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a: Xét ΔABC có
M là trung điểm của AB
N là trung điểm của AC
Do đó: MN là đường trung bình của ΔBAC
đặt \(A=2+2^2+2^3+...+2^{2018}\)
\(\Rightarrow2A=2^2+2^3+2^4+...+2^{2019}\)
\(\Rightarrow2A-A=2^{2019}-2\)
\(\Rightarrow A=2^{2019}-2\)
1. The boy is intelligent enough to understand you
2. He studied too bad to pass the exam
3. Kent is tall enough to take the book on the top of shelf
4. The milk is too hot for my sister to drink
5. It took my mother 30 minutes to cook our dinner yesterday
6. It will take we 1 hour to clean our classroom next Monday
7. Mary spends 15 minutes doing her homework
8. She spent 20 minutes washing her dog yesterday
9. Her old house is bigger than her new house
10. Mary is the most intelligent student in my group
a)Xét ΔAKB và ΔCAB có:
\(\widehat{AKB}=\widehat{BAC}=90^o\left(gt\right)\)
\(\widehat{C}chung\)
⇒ΔAKB ~ ΔCAB(g-g)
b)Xét ΔABC có:OB=OC(O là trung điểm BC);BI=AI(I là trung điểm AB)
⇒OI là đường TB ΔABC(đ/n)
⇒OI//AC(t/c)
Mà AC⊥AB(gt) ⇒OI⊥AB(t/c)
Xét ΔBOI và ΔBAK có:
\(\widehat{BIO}=\widehat{BKA}=90^o\)
\(\widehat{B}\) chung
⇒ΔBOI ~ ΔBAK(g-g)
⇒\(\dfrac{BI}{BK}=\dfrac{BO}{BA}\Rightarrow BI.BA=BK.BO\)(đpcm)
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
1 English isn't spoken in this country
2 Washing machine is sold in that shop by him
3 That project will be completed by the army next year
4 He was let to write a letter to his wife
5 She was made to go to bed before 9 pm by her parents
6 I heard they talk in the next room
7 It is wonderful to go for a picnic with friends on holidays
8 It is not easy to be the best student in the class
9 It is difficult to answer all of the long questions in a short time
10 My boss let him be on leave for wedding