Mathematics Question Thread

[jamonwindeyer]

Could i please get help with these two questions?
I am not sure how to draw the diagrams 

Hey! I've popped the diagrams below for you; let me know how you go!

Images

[Blissfulmelodii]

how to do this without guess and check

find the two numbers whose sum is 28 and whose product is a maximum

Edit: This was deleted, but I've legit never seen this question done this way before. I love it, and I think everyone will benefit from seeing it. Bliss, if you don't want it here, feel free to re-delete but I think its great! Doesn't matter that Rui already answered

I'm not sure how to write equations on here so I hope you will understand my working out.

Let x be the first number. The sum of the two numbers is 28 so 28-x is an expression for the second number.

Let y be the product of the two numbers
Then you will end up with an equation like this y=x(28-x)
Expand it: y=28x-x^2
Since it is a quadratic equation, it will graph a concave down parabola which means that the vertex will be the maximum value.

If the vertex of a parabola is the point (h,k) then h=-b/2a so you just have to substitute the 'a' and 'b' values from the previous equations
h= -28/2(-1)
h= 14

substitute this value into the quadratic to find the y-value which should come out as 196 and you end up with the vertex of the parabola having coordinates of (14,196)

Now if you go back to the start we created an expression for the second number with was 28-x. Sub in x=14 and you end up with the second number also being 14. Hence the two numbers are 14 and 14

[RuiAce]

Edit: This was deleted, but I've legit never seen this question done this way before. I love it, and I think everyone will benefit from seeing it.

Yeah it's pretty standard. Just not common.

Most people vouch for the calculus approach because it's what they're used to. What they're used to is what works universally, i.e. for every question of the sort.
And because I don't know how HSC examiners mark, I've just been using it as well. I would've used this approach, if I had more reassurance with it, HEAPS more times in my life. It's clearly faster

The important thing, however, is to explicitly state the concavity (as Bliss did). If you don't state the concavity, then you don't justify why the turning point offers a maximum and I would deduct one mark for the working out.

[Blissfulmelodii]

Edit: This was deleted, but I've legit never seen this question done this way before. I love it, and I think everyone will benefit from seeing it. Bliss, if you don't want it here, feel free to re-delete but I think its great! Doesn't matter that Rui already answered

No worries at all. I only deleted it because I had noticed afterwards that Rui had answered the question already so I figured mine was irrelevant hahaha 

[anotherworld2b]

Could you explain the process of how you drew the diagrams please?
I am still a bit confused on how interpret info from a question.

I was also wondering if i could get help answering this question. I have tried to figure out the answer but i keep getting the wrong answer.

 

Hey! I've popped the diagrams below for you; let me know how you go!

Images

[jamonwindeyer]

Could you explain the process of how you drew the diagrams please?
I am still a bit confused on how interpret info from a question.

I was also wondering if i could get help answering this question. I have tried to figure out the answer but i keep getting the wrong answer.

The first one (Q6) is a standard angles of elevation question. Remember, an angle of elevation is the angle formed by your eye line when you look up at something. So at point A, that angle is 40 degrees. Then we move 4 metres closer to the tree that the ball in (as represented by that vertical line on the right), and the angle becomes 45 degrees. That's at the point B in the diagram

The second one is harder (Q5); the line on the top represents the flight of the plane in two halves. First, the question identifies a point where the angle of depression is 40 degrees. That is the top left vertex of that bottom triangle. The plane then flies until it is directly above the farmhouse; that forms the right angled triangle at the bottom. After that it elevates at an angle of 15 degrees, that's where the line slants upwards into the right hand side of the diagram!

Try to work through the information one piece at a time. Draw the diagrams yourself, from scratch, piece by piece and see if you get something similar to mine! Ensure you have tried a few easier 'angles of elevation/depression' questions before tackling these, if you are having trouble

For that question you posted, do you learn the formula for finding the area of a minor segment of a circle? That will help me answer it in a way that makes sense for you

[katnisschung]

stuck on the second part of this question

[RuiAce]

stuck on the second part of this question

[katnisschung]

what de.. im lost

[RuiAce]

what de.. im lost

[anotherworld2b]

For q5. How did you get 15 degrees?
Would this diagram(below) be right?

In regards to the question i posted prior i have learnt the formula for finding tha area for a minor segement of a circle.

I also wanted to ask for this question attached below I'm not sure what I'm supposed to find

The first one (Q6) is a standard angles of elevation question. Remember, an angle of elevation is the angle formed by your eye line when you look up at something. So at point A, that angle is 40 degrees. Then we move 4 metres closer to the tree that the ball in (as represented by that vertical line on the right), and the angle becomes 45 degrees. That's at the point B in the diagram

The second one is harder (Q5); the line on the top represents the flight of the plane in two halves. First, the question identifies a point where the angle of depression is 40 degrees. That is the top left vertex of that bottom triangle. The plane then flies until it is directly above the farmhouse; that forms the right angled triangle at the bottom. After that it elevates at an angle of 15 degrees, that's where the line slants upwards into the right hand side of the diagram!

Try to work through the information one piece at a time. Draw the diagrams yourself, from scratch, piece by piece and see if you get something similar to mine! Ensure you have tried a few easier 'angles of elevation/depression' questions before tackling these, if you are having trouble

For that question you posted, do you learn the formula for finding the area of a minor segment of a circle? That will help me answer it in a way that makes sense for you

[jamonwindeyer]

For q5. How did you get 15 degrees?
Would this diagram(below) be right?

In regards to the question i posted prior i have learnt the formula for finding tha area for a minor segement of a circle.

I also wanted to ask for this question attached below I'm not sure what I'm supposed to find

15 degrees comes from the question itself, that looks okay to me!

For the circles one, you are finding two minor segments. The minor segment in circle 1 and the minor segment in circle 2, the formula should be something like this:



The radii are in the question; you've found the angles already! What this formula does is takes the area of the sector, and subtracts the area of the triangle, leaving only the area of the minor segment. So you don't need to find the areas of the triangles separately like you did in your earlier working; if you know this formula, you can just substitute it into here!

Unfortunately I can't see that diagram for the last question properly, too small

[katnisschung]

hi again!

stuck on finding the third equation for this word problem

The sum of the dimensions of a box with a square base is 60cm.
Find the dimensions that will give the box a maximum volume

the two equations i have are
l+b+h=60
SA= 2lb+2lh+2bh

but there are 3 unknowns so presumably i need another one.....
sighs

[RuiAce]

hi again!

stuck on finding the third equation for this word problem

The sum of the dimensions of a box with a square base is 60cm.
Find the dimensions that will give the box a maximum volume

the two equations i have are
l+b+h=60
SA= 2lb+2lh+2bh

but there are 3 unknowns so presumably i need another one.....
sighs

The base is a square. Two sets of sides are equal (l=b is the third equation)

And remember that you're interested in the volume. Not surface area.

[katnisschung]

ahaha thanks ruiace
im such an idiot