how to do these qs (maths)-ORD

ayumi

I'm having difficulty in solving the following questions,can anyone help me in solving them.

1. write (1/4)3 as a power of 2 and hence solve equation 2(2x)-15=(1/4)3.
2(2x) is 2 to the power to 2x and (1/4)3 is a quarter to the power to 3


2. z1 =3+4i z2=1-7i

(i)find value of the real number k such that [z1]=k[z2]
(ii) if sand t are real numbers such that z1/z2=s(t+i)
find the value of s and the value of t

3. solve z squared -8z+25=0
write your answer in the form a+bi where a,b E R

4.the area of square abcd is 36cm2
(i) find length of side ab
(ii) find length of diagonal ac

THANK YOU

phasers

Sorry, that's paper one stuff so I remember nothing anymore

pathway33

ayumi wrote: »

4.the area of square abcd is 36cm2
(i) find length of side ab
(ii) find length of diagonal ac

THANK YOU

if the area is 36cm squared then each side must be 6 cm

when you draw the square you will have a, b, c and d on the four corners

(i) therefore the length of side ab is 6cm

(ii) the length of diagonal ac is the hypotenuese of a right angled triangle with sides 6cm and 6cm.

Using pythagoras to get the hypotenuese we get

sorry fire alarm going off

Claypigeon

Yeah I wondered the same why the paper 1 stuff

platypus

Q1. Looks way too hard for LC ord. (1/4)^3=1/64=1/(2^6)=2^-6. Definitely a mistake in the 2nd part somewhere

Q2 Im assuming part (i) is modulus signs. if so
Mod z1=sqroot (3^2+4^2)= 5
Mod z2 = sqrt (1^2+7^2)=sqrt50=5sqrt2

Therefore 5=k(5sqrt 2)
1=ksqrt2
k=1/sqrt2

Again this looks too hard for OL

(ii) Multiply top and bottom by conjugate of bottom line
(3+4i)/(1-7i) multiply by (1+7i)/(1+7i)
= (3+21i+4i-28)/(1+7i-7i+49)
=(-25+25i)/50
=(-1+i)/2
=1/2(-1+i)
so s=1/2 t=-1

3
use quadratic formula: a=1 b=-8 c=25
gives you (8+-sqrt-36)/2
srt -36=sqrt36*sqrt-1
=6i
so (8+-6i)/2
=4+-3i

4 What pathway said

Ina hurry will check for mistakes later

ayumi

well I'm not doing my leavng cert this yr but next yr and these qs are from my summer exams

phasers

ayumi wrote: »

well I'm not doing my leavng cert this yr but next yr and these qs are from my summer exams

Aren't you on your Summer holidays?

ayumi

yea but I just want to know how to do them

Liam O

phasers wrote: »

Aren't you on your Summer holidays?

Funny, I don't remember doing any maths on my Summer holidays last year

Just wait 'til September OP

ayumi

i thought it was hard and my teacher doesn't correct them,after Christmas she corrected 3 qs out of 10.I also think that they way I wrote the qs are not understood properly by pple.

but thanks