

   2x +y = 4

This can be solved for x, so you have ...

  x = (4 -y)/2 = 2 -(y/2)

Filling in the above value of y, we find x to be ...

  x = 2 -(-3/4)/2

  x = 2 3/8

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<em>Comment on eliminating y instead of x</em>

If you divide the second equation by 2 so that y has a coefficient of 1, then you can multiply this equation by 5 to give y a coefficient that is the opposite of the coefficient -5 in the first equation. Then the elimination looks like

  (-2x -5y) +5(2x +y) = (-1) +5(4)

  -2x -5y +10x +5y = -1 +20 . . . . eliminate parentheses

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  x = 19/8 = 2 3/8 . . . . divide by the coefficient of x

5 0
3 years ago
Determine whether the quantitative variable is discrete or continuous. Depth of the ocean floor Is the variable discrete or cont
Vesna [10]

Answer:

B. The variable is continuous because it is not countable.

Correct, from the definition about of continuous data we see that is a random variable is continuous then it can't be countable.

Step-by-step explanation:

Previous concepts

A discrete random variable "has a countable number of possible values" in a domain defined. So then the possible values for these types of random variables are the integers.

A continuous is a random variable "where the data can take infinitely many values" that means that can take values from the rational with decimals. Ans is not countable.

Solution to the problem

Let's analyze one by one the possible options:

A. The variable is discrete because it is countable.

False, the depth of the ocean is a continuous random variable since we can have for exampe a depth of 1200.56 mi and we can't express this as a discrete random variable.

B. The variable is continuous because it is not countable.

Correct, from the definition about of continuous data we see that is a random variable is continuous then it can't be countable.

C. The variable is discrete because it is not countable.

False, the depth of the ocean is a continuous random variable since we can have for exampe a depth of 504.67 Km and we can't express this as a discrete random variable.

D. The variable is continuous because it is countable.

False the variable is continuous but cannot be countable since that's the opposite from the definition of continuous random variable.

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