~~Mathematics Revising Game~~ (1 Viewer)

[lyounamu]

13/52 * 39/51 * 26/50 * 13/49 = 2197/83300 or 0.2637 (4d.p)

Question = find d(sec^2(x))/dx.

y = 1/cos^2x
y' = 2cosx sinx/cos^4(x)
= 2sinx/cos^3(x)

http://www.boredofstudies.org/courses/maths/2u/2002_Maths2_T_Manly_q.pdf

9(B)

Very good practice for this type of question in HSC

 

[Graceofgod]

y = 1/cos^2x
y' = 2cosx sinx/cos^4(x)
= 2sinx/cos^3(x)

http://www.boredofstudies.org/courses/maths/2u/2002_Maths2_T_Manly_q.pdf

9(B)

Very good practice for this type of question in HSC

9bi) t = 0 to t = 10

ii) t = 25 to t = 30

iii) t = 10

iv) t = 30

v) t = 20

vi) ...How?

Question:
Prove that:

Root[(cos^2(x) + sin^2(x) + cot^2(x))*sin^2(x)] = 1

 

[lyounamu]

9bi) t = 0 to t = 10

ii) t = 25 to t = 30

iii) t = 10

iv) t = 30

v) t = 20

vi) ...How?

Question:
Prove that:

Root[(cos^2(x) + sin^2(x) + cot^2(x))*sin^2(x)] = 1

well done - all correct except vi but you cannot really post that up here anyway.

your q: doesn't work.

 

[tommykins]

回复: Re: ~~Mathematics Revising Game~~

thought so, it wasn't just my shitty working via computer ^^

 

[Graceofgod]

Woops =S Sorry must have made mistake =S Should i post another?

EDIT: I am pretty sure it works... =S

EDIT: Yeah I couldn't do it on computer is what I meant.
My question: It is relatively simple, are you sure you aren't messing up the grouping symbols?

 

[tommykins]

回复: Re: ~~Mathematics Revising Game~~

tried it again, doens't work.

 

[lyounamu]

Woops =S Sorry must have made mistake =S Should i post another?

EDIT: I am pretty sure it works... =S

EDIT: Yeah I couldn't do it on computer is what I meant.
My question: It is relatively simple, are you sure you aren't messing up the grouping symbols?

that doesn't work because i got this in the end:

root (1+cos^2(x))

and that is NOT equal to 1.

 

[Graceofgod]

Re: 回复: Re: ~~Mathematics Revising Game~~

Root[(cos^2(x) + sin^2(x) + cot^2(x))*sin^2(x)] = 1

LHS = Root[(cos^2(x) + sin^2(x) + cot^2(x))*sin^2(x)]
= Root[(1 + cot^2x)sin^2(x)]
= Root(sin^2(x) + cos^2(x))
= Root(1)
= 1

 

[lyounamu]

Re: 回复: Re: ~~Mathematics Revising Game~~

Root[(cos^2(x) + sin^2(x) + cot^2(x))*sin^2(x)] = 1

LHS = Root[(cos^2(x) + sin^2(x) + cot^2(x))*sin^2(x)]
= Root[(1 + cot^2x)sin^2(x)]
= Root(sin^2(x) + cos^2(x))
= Root(1)
= 1

ah ok, I think both of us got confused with your sign use.

 

[Graceofgod]

that doesn't work because i got this in the end:

root (1+cos^2(x))

and that is NOT equal to 1.

Yep it was grouping symbols. My bad.. Should have made it clearer.

 

[tommykins]

回复: Re: 回复: Re: ~~Mathematics Revising Game~~

Root[(cos^2(x) + sin^2(x) + cot^2(x))*sin^2(x)] = 1

LHS = Root[(cos^2(x) + sin^2(x) + cot^2(x))*sin^2(x)]
= Root[(1 + cot^2x)sin^2(x)]
= Root(sin^2(x) + cos^2(x))
= Root(1)
= 1

cos^2x+sin^2x = 1, not sin^2x.

NVM i see the grouping now.

 

[lyounamu]

http://www.boredofstudies.org/courses/maths/2u/1139495695_2004_Mathematics_Trial_Paper.pdf

Let's get the thread going, shall we?

Try this awesome q 10 b)

Hint: Don't LOOK AT THE ANSWERS!

 

[axlenatore]

find the integral of e^x

 

[kaz1]

find the integral of e^x

e^x +c?

 

[pLuvia]

Re: 回复: Re: 回复: Re: ~~Mathematics Revising Game~~

Check out this thread for a lot of practice questions for you current HSCers or anyone interested

Marathon 1

From the last question from that thread

Stephen has a loan of 100,000.00 to pay. each month, interest of 0.8% is charged on the outstanding amount
a) If stephen pays 5,000 each month starting one month from now how long will it take him to repay the loan?
b) Now suppose stephen pays different amounts every months, but according to the rule that for every dollar of the balance, he'll pay eight cents, so he'll pay more initially, but less later. Find the outstanding amount after the n-th payment

 

[duy.le]

that is a very hard 2 unit question. it was really confusing and i got it wrong... wow that was a bit queer.

note i was referring to lyounamu's question.

 

[Shadose]

http://www.boredofstudies.org/courses/maths/2u/1139495695_2004_Mathematics_Trial_Paper.pdf

Let's get the thread going, shall we?

Try this awesome q 10 b)

Hint: Don't LOOK AT THE ANSWERS!

So how do you do it?

(i) d@/dt=2
@=2t+C
@=2t

(ii)tan(@)=x/10
x=10tan(@)
=10tan2t

(iii)when @=30
t=15s

dx/dt=20sec^2(@)
=20sec^230
=20 x 4/3 km/s ... :S
=80/3 x 3600
=96 000 km/hour Its wrong.... I' know ... I looked at the answers

 

[Timothy.Siu]

Re: 回复: Re: 回复: Re: ~~Mathematics Revising Game~~

Check out this thread for a lot of practice questions for you current HSCers or anyone interested

Marathon 1

From the last question from that thread

Stephen has a loan of 100,000.00 to pay. each month, interest of 0.8% is charged on the outstanding amount
a) If stephen pays 5,000 each month starting one month from now how long will it take him to repay the loan?
b) Now suppose stephen pays different amounts every months, but according to the rule that for every dollar of the balance, he'll pay eight cents, so he'll pay more initially, but less later. Find the outstanding amount after the n-th payment

for a)i got 23.0726 --->24 months
doesn't seem right maybe

time for b, i'll assume he starts paying from month 1
i got nth month=PRⁿ(1-Q)ⁿ
where P=$100 000 R=1.008 and Q=0.08

 

[duy.le]

So how do you do it?

(i) d@/dt=2
@=2t+C
@=2t

(ii)tan(@)=x/10
x=10tan(@)
=10tan2t

(iii)when @=30
t=15s

dx/dt=20sec^2(@)
=20sec^230
=20 x 4/3 km/s ... :S
=80/3 x 3600
=96 000 km/hour Its wrong.... I' know ... I looked at the answers

yeah thats what i got, except i got u=75 +2/(3sqr 3)

 

[tommykins]

回复: Re: ~~Mathematics Revising Game~~

you need to do d@/dt in radians i believe.