Δ:3x-4y+7=0=> VTPT n(3;-4)

Δ1
​:12x−5y+7=0=> VTPTn1(12;-5)

cos\(\alpha\)=\(\dfrac{\left|n\cdot n1\right|}{\left|n\right|\cdot\left|n1\right|}=\dfrac{\left|3\cdot12+\left(-4\right)\cdot\left(-5\right)\right|}{\sqrt{3^2+4^2}+\sqrt{12^2+5^2}}=\dfrac{56}{5+13}=\dfrac{56}{18}=4\)

\(\alpha\)=

b) d//Δ=> d: 3x-4y+m=0

để d tiếp xúc với (C) thì d(I;d)=R

ta có I(-3;2); R =6

=> \(\dfrac{3\cdot\left(-3\right)-4\cdot2+m}{\sqrt{3^2+4^2}}=6\Leftrightarrow\dfrac{-9-8+m}{5}=6\Leftrightarrow m-17=30\)\(\Leftrightarrow m=47\)

Vậy d:3x-4y+47=0

a) Δ = 18^2-4*(-2)*20=484>0

-2x^2+18x+20=0=> x=10 hoặc x=-1

-2x^2+18x+20≥0 <=> \(\forall\)x\(\in\)(-\(\infty\);-1)hợp(10;\(\infty\))