simultaneous equations

[crystal light]

Can anyone please help me with question 4 and 7?

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[lapis goblet]

For number 7 you can name two variables, x and y for the two positive numbers. We will say y is bigger than x.
It says the two positive numbers differ by 1.5. We can write this as y - x = 1.5
It also says that the sum of their squares is 9.125. We can write this as x^2 + y^2 = 9.125
Solve the system of equations. I would suggest substitution by replacing y from the second equation with 1.5 + x from the first equation. Solve for x by and plug that into y

Try derive the equations the same way for 4

[crystal light]

Thank you soo much

[torpid pendant]

@crystal light has given 1 rep to @lapis goblet

[lapis goblet]

What does rep do

And np

[crystal light]

They asked for it it’s a reward

[lapis goblet]

Oh

[crystal light]

Can u help with 4 ?

[lapis goblet]

A good approach to any word problem is to try to covert words to equations. If you have trouble start writing out equations that probably relates to the problem like pi * r^2 and see if it’s applicable

[lapis goblet]

I can

So we are comparing two circles area and circumferences

[crystal light]

Yes

[lapis goblet]

So

c = pi * d right?

And d = 2r

[crystal light]

Yes

[lapis goblet]

So c = pi * 2 * r

Let’s call the two circles’s radiuses x and y

So their circumferences must add up to 38 * pi

Circumference is 2 * pi * r

We named the circumference of the two circles

The circle with radius y would have circumference of 2 * pi * y

[lapis goblet]

And the circle with radius x would have circumference of 2 * pi * x

And these two have to add up to 38 * pi

So 2 * pi * x + 2 * pi * y = 38 * pi

I’ll just use latex

$2x(pi) + 2y(pi) = 38(pi)$

[neon ingot]

Block of Cheese

[lapis goblet]

So you get how I got that?

Try doing it again

[crystal light]

Yes

Don’t we also form an equation for area ?

[lapis goblet]

I mean as it try it with the area

Relate the two circles area with the information given like how I did

We got the circumference of the two circles in mathematical terms and used the information given to write an equation

Try doing the same with area

Gtg though good luck

[crystal light]

Alr

[crystal light]

Allah Hafez and once again thank you so much

[torpid pendant]

@crystal light has given 1 rep to @lapis goblet

[lapis goblet]

No problem

[crystal light]

@lapis goblet sorry to bother you again but I cannot solve no 4

Could u please help me

From bothe the equation we made

The answer comes out wrong

The answer shud be 7 and 12 cm

[upper ether]

i can do the simul equation

can i @crystal light

?

[crystal light]

Sure please

[upper ether]

ok be

bet

so heads up- for simultaneous equations we want to replace y with x, and vice versa

so

[crystal light]

I did this

It’s wrong

[upper ether]

you have nice handwriting

[crystal light]

I can feel the sarcasm frm miles away but alr

[upper ether]

not sarcasm fr

you wanna see my handwriting?

its horrible

[crystal light]

That’s my rough work

[upper ether]

i lost 5 marks on a mock paper because the examiner couldnt read it

💀

[crystal light]

It’s messy as hell

[crystal light]

It’s al right no one cares abt handwriting

Now how do we do no 4 ?

@upper ether

[upper ether]

hmmm

[upper ether]

are the 2 circles congruent

[crystal light]

Nah

The question doesn’t say so

[upper ether]

oh shi

this is a hard one

[crystal light]

The answer to this question will be 7 and 12

Does that help anyway?

[upper ether]

the formula for circumference is 2πr

[crystal light]

Yep

Area is pi r square

@upper ether really really sorry to bother you but can u help me

[upper ether]

ok i will hol up

i need to figure this out

[crystal light]

It’s alright I did it

[foggy zephyr]

need answer'

[crystal light]

Can anyone help me with number 4

[wraith dagger]

Use Pythagorean theorem if u don’t know trigonometric identities for (a) part

[crystal light]

Thank you soooo. Much !