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enot [183]
3 years ago
9

29.2/10.4 and 7.3/2.3 equivalent ratios

Mathematics
1 answer:
Marina86 [1]3 years ago
7 0

Answer:

follow pcllord on twitch

Step-by-step explanation:

smp content

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Use the given information to find the exact value of the trigonometric function
eimsori [14]
\begin{gathered} \csc \theta=-\frac{6}{5} \\ \tan \theta>0 \\ \cos \frac{\theta}{2}=\text{?} \end{gathered}

Half Angle Formula

\cos \frac{\theta}{2}=\pm\sqrt[\square]{\frac{1+\cos\theta}{2}}\tan \theta>0\text{ and csc}\theta\text{ is negative in the third quadrant}\begin{gathered} \csc \theta=-\frac{6}{5}=\frac{r}{y} \\ x^2+y^2=r^2 \\ x=\pm\sqrt[\square]{r^2-y^2} \\ x=\pm\sqrt[\square]{6^2-(-5)^2} \\ x=\pm\sqrt[\square]{36-25} \\ x=\pm\sqrt[\square]{11} \\ \text{x is negative since the angle is on the 3rd quadrant} \end{gathered}\begin{gathered} \cos \theta=\frac{x}{r}=\frac{-\sqrt[\square]{11}}{6} \\ \cos \frac{\theta}{2}=\pm\sqrt[\square]{\frac{1+\cos\theta}{2}} \\ \cos \frac{\theta}{2}is\text{ also negative in the 3rd quadrant} \\ \cos \frac{\theta}{2}=-\sqrt[\square]{\frac{1+\frac{-\sqrt[\square]{11}}{6}}{2}} \\ \cos \frac{\theta}{2}=-\sqrt[\square]{\frac{\frac{6-\sqrt[\square]{11}}{6}}{2}} \\ \cos \frac{\theta}{2}=-\sqrt[\square]{\frac{6-\sqrt[\square]{11}}{12}} \\  \\  \end{gathered}

Answer:

\cos \frac{\theta}{2}=-\sqrt[\square]{\frac{6-\sqrt[\square]{11}}{12}}

Checking:

\begin{gathered} \frac{\theta}{2}=\cos ^{-1}(-\sqrt[\square]{\frac{6-\sqrt[\square]{11}}{12}}) \\ \frac{\theta}{2}=118.22^{\circ} \\ \theta=236.44^{\circ}\text{  (3rd quadrant)} \end{gathered}

Also,

\csc \theta=\frac{1}{\sin\theta}=\frac{1}{\sin (236.44)}=-\frac{6}{5}\text{ QED}

The answer is none of the choices

7 0
1 year ago
A rectangle has a height of 3 and a width of 2x*2 + 3x - 5 , express area of whole rectangle, please answer this ASAP !!!
monitta
Area is height time width, or in this case, 3(2x^2+3x+5), which is 6x^2+9x+15.
8 0
3 years ago
Round 6.85565 to the nearest tenth !
emmasim [6.3K]

Answer:

It is 6.9

Step-by-step explanation:

6.85565

put

6.85

5 can be rounded up so

6.9 is answer

3 0
3 years ago
For which equation is m = 12 the solution? a. 4m=40 b. m+20=42. c. 4m=48. d. m-4=9
Gelneren [198K]
To solve this question, we just need to insert 12 into the m position of each question and see if the equation holds true.

a. 4m = 40

4(12) = 40

48 = 40

48 obviously does not equal 40, so it is not choice A.

b. m + 20 = 42

12 + 20 = 42

32 = 42

Again, 32 isn't the same as 42, so not choice B either.

c. 4m = 48

4(12) = 48

48 = 48

It looks like this one is true, but let's solve D also just to make sure.

d. m - 4 = 9

12 - 4 = 9

8 = 9

This is false, since 8 does not equal 9.

Therefore, choice C (4m = 48) is the correct answer.
Hope that helped! =)
6 0
3 years ago
Read 2 more answers
Solve for x<br><img src="https://tex.z-dn.net/?f=4%20%20%7Bx%7D%5E%7B2%7D%20%20%3D%207x%20%2B%202" id="TexFormula1" title="4 {x
Alina [70]

\bf 4x^2=7x+2\implies 4x^2-7x-2=0\implies (4x+1)(x-2)=0 \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ 4x\cdot x=\boxed{4x^2}~\hfill (1)(-2)=\boxed{-2}\hfill (4x\cdot -2)+(1\cdot x)=\boxed{-7x} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \begin{cases} 4x+1=0\implies 4x=-1\implies &x=-\cfrac{1}{4}\\[1em] x-2=0\implies &x=2 \end{cases}

7 0
3 years ago
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