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agasfer [191]
3 years ago
7

3. The measure of one angle is ten less than four times the measure of the other angle. The sum of the measures of the two angle

s is 90°. Determine the measure of each of the angles.
Mathematics
1 answer:
Leviafan [203]3 years ago
3 0

Answer:

go to Mr.beast.com

Step-by-step explanation:

he can give you a lot of money and free stuf

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Square root of 2tanxcosx-tanx=0
kobusy [5.1K]
If you're using the app, try seeing this answer through your browser:  brainly.com/question/3242555

——————————

Solve the trigonometric equation:

\mathsf{\sqrt{2\,tan\,x\,cos\,x}-tan\,x=0}\\\\ \mathsf{\sqrt{2\cdot \dfrac{sin\,x}{cos\,x}\cdot cos\,x}-tan\,x=0}\\\\\\ \mathsf{\sqrt{2\cdot sin\,x}=tan\,x\qquad\quad(i)}


Restriction for the solution:

\left\{ \begin{array}{l} \mathsf{sin\,x\ge 0}\\\\ \mathsf{tan\,x\ge 0} \end{array} \right.


Square both sides of  (i):

\mathsf{(\sqrt{2\cdot sin\,x})^2=(tan\,x)^2}\\\\ \mathsf{2\cdot sin\,x=tan^2\,x}\\\\ \mathsf{2\cdot sin\,x-tan^2\,x=0}\\\\ \mathsf{\dfrac{2\cdot sin\,x\cdot cos^2\,x}{cos^2\,x}-\dfrac{sin^2\,x}{cos^2\,x}=0}\\\\\\ \mathsf{\dfrac{sin\,x}{cos^2\,x}\cdot \left(2\,cos^2\,x-sin\,x \right )=0\qquad\quad but~~cos^2 x=1-sin^2 x}

\mathsf{\dfrac{sin\,x}{cos^2\,x}\cdot \left[2\cdot (1-sin^2\,x)-sin\,x \right]=0}\\\\\\ \mathsf{\dfrac{sin\,x}{cos^2\,x}\cdot \left[2-2\,sin^2\,x-sin\,x \right]=0}\\\\\\ \mathsf{-\,\dfrac{sin\,x}{cos^2\,x}\cdot \left[2\,sin^2\,x+sin\,x-2 \right]=0}\\\\\\ \mathsf{sin\,x\cdot \left[2\,sin^2\,x+sin\,x-2 \right]=0}


Let

\mathsf{sin\,x=t\qquad (0\le t


So the equation becomes

\mathsf{t\cdot (2t^2+t-2)=0\qquad\quad (ii)}\\\\ \begin{array}{rcl} \mathsf{t=0}&\textsf{ or }&\mathsf{2t^2+t-2=0} \end{array}


Solving the quadratic equation:

\mathsf{2t^2+t-2=0}\quad\longrightarrow\quad\left\{ \begin{array}{l} \mathsf{a=2}\\ \mathsf{b=1}\\ \mathsf{c=-2} \end{array} \right.


\mathsf{\Delta=b^2-4ac}\\\\ \mathsf{\Delta=1^2-4\cdot 2\cdot (-2)}\\\\ \mathsf{\Delta=1+16}\\\\ \mathsf{\Delta=17}


\mathsf{t=\dfrac{-b\pm\sqrt{\Delta}}{2a}}\\\\\\ \mathsf{t=\dfrac{-1\pm\sqrt{17}}{2\cdot 2}}\\\\\\ \mathsf{t=\dfrac{-1\pm\sqrt{17}}{4}}\\\\\\ \begin{array}{rcl} \mathsf{t=\dfrac{-1+\sqrt{17}}{4}}&\textsf{ or }&\mathsf{t=\dfrac{-1-\sqrt{17}}{4}} \end{array}


You can discard the negative value for  t. So the solution for  (ii)  is

\begin{array}{rcl} \mathsf{t=0}&\textsf{ or }&\mathsf{t=\dfrac{\sqrt{17}-1}{4}} \end{array}


Substitute back for  t = sin x.  Remember the restriction for  x:

\begin{array}{rcl} \mathsf{sin\,x=0}&\textsf{ or }&\mathsf{sin\,x=\dfrac{\sqrt{17}-1}{4}}\\\\ \mathsf{x=0+k\cdot 180^\circ}&\textsf{ or }&\mathsf{x=arcsin\bigg(\dfrac{\sqrt{17}-1}{4}\bigg)+k\cdot 360^\circ}\\\\\\ \mathsf{x=k\cdot 180^\circ}&\textsf{ or }&\mathsf{x=51.33^\circ +k\cdot 360^\circ}\quad\longleftarrow\quad\textsf{solution.} \end{array}

where  k  is an integer.


I hope this helps. =)

3 0
3 years ago
The following data points represent the number of points scored by each player on the Wildcats basketball team last game. ______
scoundrel [369]

Answer:

4

Step-by-step explanation:

  • If you take the lowest half of the data (from the lower extreme to the median) and find the median of these numbers, that is called the lower quartile or quartile 1.
  • If you take the upper half of the data (from the upper extreme to the median) and find the median of these numbers, that is called the upper quartile or quartile 3.
  • The interquartile range is the difference between quartile 1 and quartile 3.

  • 4, 5, 6, 8, 9, 10, 11, 13
  • Median=8.5
  • Q1=6.5
  • Q3=10.5
  • 10.5-6.5=4

I also added my PowerPoint if you didn't get what I was saying.

Download pptx
7 0
3 years ago
Graph f(x)=3x+5 and g(x)=3x-2
IgorLugansk [536]

Answer:

Two parallel lines

Step-by-step explanation:

the slopes are the same: slope = 3

f(x) 3x + 5                          g(x) = 3x - 2

Pick at least three x values and find their corresponding values for y. Remember the f(x)  and g(x) represent y

                                   f(x) = 3x + 5                           g(x) = 3x - 2

                                    y = 3x + 5                              y = 3x - 2

let x = 0                       y = 3(0) + 5                              y = 3(0) - 2

                                     y = 5                                         y   =  -2

Ordered pair                (0, 5)                                        (0, -2)

Let x = 1                      y = 3(1) +5                                y  = 3(1) - 2

                                  y = 8                                         y = 1

ordered pair                (1, 8)                                        (1, 1)

Let x = -1                  y = 3(-1) + 5                               y = 3(-1) - 2                  

                                  y = 2                                        y =  -5

ordered pair             (-1, 2)                                         ( -1, -5)

Locate the ordered pairs and draw the graph on the lines.  

you will graph two parallel lines        

4 0
2 years ago
A loan is payed off in 15 years with a total of 250,000. It had 4% interest
sasho [114]

Answer:

5.2%po joke Lang Hahahahahahah

5 0
3 years ago
a movie theater has 15 rows of State each rows have 24. if there where 28 empty seats during one show how many people where ther
ale4655 [162]

Answer:

332

Step-by-step explanation:

To find how many seats there were, multiply the number of rows with the number of seats in each row:

15 (24) = 360

From these total seats, there are 28 empty seats, meaning:

360 - 28 = 332

There were 332 people.

4 0
3 years ago
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