\displaystyle 3 + 2 \sqrt{2}

152:T7f0,

\displaystyle 5 + \sqrt{2}

8c:["$","p","p0-2",{"className":"mt-0 mb-[1.2em] [tab-size:3] whitespace-pre-wrap","children":["① ",["$","span","p0-2-t0-m1",{"className":"my-[3px] inline-block align-middle leading-none","dangerouslySetInnerHTML":{"__html":"$151"}}],"\n② ",["$","span","p0-2-t0-m3",{"className":"my-[3px] inline-block align-middle leading-none","dangerouslySetInnerHTML":{"__html":"$152"}}],"\n③ ","$L153","\n④ ","$L154","\n⑤ ","$L155",""]}] 156:T50f,

\displaystyle \frac{55}{216}

8e:["$","span","p0-0-t0-m9",{"className":"my-[3px] inline-block align-middle leading-none","dangerouslySetInnerHTML":{"__html":"$156"}}] 157:T50f,

\displaystyle \frac{29}{108}

8f:["$","span","p0-0-t0-m11",{"className":"my-[3px] inline-block align-middle leading-none","dangerouslySetInnerHTML":{"__html":"$157"}}] 158:T50f,

\displaystyle \frac{61}{216}

90:["$","span","p0-0-t0-m13",{"className":"my-[3px] inline-block align-middle leading-none","dangerouslySetInnerHTML":{"__html":"$158"}}] 159:T509,

\displaystyle \frac{8}{27}

91:["$","span","p0-0-t0-m15",{"className":"my-[3px] inline-block align-middle leading-none","dangerouslySetInnerHTML":{"__html":"$159"}}] 15a:T61e,

y = t - \ln ( t + 1 )

93:["$","span","p0-0-t0-m9",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"$15a"}}] 94:["$","span","p0-0-t0-m11",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

{\\mathrm{P}}

"}}] 15b:T9e3,

\displaystyle \frac{\sqrt{3}}{8}

95:["$","span","p0-0-t0-m13",{"className":"my-[3px] inline-block align-middle leading-none","dangerouslySetInnerHTML":{"__html":"$15b"}}] 15c:T9e3,

\displaystyle \frac{\sqrt{6}}{8}

96:["$","span","p0-0-t0-m15",{"className":"my-[3px] inline-block align-middle leading-none","dangerouslySetInnerHTML":{"__html":"$15c"}}] 15d:T9e3,

\displaystyle \frac{\sqrt{3}}{4}

97:["$","span","p0-0-t0-m17",{"className":"my-[3px] inline-block align-middle leading-none","dangerouslySetInnerHTML":{"__html":"$15d"}}] 15e:T9e3,

\displaystyle \frac{\sqrt{6}}{4}

98:["$","span","p0-0-t0-m19",{"className":"my-[3px] inline-block align-middle leading-none","dangerouslySetInnerHTML":{"__html":"$15e"}}] 15f:T9e3,

\displaystyle \frac{\sqrt{3}}{2}

99:["$","span","p0-0-t0-m21",{"className":"my-[3px] inline-block align-middle leading-none","dangerouslySetInnerHTML":{"__html":"$15f"}}] 160:T891,

g' ( \pi ) = e ^{\pi} g ( \pi )

9b:["$","span","p0-0-t0-m7",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"$160"}}] 161:T8e0,

\displaystyle \frac{f' ( \pi )}{f ( \pi )}

9c:["$","span","p0-0-t0-m9",{"className":"my-[3px] inline-block align-middle leading-none","dangerouslySetInnerHTML":{"__html":"$161"}}] 162:T542,

f ( \pi ) \neq 0

9d:["$","span","p0-0-t0-m11",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"$162"}}] 9e:["$","span","p0-0-t0-m13",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

e ^{- 2 \\pi}

"}}] 9f:["$","span","p0-0-t0-m15",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

1

"}}] 163:T4d9,

e ^{- \pi} + 1

a0:["$","span","p0-0-t0-m17",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"$163"}}] 164:T49a,

e ^{\pi} + 1

a1:["$","span","p0-0-t0-m19",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"$164"}}] a2:["$","span","p0-0-t0-m21",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

e ^{2 \\pi}

"}}] a3:["$","span","p0-0-t0-m15",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

k

"}}] 165:T40a,

A _{k}

a4:["$","span","p0-0-t0-m17",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"$165"}}] a5:["$","p","p0-1",{"className":"mt-0 mb-[1.2em] [tab-size:3] whitespace-pre-wrap","children":[["$","img","p0-1-i2",{"src":"https://2vcomivapkynmsnb.public.blob.vercel-storage.com/problems/196/image2-zovdyvgB39UqfD7H8jKsnK7BOfmk7j.png","alt":"","className":"problem-img my-[1em] block","style":{"--img-w":"91cqw"}}]]}] 166:T6aa,

m , n ( 1 \leq m < n \leq 8 )

a6:["$","p","p0-2",{"className":"mt-0 mb-[1.2em] [tab-size:3] whitespace-pre-wrap","children":["다음은 두 자연수 ",["$","span","p0-2-t0-m1",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"$166"}}],"에 대하여 두 사건 ",["$","span","p0-2-t0-m3",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

A _{m}

"}}],"과 ",["$","span","p0-2-t0-m5",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

A _{n}

"}}],"이 서로 독립이 되도록 하는 ","$L167","의 모든 순서쌍 ","$L168","의 개수를 구하는 과정이다."]}] 169:T40a,

A _{k}

a7:["$","p","p0-3",{"className":"mt-0 mb-[1.2em] [tab-size:3] whitespace-pre-wrap","children":["",["$","span","p0-3-t0-m1",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"$169"}}],"는 ",["$","span","p0-3-t0-m3",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

k

"}}],"번째 자리에 ",["$","span","p0-3-t0-m5",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

k

"}}]," 이하의 자연수 중 하나가 적힌 카드가 놓여있고, ",["$","span","p0-3-t0-m7",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

k

"}}],"번째 자리를 제외한 ",["$","span","p0-3-t0-m9",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

7

"}}],"개의 자리에 나머지 ",["$","span","p0-3-t0-m11",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

7

"}}],"장의 카드가 놓여 있는 사건이므로\n ","$L16a","","$L16b","\n이다.\n","$L16c","은 ","$L16d","번째 자리에 ","$L16e"," 이하의 자연수 중 하나가 적힌 카드가 놓여 있고, ","$L16f","번째 자리에 ","$L170"," 이하의 자연수 중 ","$L171","번째 자리에 놓인 카드에 적힌 수가 아닌 자연수가 적힌 카드가 놓여 있고, ","$L172","번째와 ","$L173","번째 자리를 제외한 ","$L174","개의 자리에 나머지 ","$L175","장의 카드가 놓여있는 사건이므로\n ","$L176","","$L177","\n이다.\n한편, 두 사건 ","$L178","과 ","$L179","이 서로 독립이기 위해서는\n ","$L17a","\n을 만족시켜야 한다.\n따라서 두 사건 ","$L17b","과 ","$L17c","이 서로 독립이 되도록 하는 ","$L17d","의 모든 순서쌍 ","$L17e","의 개수는 ","$L17f","이다."]}] 180:T489,

m = 3 , n = 5

a8:["$","p","p0-4",{"className":"mt-0 mb-[1.2em] [tab-size:3] whitespace-pre-wrap","children":["위의 (가)에 알맞은 식에 ",["$","span","p0-4-t0-m1",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

k = 4

"}}],"를 대입한 값을 ",["$","span","p0-4-t0-m3",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

p

"}}],", (나)에 알맞은 식에 ",["$","span","p0-4-t0-m5",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"$180"}}],"를 대입한 값을 ",["$","span","p0-4-t0-m7",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

q

"}}],", (다)에 알맞은 수를 ",["$","span","p0-4-t0-m9",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

r

"}}],"라 할 때, ","$L181","의 값은? [4점]\n① ","$L182","\n② ","$L183","\n③ ","$L184","\n④ ","$L185","\n⑤ ","$L186",""]}] a9:["$","span","p0-0-t0-m9",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

{\\mathrm{Q}}

"}}] 187:T534,

\displaystyle \frac{\pi}{2}

aa:["$","span","p0-0-t0-m11",{"className":"my-[3px] inline-block align-middle leading-none","dangerouslySetInnerHTML":{"__html":"$187"}}] ab:["$","span","p0-0-t0-m13",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

{\\mathrm{OAB}}

"}}] ac:["$","span","p0-0-t0-m15",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

{\\mathrm{AB}}

"}}] 188:T128a,

\mathrm{\left| \vec{OP} + \vec{OQ} \right|}

ad:["$","span","p0-0-t0-m17",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"$188"}}] ae:["$","span","p0-0-t0-m19",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

f ( a )

"}}] af:["$","span","p0-0-t0-m21",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

f ( a ) = 5

"}}] b0:["$","span","p0-0-t0-m23",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

a

"}}] b1:["$","span","p0-0-t0-m25",{"className":"$undefined","dangerouslySetInnerHTML":{"__html":"

{\\mathrm{O}}

"}}] 189:T70b,

\displaystyle - 5 \sqrt{3}

2019년-06월-고3-수리(가형)