? means I need translation or explanation of the question.
(1) Ans c (as you've indicated)
(2) S8=3+6+12+...=3(20+21+22+23+...)=3(2n-1)=3×255=765 when n=8 Ans a (as you've indicated).
(3) f(x)=2x+5; f-1(x)=(x-5)/2; f-1(-3)=(-3-5)/2=-4 Ans b.
(4) [5x2/2-4x]24=(40-16)-(10-8)=24-2=22 Ans b.
(5) √((-2)2+32+(-5)2)=√(4+9+25)=√38 Ans c.
(6) Still waiting for translation.
(7) sin(x)+cos(x)=0.8; sin2(x)+2sin(x)cos(x)+cos2(x)=1+2sin(x)cos(x)=0.64,
sin(x)cos(x)=(0.64-1)/2=-0.36/2=-0.18=-18/100=-9/50 Ans C.
(8) W=white, B=black, R=red. The table shows 3-ball selections. Each random selection has a probability listed in the penultimate column.
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WWW |
1/30 |
1/30 |
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BWW |
WBW |
WWB |
1/12 |
1/4 |
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RWW |
WRW |
WWR |
1/60 |
1/20 |
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BWB |
BBW |
WBB |
1/9 |
1/3 |
| WRB |
BWR |
BRW |
RWB |
RBW |
WBR |
1/36 |
1/6 |
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BBB |
1/12 |
1/12 |
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RBB |
BRB |
BBR |
1/36 |
1/12 |
The table shows the probabilities for all possible outcomes of selecting 3 balls. The last column sums to 1 (total of all probabilities), confirming that all 20 outcomes have been covered.
Since there is only one red ball the table doesn't include the 7 zero probabilities involving more than red ball. This table may assist in determining the answer once it's clear what the question actually is. (More to follow in due course)
The probability of selecting three balls of the same colour is p(WWW) + p(BBB)=1/30+1/12=7/60 (answer B). This example would therefore have a solution which is listed.
(2.1) f(x)=-x3-2x2-2; f'(x)=-3x2-4x.
1. f(-1)=-(-1)3-2(-1)2-2=1-2-2=-3
2. f'(-1)=-3(-1)2-4(-1)=-3+4=1=-(-1) (b=-1?)
3. Gradient at (-1,-3) is f'(-1)=1. So 1/c=1, and c=1?.
Tangent line at (-1,-3) is y-f(-1)=f'(-1)(x-(-1))=1(x+1); y=f(-1)+x+1=-3+x+1; y=x-2 is the tangent line at (-1,-3).
4. y=x-2 (d=2)
(2.2) A(3,-1,1); B(4,1,1); C(2,1,-1)
a. Vector AB=<4-3,1+1,1-1>=<1,2,0>; Vector AC=<2-3,1+1,-1-1>=<-1,2,-2>
b. |AB|=√(12+22+02)=√5
c. |AC|=√(1+4+4)=3
d. Dot product AB.AC=-1+4+0=3
e. cosα=AB.AC/|AB||AC|=3/(3√5)=1/√5=√5/5