Misc. Questions (1 Viewer)

[acmilan]

Hi I was wondering if people could help out with some questions:

1.
Tom is playing 50 black jack games tomorrow
The probability that he wins is 0.3 on a fine day and 0.6 on a wet day
The probability that it will rain tomorrow is 0.8
How many games would Tom expect to win tomorrow?

2. If a,b,c are in proportion (ie. a/b = b/c) show that the roots of
ax^2 + bx + c = 0 are imaginary

3.Find the equation to the tangent to the curve y = a^3 - 2a and x = 2a^2 - 3 at the point where a = 2

Thanks

 

[withoutaface]

Hi I was wondering if people could help out with some questions:

1.
Tom is playing 50 black jack games tomorrow
The probability that he wins is 0.3 on a fine day and 0.6 on a wet day
The probability that it will rain tomorrow is 0.8
How many games would Tom expect to win tomorrow?

2. If a,b,c are in proportion (ie. a/b = b/c) show that the roots of
ax^2 + bx + c = 0 are imaginary

3.Find the equation to the tangent to the curve y = a^3 - 2a and x = 2a^2 - 3 at the point where a = 2

Thanks

2. discriminant= b²-4ac=b²-4(b²/c)*c=-3b²<0

the roots are complex, not imaginary because you end up with x=-b(1+sqrt3)/2a

3. find values of x and y

y=8-4=4

x=8-3=5

Find m

dy/dx=(dy/da)/(dx/da)=(3a²-2)/(4a)
m=10/8=5/4

then you substitute into m(x-x1)=y-y1, but you get the idea
Ill have a look at number one and post a solution when I can.

EDIT: For 1 try finding the greatest coefficient on both a rainy day and sunny day, then:

.8*(rainy day games)+.2*(sunny day games)

I think.

 

[mojako]

no, the roots are imaginary

discriminant: b^2 - 4ac, where b^2 = ac from a/b=b/c
So, discriminant = -3ac, where ac = b^2 and is therefore positive
hence the discriminant is negative and the root is imaginary.. (i.e. not real)
in 3U context, imaginary means it doesnt belong to the real number field
btw, I think there's a minor typo in ur answer/explanation to this question.

 

[wogboy]

1.
Tom is playing 50 black jack games tomorrow
The probability that he wins is 0.3 on a fine day and 0.6 on a wet day
The probability that it will rain tomorrow is 0.8
How many games would Tom expect to win tomorrow?

P(WIN) = P(RAIN)*P(WIN | RAIN) + P(FINE)*P(WIN | FINE)
= 0.8*0.6 + 0.3*0.2
= 0.54

So the expected value of wins in 50 games is 50*P(WIN)
= 27