SOS. Giúp em với. Cần gấp 🙏🙏🙏🥲🥲
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1 If I were you I would recycle these plastic carrier bags
2 The pilots suddenly struck, so all flights had to be cancelled
3 The polluted environment causes the death of birds and plants
4 The contaminated food leads to people's poor health
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Bán kính hình tròn:
\(18,84:3,14:2=3\left(cm\right)\)
Diện tích hình tròn:
\(3\times3\times3,14=28,26\left(cm^2\right)\)
Đường kính hình tròn:
\(3\times2=6\left(cm\right)\)
Diện tích hình thoi:
\(\dfrac{6\times6}{2}=18\left(cm^2\right)\)
Diện tích phần gạch chéo:
\(28,26-18=10,26\left(cm^2\right)\)
![](https://rs.olm.vn/images/avt/0.png?1311)
4b.
\(\dfrac{\pi}{2}< a< \pi\Rightarrow cosa< 0\Rightarrow cosa=-\sqrt{1-sin^2a}=-\dfrac{4}{5}\)
\(\Rightarrow tana=\dfrac{sina}{cosa}=-\dfrac{3}{4}\)
\(tan\left(a+\dfrac{\pi}{3}\right)=\dfrac{tana+tan\left(\dfrac{\pi}{3}\right)}{1-tana.tan\left(\dfrac{\pi}{3}\right)}=\dfrac{-\dfrac{3}{4}+\sqrt{3}}{1-\left(-\dfrac{3}{4}\right).\sqrt{3}}=...\)
c.
\(\dfrac{3\pi}{2}< a< 2\pi\Rightarrow cosa>0\Rightarrow cosa=\sqrt{1-sin^2a}=\dfrac{5}{13}\)
\(cos\left(\dfrac{\pi}{3}-a\right)=cos\left(\dfrac{\pi}{3}\right).cosa+sin\left(\dfrac{\pi}{3}\right).sina=\dfrac{1}{2}.\dfrac{5}{13}+\left(-\dfrac{12}{13}\right).\dfrac{\sqrt{3}}{2}=...\)
![](https://rs.olm.vn/images/avt/0.png?1311)
4:
a: -90<a<0
=>cos a>0
cos^2a=1-(-4/5)^2=9/25
=>cosa=3/5
\(sin\left(45-a\right)=sin45\cdot cosa-cos45\cdot sina=\dfrac{\sqrt{2}}{2}\left(cosa-sina\right)\)
\(=\dfrac{\sqrt{2}}{2}\left(\dfrac{3}{5}-\dfrac{4}{5}\right)=\dfrac{-\sqrt{2}}{10}\)
b: pi/2<a<pi
=>cosa<0
cos^2a+sin^2a=0
=>cos^2a=16/25
=>cosa=-4/5
tan a=3/5:(-4/5)=-3/4
\(tan\left(a+\dfrac{pi}{3}\right)=\dfrac{tana+\dfrac{tanpi}{3}}{1-tana\cdot tan\left(\dfrac{pi}{3}\right)}\)
\(=\dfrac{-\dfrac{3}{4}+\sqrt{3}}{1-\dfrac{-3}{4}\cdot\sqrt{3}}=\dfrac{48-25\sqrt{3}}{11}\)
c: 3/2pi<a<pi
=>cosa>0
cos^2a+sin^2a=1
=>cos^2a=25/169
=>cosa=5/13
cos(pi/3-a)
\(=cos\left(\dfrac{pi}{3}\right)\cdot cosa+sin\left(\dfrac{pi}{3}\right)\cdot sina\)
\(=\dfrac{5}{13}\cdot\dfrac{1}{2}+\dfrac{-12}{13}\cdot\dfrac{\sqrt{3}}{2}=\dfrac{5-12\sqrt{3}}{26}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
5:
a: sin x=2*cosx
\(A=\dfrac{6cosx+2cosx-4\cdot8\cdot cos^3x}{cos^3x-2cosx}\)
\(=\dfrac{8-32cos^2x}{cos^2x-2}\)
b: VT=sin^4(pi/2-x)+cos^4(x+pi/2)+6*1/2*sin^22x+1/2*cos4x
=cos^4x+sin^4x+3*sin^2(2x)+1/2*(1-2*sin^2(2x))
=1-2*sin^2x*cos^2x+3*sin^2(2x)+1/2-sin^2(2x)
==3/2=VP
![](https://rs.olm.vn/images/avt/0.png?1311)
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Ta có: \(E=9x^2+6x-1\)
\(=9x^2+6x+1-2\)
\(=\left(3x+1\right)^2-2\ge-2\forall x\)
Dấu '=' xảy ra khi \(x=-\dfrac{1}{3}\)
\(F=\left(3x\right)^2+2.3x.1+1-2=\left(3x+1\right)^2-2\ge-2\)
Dấu = xảy ra ⇔ \(3x+1=0\Rightarrow x=\dfrac{-1}{3}\)
Vậy min của F là -2
![](https://rs.olm.vn/images/avt/0.png?1311)
Xét BPT: \(x^2-8x+15\le0\Leftrightarrow3\le x\le5\Rightarrow D_1=\left[3;5\right]\)
Xét BPT: \(\left(m^2+1\right)x+m\ge23+2mx\)
\(\Leftrightarrow\left(m^2-2m+1\right)x\ge23-m\)
\(\Leftrightarrow\left(m-1\right)^2x\ge23-m\) (1)
- Với \(m=1\Rightarrow\left(1\right)\) trở thành \(0\ge22\) (vô lý) \(\Rightarrow\left(1\right)\) vô nghiệm (loại)
- Với \(m\ne1\Rightarrow\left(m-1\right)^2>0;\forall m\)
\(\left(1\right)\Leftrightarrow x\ge\dfrac{23-m}{\left(m-1\right)^2}\) \(\Rightarrow D_2=\left[\dfrac{23-m}{(m-1)^2};+\infty \right)\)
Hệ đã cho có nghiệm khi và chỉ khi \(D_1\cap D_2\ne\varnothing\)
\(\Rightarrow\dfrac{23-m}{\left(m-1\right)^2}\le5\)
\(\Leftrightarrow23-m\le5\left(m-1\right)^2\)
\(\Leftrightarrow5m^2-9m-18\ge0\Rightarrow\left[{}\begin{matrix}m\ge3\\m\le-\dfrac{6}{5}\end{matrix}\right.\)