Some maths question (MC) (2 Viewers)

[Fiction]

Hey guys,
Could anyone work out a step-by-step answer to the following two questions (please and thank you )

Trig
http://imgur.com/Oa0qWLO

Probability
http://imgur.com/Aa7p5ae

 

[qwert73]

for probability I got 5/8 which is D
= 1 - P(no one getting under 10 seconds)
= 1 - 3/4 x 5/6 x 3/5
= 5/8

for trig I got 4 but I'm not too sure about it. What you do is find the values where sinx=1 and where tanx=-2. Where these occur the equation will equal zero.

 

[Fiction]

for probability I got 5/8 which is D
= 1 - P(no one getting under 10 seconds)
= 1 - 3/4 x 5/6 x 3/5
= 5/8

for trig I got 4 but I'm not too sure about it. What you do is find the values where sinx=1 and where tanx=-2. Where these occur the equation will equal zero.

Opps, should've put up the answers; the probability one is D and the trig one is 2 so B.

For the probability question; why is it times and not plus?

Thanks~ (Can you tell I'm shit at this subject yet hahah)

 

[InteGrand]

Opps, should've put up the answers; the probability one is D and the trig one is 2 so B.

For the probability question; why is it times and not plus?

Thanks~ (Can you tell I'm shit at this subject yet hahah)

In general for probability Q's, "times" corresponds to "and", and "plus" corresponds to "or".

 

[photastic]

Solution for the trig

It is not 3 solutions because tan(pi/2) is undefined, hence there are only 2 solutions.

 

[davidgoes4wce]

It is not 3 solutions because tan(pi/2) is undefined, hence there are only 2 solutions.

Tan has 2 solutions, Sin has 1 solution. Hence, there are a total of 3 solutions for the equation (sin x-1) (tan x +2)=0

 

[davidgoes4wce]

I don't draw my asymptotes very well (dark line). My apologies.

 

[photastic]

Tan has 2 solutions, Sin has 1 solution. Hence, there are a total of 3 solutions for the equation (sin x-1) (tan x +2)=0

But the solution from sin which is pi/2 cannot be a solution for the equation (sin x-1) (tan x +2)=0 because if you substitute pi/2, you get an undefined answer, hence there are only 2 solutions, you've drawn the diagram yourself and it is clear that pi/2 is not a solution because it is the assymptote for tan. This was something a lot students got wrong from last year's HSC exam.

 

[Mr_Kap]

the trig one:


sinx = 1

x = 90 degrees (only one solution here as 180-90 is also equal to 90)
HOWEVER if you test it in the original..it doesn't equal zero because tan(90) = undefined.


tanx = -2
has two solution


hence the answer is 2

 

[Mr_Kap]

But the solution from sin which is pi/2 cannot be a solution for the equation (sin x-1) (tan x +2)=0 because if you substitute pi/2, you get an undefined answer, hence there are only 2 solutions, you've drawn the diagram yourself and it is clear that pi/2 is not a solution because it is the assymptote for tan. This was something a lot students got wrong from last year's HSC exam.

including yourself hahaha.

 

[davidgoes4wce]

I delete my solution cause I suck

 

[photastic]

including yourself hahaha.

Scarred for life

 

[Mr_Kap]

Scarred for life

i remember reading the exam thoughts 2014 last year and i remember you sayin you spent all this time drawing the graph and everything.
haha

 

[photastic]

i remember reading the exam thoughts 2014 last year and i remember you sayin you spent all this time drawing the graph and everything.
haha

Please, I wanted that state rank

 

[Fiction]

In general for probability Q's, "times" corresponds to "and", and "plus" corresponds to "or".

ooooh
Sweet, thanks

the trig one:


sinx = 1

x = 90 degrees (only one solution here as 180-90 is also equal to 90)
HOWEVER if you test it in the original..it doesn't equal zero because tan(90) = undefined.


tanx = -2
has two solution


hence the answer is 2

How do you figure out that tan =-2 has two solutions? Do you draw it out?

I delete my solution cause I suck

Aww no you don't
At least you didn't try to draw out the two graphs and count how many times they touched the X-axis like what I did lol

 

[InteGrand]

How do you figure out that tan =-2 has two solutions? Do you draw it out?

Sketch is here: https://graphsketch.com/?eqn1_color..._lines=1&line_width=4&image_w=850&image_h=525