\(\dfrac{180}{x-4}-\dfrac{180}{x}=\dfrac{1}{2}\)

\(\Leftrightarrow\) \(\dfrac{2x\cdot180}{2x\left(x-4\right)}-\dfrac{2\cdot180\cdot\left(x-4\right)}{2x\left(x-4\right)}=0\)

\(\Leftrightarrow\) \(\dfrac{360x-360x+1440-x^2+4x}{2x\left(x-4\right)}=0\)

\(\Leftrightarrow\) \(\dfrac{-x^2+4x+1440}{2x\left(x-4\right)}=0\)

\(\Leftrightarrow-x^2+4x+1440=0\)

\(\Leftrightarrow-x^2+40x-36x+1440=0\)

\(\Leftrightarrow-x\cdot\left(x-40\right)\cdot\left(-36\right)\cdot\left(x-40\right)=0\)

\(\Leftrightarrow\left(x-40\right)\cdot\left(x-36\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x-40=0\\x+36=0\end{matrix}\right.\)

 \(x-40=0\)

  \(x=0+40\)

 \(x=40\)

\(x+36=0\)

   \(x=0-36\)

   \(x=-36\)

\(\Leftrightarrow\left[{}\begin{matrix}x=40\\x=-36\end{matrix}\right.\)

\(180\left(\dfrac{1}{x-4}-\dfrac{1}{x}\right)=\dfrac{1}{2}\)

\(\dfrac{1}{x-4}-\dfrac{1}{x}=\dfrac{1}{360}\left(đk:x\ne0,4\right)\)

\(\dfrac{x-x+4}{x\left(x-4\right)}=\dfrac{1}{360}\)

\(\dfrac{4}{x\left(x-4\right)}=\dfrac{1}{360}\)

\(x^2-4x=1440\)

\(x^2-4x+4=1444\)

\(\left(x-2\right)^2=1444=38^2\)

\(\Leftrightarrow\left[{}\begin{matrix}x-2=38\\x-2=-38\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=40\\x=-36\end{matrix}\right.\)

1.

\(\Leftrightarrow2sinx.cosx+2cosx=0\)

\(\Leftrightarrow2cosx\left(sinx+1\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}cosx=0\\sinx=-1\end{matrix}\right.\)

\(\Leftrightarrow cosx=0\) (do \(cosx=0\Leftrightarrow sinx=\pm1\) bao hàm luôn cả pt \(sinx=-1\))

\(\Leftrightarrow x=\dfrac{\pi}{2}+k\pi\)

2.

\(\Leftrightarrow\left[{}\begin{matrix}2x-10^0=60^0+k360^0\\2x-10^0=120^0+n360^0\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=35^0+k180^0\\x=65^0+n180^0\end{matrix}\right.\)

Do \(-120^0< x< 90^0\Rightarrow\left\{{}\begin{matrix}-120^0< 35^0+k180^0< 90^0\\-120^0< 65^0+n180^0< 90^0\end{matrix}\right.\)

\(\Rightarrow\left\{{}\begin{matrix}k=0\\n=\left\{-1;0\right\}\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}x=35^0\\x=-115^0\\x=65^0\end{matrix}\right.\)

3. Làm tương tự câu 2

4.

\(\Leftrightarrow\dfrac{1}{2}-\dfrac{1}{2}cos\left(10x+\dfrac{4\pi}{5}\right)-\left(\dfrac{1}{2}+\dfrac{1}{2}cos\left(\dfrac{x}{2}-2\pi\right)\right)=0\)

\(\Leftrightarrow cos\left(10x+\dfrac{4\pi}{5}\right)+cos\left(\dfrac{x}{2}-2\pi\right)=0\)

\(\Leftrightarrow cos\left(10x+\dfrac{4\pi}{5}\right)+cos\left(\dfrac{x}{2}\right)=0\)

\(\Leftrightarrow cos\left(10x+\dfrac{4\pi}{5}\right)=-cos\left(\dfrac{x}{2}\right)=cos\left(\pi-\dfrac{x}{2}\right)\)

\(\Leftrightarrow\left[{}\begin{matrix}10x+\dfrac{4\pi}{5}=\pi-\dfrac{x}{2}+k2\pi\\10x+\dfrac{4\pi}{5}=\dfrac{x}{2}-\pi+k2\pi\end{matrix}\right.\)

\(\Leftrightarrow...\)

a) 

Trên nửa đường tròn đơn vị, lấy điểm M sao cho \(\widehat {xOM} = \alpha \)

Gọi H, K lần lượt là các hình chiếu vuông góc của M trên Ox, Oy.

Ta có: tam giác vuông OHM vuông tại H và \(\alpha  = \widehat {xOM}\)

Do đó: \(\sin \alpha  = \frac{{MH}}{{OM}} = MH;\;\cos \alpha  = \frac{{OH}}{{OM}} = OH.\)

\( \Rightarrow {\cos ^2}\alpha  + {\sin ^2}\alpha  = O{H^2} + M{H^2} = O{M^2} = 1\)

b) Ta có:

\(\begin{array}{l}\;\tan \alpha  = \frac{{\sin \alpha }}{{\cos \alpha }};\;\cot \alpha  = \frac{{\cos \alpha }}{{\sin \alpha }}.\\ \Rightarrow \;\tan \alpha .\cot \alpha  = \frac{{\sin \alpha }}{{\cos \alpha }}.\frac{{\cos \alpha }}{{\sin \alpha }} = 1\end{array}\)

c) Với \(\alpha  \ne {90^o}\) ta có:

\(\begin{array}{l}\;\tan \alpha  = \frac{{\sin \alpha }}{{\cos \alpha }};\;\\ \Rightarrow \;1 + {\tan ^2}\alpha  = 1 + \frac{{{{\sin }^2}\alpha }}{{{{\cos }^2}\alpha }} = \frac{{{{\sin }^2}\alpha  + {{\cos }^2}\alpha }}{{{{\cos }^2}\alpha }} = \frac{1}{{{{\cos }^2}\alpha }}\;\end{array}\)

d) Ta có:

\(\begin{array}{l}\cot \alpha  = \frac{{\cos \alpha }}{{\sin \alpha }};\;\\ \Rightarrow \;1 + {\cot ^2}\alpha  = 1 + \frac{{{{\cos }^2}\alpha }}{{{{\sin }^2}\alpha }} = \frac{{{{\sin }^2}\alpha  + {{\cos }^2}\alpha }}{{{{\sin }^2}\alpha }} = \frac{1}{{{{\sin }^2}\alpha }}\;\end{array}\)

ẦN GẤP Ạ

20 PHÚT NỮA ĐI HỌC RÙI Ạ

\(B=\dfrac{1}{2}+\dfrac{3}{10}+\dfrac{4}{45}+\dfrac{11}{180}+\dfrac{1}{20}\)

\(B=\dfrac{90}{180}+\dfrac{54}{180}+\dfrac{16}{45}+\dfrac{11}{180}+\dfrac{9}{180}\)

\(B=\dfrac{90+54+16+11+9}{180}\)

\(B=\dfrac{180}{180}\)

\(B=1\)

1. Write a paragragh about what we should do to save energy. (180 - 200 words)

                                                 Write

Energy is classified into two main groups: renewable and non-renewable.
The energy generated from natural sources such as the sun, wind, rain, and tides is called renewable energy. They are plentiful and can be generated again and again. They also have low carbon emissions so they are considered green and environment-friendly. Moreover, using renewable energy can reduce your electricity bills. Unfortunately, solar energy can be only used during the daytime but not during night or the rainy season. Geothermal energy also can bring toxic chemicals beneath the earth's surface to the top and can create environmental changes.
Non-renewable energy is the energy taken from other sources that are available on earth.They are limited and will run out in the future. They can't be re-generated in a short time.Fossil fuels - natural gas, oil and coal - are examples of them. They are cheap and easy to use. However, when burnt, they release toxic gases in the air so they cause serious environmental changes such as global warming. And the important thing is that non-renewable sources will expire someday.

 2. Write a paragragh about one person you love in a book. (180 - 200 words)

                                               Write 

We meet many people in our lives, but there are some people who have a great impact on our lives. I admire my mother a lot. She is an ideal housewife of fifty. She was born in a respectable Catholic family. She is very polite, affectionate and intelligent. Besides, she manages the family very nicely. She does every piece of household work. Moreover, she takes great care of all of us. She loves me very darely. She is ready to sacrifice her own happiness for my happiness. She hopes to see me happy even at the cost of her own life. She holds my good above everytthing in the world. Her anxiety knows no bounds if I fall ill. She does not enjoy a wink of sleep. But her face beams with joys when I come around. Next,my mother is very religious. She says her prayers five times a day. Then, she is also very kind to the poor. She tries to help the poor as far as possible. My mom possesses a good sense of sanitation. She keeps our house neat and clean. She is a woman of delicate taste. She reads books when she gets time. She bears a good moral character. She advives us to follow the path of the truth and honesty. She also advises us to be polite, gentle and modest. And finally, I hold my mother in profound respect. I am greatly indebted to my mother.

1. Write a paragragh about what we should do to save energy.
Energy is classified into two main groups: renewable and non-renewable.
The energy generated from natural sources such as the sun, wind, rain, and tides is called renewable energy. They are plentiful and can be generated again and again. They also have low carbon emissions so they are considered green and environment-friendly. Moreover, using renewable energy can reduce your electricity bills. Unfortunately, solar energy can be only used during the daytime but not during night or the rainy season. Geothermal energy also can bring toxic chemicals beneath the earth's surface to the top and can create environmental changes.
Non-renewable energy is the energy taken from other sources that are available on earth.They are limited and will run out in the future. They can't be re-generated in a short time.Fossil fuels - natural gas, oil and coal - are examples of them. They are cheap and easy to use. However, when burnt, they release toxic gases in the air so they cause serious environmental changes such as global warming. And the important thing is that non-renewable sources will expire someday.

2. Write a paragragh about one person you love in a book
My favorite character from a book would be Liam Hens worth. He is awesome an the story is about him and how he didn't stop trying for the girl he fell in love with. I think it just so awesome how in the book he looks because there is pictures in the book. I how he is in the book and how he is just so cute. 
Also, my favorite character from a movie would be Adam Sandler because he is hilarious, funny, and an amazing in movies. I have pracally seen all his movies and every movie is hilarious and interesting to watch. He has been amazing in doing movies because every time I see him every time he is funny. I think he would be my favorite character an has a amazing attitude for the television.
In television my favorite actor would be William Levy. My favorite actress would be Eiza Gonzalez because she is beautiful, skinny, has a good attitude in the episodes, a great role model and fabulous designer. William Levy is hot and on tv. he is a great actor and he is lovely on the television because he is sweet and such a gentleman.

1.

B=5^5 x 5 + 2014⁰

B= 3125 x 5 + 0

B=15625+0

=>B=15625

2.

a) x + 180 :18=30

   x +  10 =30

=>x=30-10

   x=20

b) (x + 180):18=30

   x +180      =30 x 18

   x +180     = 540

   x              =540 -180

==>x           = 360

1) \(x+y=10\) mà \(x=y\) nên: \(x=y=\dfrac{10}{2}=5\)

2) \(2x+3y=180\) mà \(x=y\)

Ta có: \(2y+3y=180\Rightarrow5y=180\Rightarrow y=180:5=36\)

Vậy \(x=y=36\)

3) \(x+y=180\) mà \(x=y\) nên: \(x=y=\dfrac{180}{2}=90\)

4) \(3x+5y=13\) mà \(y=2x\) ta có:

\(3x+5\cdot2x=13\Rightarrow13x=13\Rightarrow x=1\)

\(y=2x=2\cdot1=2\)

Các câu còn lại bạn làm tương tự

`@` `\text {Ans}`

`\downarrow`

`a)`

`x - 452 \times 2 = 180`

`x - 904 = 180`

`x = 180 + 904`

`x = 1084`

`b)`

`x + 58 \div 2 = 60`

`x + 29 = 60`

`x = 60 - 29`

`x = 31`

`c)`

`x - 1 - 2 - 3 - 4 = 0`

`x - (1 + 2 + 3 + 4) = 0`

`x - 10 = 0`

`x = 0 + 10`

`x = 10`

$a)$

$x-452\times 2=180$

$x-904=180$

$x=180+904$

$x=1084$

$b)$

$x+58÷2=60$

$x+29=60$

$x=60-29$

$x=31$

$c)$

$x-1-2-3-4=0$

$x-(1+2+3+4)=0$

$x-10=0$

$x=0+10$

$x=10$