Need help with this question. Here goes:

 

Find the values of x, where 0 deg < x < 180 deg, such that

8 cosec 2x cot 2x = 3

 

Thanks guys!

 

Thanks ^tamago^

There is this question which I have problem solving. I got the wrong answers although I think my graph has got no problem. Can someone please take a look?

Sketch, on the same diagram, the graphs of y = sin x and y = 2 cos x, for the values of x from 0 and 2 pi. Hence,state

(a)the number of roots of the equation sin x = 2 cos x in the range 0 to 2 pi

(b) the range of values of x, between 0 and 2 pi, for which sin x and 2 cos x are both decreasing as x increases

For (a) the actual answer is 2... but i got 4 instead.

As for (b), my range is pi<x<3pi/2. the answer sheet writes pi/2 <x <pi

If possible, can someone help check whether I have done wrongly or are the answers correct?

 

Another question goes like this.

Sketch, on the same diagram, the graphs of y =3 cos x -2 and y =4 |sin x| for the doman 0 deg< or equal to x< or equal to 360 deg. Hence deduce the value of k for which the equation 3 cos x -2 = |4 sin x| + k has 3 solutions in this domain.

 

Is it really possible to solve this graph? I realise all the degree units are too close to one another such that one cannot even really read the values correctly.

 

Thanks.

 

Hey there, here's an equation which I have difficulty drawing out the graph.

 

|4 cos x/2 - 1 | for 0 < or equal x < or equal to pi

 

amplitude's 4 and period is 4 pi.

 

I drew out the graph but it looks weird. Would like someone to help me with this. Thank you. (:

 

And yea, I wanna check the shape of the graph for y =|2 tan 3x|

wishboy is correct. ^tamago^'s way of deriving the answer isn't wrong too. But he has to eliminate one of the signs (+ / -) since the answer isn't going to really be lying in all 4 quadrants.

 

By the way, towards the end where wishboy tried to find the answer for cos(pi/2 -A) = sin A, did you do so using the complementary angle formula? where cos x = sin (90 - x)? may i know why we can apply this formula here? how do you know it is a complementary angle without the question telling us so?

 

Thanks lots.

 

 

That's a lot of help. Thanks!

Steam passes into a jug to warm up some cold water. In this question, you may ignore any heating of atmosphere.

 

Pure steam enters at 100deg cel and jug initially contains 500g of water at 20 deg cels. Eventually water in the jug reachers a temperature of 100 deg cel. Specific heat capacity of water is 4.20J/g deg cel and specific latent heat of vaporisation of water is 2250J/g.

 

1calculate energy needed to warm 500g of water from 20 deg cel to 100 deg cel.

 

2. calculate final mass of water in jug when temperature has reached 100 deg cel.

 

For the first question, do i just find the energy using the S. heat capacity method or do i need to include the s. latent of of vaporisation method? I don't think we needa find the energy for the latter since there's no change in state anyway.

 

as for the second question do i equate the energy(FOUND USING S.HEAT CAPACITY METHOD) with the s. latent heat of vaporisation? i got 74.....g. then do i add on to the initial 500g of water? by the way, why does water in jug increase anyway?

 

ADAPTED FROM TYS (N2000 P2 Q5)

 

 

here's a logarithm question which i am not able to solve. i need the help of you guys out there.

 

express the following in the form ln x = ax + b and find a and b

 

(xe^x)^2 = 30e^-x

 

answer's a = -1.5, b = 1.7

 

here's what did...

 

2x ln xe = -x ln 30e

ln x + ln e = -x (ln 30 - ln e) / 2x

ln x + 1 = -x (ln 30 - 1) / 2x

 

after that i got stuck. ><

 

P.S the above workings may not be correct for i'm unsure of whether i should bring down the -x on the right hand side.

Originally posted by skythewood:

Convection is correct.

refrigerator cools by transfering heat out. Since the hot air is transferred into the same room, you can't cool the room

Same reason the air conditioner cooling unit is outside your house, and not inside.

Yea, thanks. I was thinking that fridge removes heat from inside and pumps hot air outside. Same concept. =D

I don't recall having any bad experience at Vivo's washrooms. They are pretty comfortable. I mean in terms of cleanliness.

I came across this question under the "Boiling & Evaporation" Chapter. It says, what is the principle used in the working of a refridgerator?"

 

My immediate answer would be convection. However, I don't have a clue how convection cuts any link with Boiling and evaporation.

 

Is there any discrepancies with my answer? (Maybe yes, haha) But, whatever the case, do give your take on this.

 

 

 

OH. Why is it a room cannot be cooled by turning on a fridge and leaving the door open? Quite worth thinking... I don't really know the exact answer to this, but still... anyone can give it a try.

 

Thank you.

does anyone here know if acids are organic solvents? I was wondering what would happen when copper oxide reacts with sulphuric acid. may i know if is copper oxide soluble?

 

and anpanman, there isn't anything wrong with the way you did the question. It was right when you find the oxidation state and compare.

Encountered a little problems with this question. Please take a look.(=

find all the angles between 0 deg and 360 deg which satisfy the equation

 

2sin y = tan y

cos y = 2

y lies in first or fourth quadrant.

cos alfa = 1/2

alfa = 60 deg

y - 60 deg, 300 deg

 

I am missing on 180 deg(stated in the answers). how can you find that?

 

THANKS!

Originally posted by wishboy:

0 < x < 2pi
0 < 2x < 4pi
-3 < 2x - 3 < 4pi - 3

3 cosec (2x - 3) + 15 = 1
cosec (2x - 3) = -14/3
sin (2x - 3) = -3/14

basic angle = 0.21596

2x - 3 = (-pi + 0.21596) , (0 - 0.21596) , (pi + 0.21596) , (2pi - 0.21596)
x = 0.0372 , 1.39 , 3.18 , 4.53

since the range goes beyond 0 to the negative region, u have to consider the angles in that region too

yea, i get what you are saying. what i do not know is why it is (-pi + 0.21596) and (0-0.21596)...

 

could you tell me how you know how to go about you doing the respective angles? why is it ( -pi +..., and 0 -....) i haven't dealt with negative regions so far so i don't kind of get the idea.

 

thanks! (=

FInd all the angles between 0 and 2 pi which satisfy the following equations.

3 cosec (2x - 3) +15 =1

managed to find that x = 3.18 and 4.53. however i am still missing 2 more answers and that is 0.0372 and 1.39. the range is -3 < 2x - 3 < 4  pi - 3

 

May I ask if there's anyone who can help assist me in this question? i tried to look at other viabilities to obtaining these 2 final answers but couldn't seem to get them. thanks.

 

Originally posted by UltimaOnline:

1) Weigh the anhydrous and hydrated salts. (the masses of both will be provided by the question.)

 

2) Calculate the molar mass of the anhydrous salts (from its formula).

 

3) Find the no. of moles of anhydrous salts. (no. of moles = sample mass / molar mass.)

 

4) Using algebra, equate mass of hyrated salts (by stoichiometry) with mass of hydrated salts (observed from experiment).

Come to think of it, I think my question goes something like this.

 

They give you a particular mass for the hydrated salt (eg 50.0g) and next they say water of crystallisation is removed by heating the salt to give the remaining anhydrous salt. They then tell you mass of anhydrous salt, say,28.0g.

 

Formula goes something like FeCl3.nH2O

 

question asks to find value of n. what i did was, i find the mass of the water that has been removed. in the case i created, the water that has evaporated is 22.0g. then i used 22 /18, where 18 is the Mr of H2O. i think i missed out some steps in between. do you know what they are?

there's this kind of question where they give you a hydrated salt, heat the salt to remove the water of crystallisation from it. I think the equation goes something like ____(salt's name)._H2O

 

How do you solve such questions? I did these questions before and looked through the required steps before the test today but I met with a hiccup midway throught the question. My answer was different from that of my friends'. could someone explain how you find out the "n" value of the H2O.

 

n is the unknown number, i think it's the mole ratio.

• if you don't mind ^tamago^, could you further explain how you solve the second question?  i mean part 2 of the question.

Originally posted by Tky35:

bonkysleuth  u mind sharing the answers for the listening comprehension?

sure. if you remember the questions, that is. i will try to recall the answers. ;DD

variables x and y are related by the equation y = ax / x-b. the graph y against y/x has gradient 3 and y-intercept 2.

 

(a) find value of a and b.

(b) find value of x for which x=y.

 

having a maths CT tomorrow, so please reply asap if you are able to help!

 

lastly thanks!

I will only be taking this november. i have heard a lot of talks going on about how diffcult the november paper will be compared to the may's paper. is it true or is this "rumour" unfounded? dead worried. anyway, the LC for this year was tricky. no one scored a perfect score in our class. the best was 18/20.

hydrogen bromide has a melting point of -87 deg celsius and a boiling point of -67 deg celsius. it dissolbes in water to form an acidic solution. describe what is seen when chlorine is bubbled through the solution.

 

the answer writes solution turns yellow. but i think it should be reddish brown. after all , isnt this a displacement reaction and chlorine displaces bromine? please check for discrepancies.

 

next. a student carried out some experiments to compare the relative strengths f dilute ethanoic acid and dilute hydrochloric acid. name a solid substance that will react with both acids. describe what you will see during the reaction.

what do you use? metal? if yes, then would the reaction be faster with HCl because it is a stronger acid and is fully ionised, thereby having a higher amount of H + ions.

 

please help ASAP because i still have got to clear my humans studying for tomorrow. thanks!

Originally posted by Maith:

walao,pri 6 got this alr ar?

i remember vividly learning this when i was in primary 6.

would you expect to take more time or less time to boil water in a saucepan if the outside curved surface of the saucepan were polished chrome rather than dull black? explain.

 

my guess is black takes a shorter time because it is a better absorber of heat. polished chrome is shiny which makes it a good reflector and a bad radiator. or does polished chrome take a shorter time since it does not radiate much heat? come to think of it, chrome seems to take a shorter time.

 

pretty perplexed by all these colours and stuff. can someone explain?

Originally posted by starmoonsun:

again, the graph x^2 + 2 does not intercept the x axis.

when x = 0, y =2. so you can expect that it is above the x-axis, but also intercepting the y-axis.

to find turning point, you can use dy/dx. at turning point, dy/dx = o. thus, find the value of x and sub it in the eqn y = x^2 +2 to find the corresponding y-value. if you have not learn differentiation, you can use the visual method to approach the question.

For example, y = x^2 +2 implies that a x^2 graph (centre at the 0,0 coordinate) moved 2 units up along the y-axis. so the turning point would be from (0,0) to (0,2).

for the next question, -x^2 graph implies that the graph is a x^2 graph, but reflected across the x-axis. i.e it is a x^2 graph that looks like you drawn it upside down and below the x-axis.

as the above question, the reflected x^2 graph should also cut the origin at (0,2). since the eqn given is y= -x^2 -3, this implies that the whole graph shifted 3 units down along the y-axis. thus the turning point of the graph is (0, -3). 

knowing the property of the graph, i.e the shape of the graph, you should be able to deduce that the line of symmetry is the x-coordinate of the turning point, i.e the line of symmetry is x=0.

How do you know the graph is centred at (0,0)?

state the turning point and sketch the graph of the following.

 

y = x^2 + 2

 

For this, you can't do the quadratic graph method like

when y =0. x =___

when x=0, y= ____

find turning point

find endpoints

 

when i sub y = 0. x^2 + 2 = 0

shift 2 to right-hand side and you get

x^2 = -2

 

i got stuck here cuz you cant square root a negative value. so what other method can i use?

 

the next question :

 

state the line of symmetry and sketch the graph of the following

 

y = -x^2 - 3. how do you get the line of symmetry? by looking at it, i can tell that it's 0 but is there anyone who can explain why?