Bài 4 ạ

Do chóp SABC đều \(\Rightarrow SG\perp\left(ABC\right)\) 

a. Gọi D là trung điểm BC \(\Rightarrow A,G,D\) thẳng hàng và \(AD\perp BC\)

\(\Rightarrow BC\perp\left(SAD\right)\) \(\Rightarrow\left(SBC\right)\perp\left(SAD\right)\)

Từ G kẻ \(GH\perp SD\Rightarrow GH\perp\left(SBC\right)\) do SD là giao tuyến 2 mp vuông góc (SBC) và (SAD)

\(\Rightarrow GH=d\left(G;\left(SBC\right)\right)\)

\(AD=\dfrac{a\sqrt{3}}{2}\) (trung tuyến tam giác đều) \(\Rightarrow\left\{{}\begin{matrix}AG=\dfrac{2}{3}AD=\dfrac{a\sqrt{3}}{3}\\GD=\dfrac{1}{3}AD=\dfrac{a\sqrt{3}}{6}\end{matrix}\right.\)

\(SG=\sqrt{SA^2-AG^2}=\dfrac{a\sqrt{33}}{3}\)

Hệ thức lượng tam giác vuông SGD:

\(GH=\dfrac{SG.GD}{\sqrt{SG^2+GD^2}}=\dfrac{a\sqrt{165}}{45}\)

8, chon \(Ox\equiv AB,O\equiv A,\) chieu(+) A->B, moc tgian luc 8h

a,\(\Rightarrow\left\{{}\begin{matrix}xA=60t\\xB=200-40t\end{matrix}\right.\)

b,\(\Rightarrow xA=xB\Rightarrow t=2h\)

vi tri 2 xe gap nhau cach A: \(S=60.2=120km\)

c,\(\Leftrightarrow60t+40t+50=200\Rightarrow t=1,5h\)

9. chon  chon \(Ox\equiv AB,O\equiv A,\) chieu(+) A->B, moc tgian luc 7h(gia su AB la quang duong chuyen dong voi nguoi di xe dap o A, nguoi di bo o B)

a,\(\Rightarrow\left\{{}\begin{matrix}xA=12t\\xB=8+4t\end{matrix}\right.\)

b,\(\Rightarrow xA=xB\Rightarrow t=1h\Rightarrow\)vi tri nguoi di xe dap duoi kip cach A:\(S=12km\)

c,\(\Rightarrow\Delta S=\left|12.0,5-8-4.0,5\right|=4km\)

7:

a, chieu(+) A->B \(\Rightarrow x=36t\)

b, chieu(+) B->A \(\Rightarrow x=-36\left(t+1\right)\)

4:

a: góc CEH+góc CDH=180 độ

=>CDHE nội tiếp

b: Xét ΔHEA vuông tại E và ΔHDB vuông tại D có

góc EHA=góc DHB

=>ΔHEA đồng dạng với ΔHDB

=>HE/HD=HA/HB

=>HE*HB=HD*HA

Câu 3:

a) 

CTPT xủa X là C_nH_2n+2O

\(n_{CO_2}=\dfrac{8,96}{22,4}=0,4\left(mol\right)\Rightarrow n_{C_nH_{2n+2}O}=\dfrac{0,4}{n}\left(mol\right)\)

=> \(n_{H_2O}=\dfrac{\dfrac{0,4}{n}.\left(2n+2\right)}{2}=\dfrac{0,4}{n}\left(n+1\right)\left(mol\right)\)

Mà \(n_{H_2O}=\dfrac{9}{18}=0,5\left(mol\right)\)

=> n = 4

=> CTPT: C₄H₁₀O

b) \(n_{C_4H_{10}O}=\dfrac{0,4}{4}=0,1\left(mol\right)\)

=> m = 0,1.74 = 7,4 (g)

c)

(1) \(CH_3-CH_2-CH_2-CH_2OH\)

(2) \(CH_3-CH_2-CH\left(OH\right)-CH_3\)

(3) \(CH_3-C\left(CH_3\right)\left(OH\right)-CH_3\)

(4) \(CH_3-CH\left(CH_3\right)-CH_2OH\)

(5) \(CH_3-CH_2-CH_2-O-CH_3\)

(6) \(CH_3-CH\left(CH_3\right)-O-CH_3\)

(7) \(CH_3-CH_2-O-CH_2-CH_3\)

d)

X là \(CH_3-C\left(CH_3\right)\left(OH\right)-CH_3\) (2-metylpropan-2-ol)

 18 x 3 + 11230 x 4

= 54 + 44920

= 44974

\(b,\Leftrightarrow\left\{{}\begin{matrix}m+2=1\\m\ne2\end{matrix}\right.\Leftrightarrow m=-1\\ c,\text{PT giao Ox: }y=0\Leftrightarrow\left(m+2\right)x-m=0\\ \text{Thay }x=2\Leftrightarrow2m+4-m=0\\ \Leftrightarrow m=-4\\ d,\text{PT giao Ox và Oy: }\\ y=0\Leftrightarrow x=\dfrac{m}{m+2}\Leftrightarrow A\left(\dfrac{m}{m+2};0\right)\Leftrightarrow OA=\left|\dfrac{m}{m+2}\right|\\ x=0\Leftrightarrow y=-m\Leftrightarrow B\left(0;-m\right)\Leftrightarrow OB=\left|m\right|\\ \Delta OAB\text{ cân }\Leftrightarrow OA=OB\Leftrightarrow\left|\dfrac{m}{m+2}\right|=\left|m\right|\\ \Leftrightarrow\left[{}\begin{matrix}\dfrac{m}{m+2}=m\\\dfrac{m}{m+2}=-m\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}m\left(m+1\right)=0\\m\left(m+3\right)=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}m=0\\m=-1\\m=-3\end{matrix}\right.\)