Two Problems

J

JoolRee

New member
Joined
Sep 25, 2021
Messages
6
Hello.
I've recently started to revise a few problems, and I'm really stuck on two in particular. I have attempted both, and written out the information it provides, but honestly on both I just can't understand how to progress. If someone could just give me a starting point I'd be really really greatful!
Question 1: https://ibb.co/NYpVkkf
Question 2: https://ibb.co/VC78DCM

Thanks for any help!
 
JoolRee said:
Hello.
I've recently started to revise a few problems, and I'm really stuck on two in particular. I have attempted both, and written out the information it provides, but honestly on both I just can't understand how to progress. If someone could just give me a starting point I'd be really really grateful!
Click to expand...
These are your problems:
17
1632620150528.png​
Have you tried finding the radius of the circle?

25
1632620205123.png​
1632620257412.png​
1632620281761.png​
Have you tried expressing various segments as vectors in terms of a and b?

Please post some work (such as what you say you wrote out, and any ideas you had), so we can see where you need help.

You don't appear to have read the READ BEFORE POSTING instructions:

READ BEFORE POSTING

Welcome to FreeMathHelp.com! Please take the time to read the following before you make your first post. It will help you to get your math questions answered promptly and in the most helpful manner. A summary is available here, but please read the complete guidelines below at your earliest...
www.freemathhelp.com
 
JoolRee said:
Hello.
I've recently started to revise a few problems, and I'm really stuck on two in particular. I have attempted both, and written out the information it provides, but honestly on both I just can't understand how to progress. If someone could just give me a starting point I'd be really really greatful!
Question 1: https://ibb.co/NYpVkkf
Question 2: https://ibb.co/VC78DCM

Thanks for any help!
Click to expand...
#1. In general, given 2 simple shapes, how do you find the area of the first shape which is not included in the second shape?
 
lev888 said:
#1. In general, given 2 simple shapes, how do you find the area of the first shape which is not included in the second shape?
Click to expand...
I'm not sure I really understand this question

EDIT: Nevermind, do you mean, you work out the area of the first shape and subtract the are of the sub-shape?
 
JoolRee said:
Yes, however I feel I am missing something quite obvious to do with that. I have no idea how to get the radius.
Click to expand...
Did you make a drawing with lengths labeled?

Do you see that the center of the circle will be the midpoint of the bottom of the rectangle?

We want to see your work, not just a general description, so we can explicitly help you.

JoolRee said:
Hey, I posted links to the two in the post. Did they not work? I can try to re-upload
Click to expand...
Clearly the links worked, as I posted images from them. It's just easier to see when they are attached or inserted (as I did) rather than links to another site we need to go to. Maybe Jomo didn't see them, or didn't want to take the links.
 
JoolRee said:
Hi, here is what I have (sorry it's so messy I had to write it with a mouse)

View attachment 29033
Click to expand...
Often in problems like this you need to draw additional segment(s). Which segment? Well, it usually connect points you already have. And why do it? Because if this segment is meaningful for multiple shapes, one shape allows you to find its length and then you can use it to find something about another shape.
 
Last edited:
JoolRee said:
Hi, here is what I have (sorry it's so messy I had to write it with a mouse)

View attachment 29033
Click to expand...
If one considers the distance, [imath]R[/imath], from the centre of the semicircle to the upper right-hand corner of the inscribed rectangle it should equal [imath]\sqrt{8^2+6^2}[/imath]. What quantity is that part of the first problem?
If [imath]r[/imath] were the radius of the semicircle then would the shaded area be [imath]\frac{1}{2}\pi r^2-(16)(6)~?[/imath]
 
JoolRee said:
sorry it's so messy I had to write it with a mouse
Click to expand...
Hi JoolRee. You don't need to write equations with a mouse. You can type them. This is your work:

16 * 6 = 96 cm^2 = a[1]

a[2] = pi * r^2 [imath]\quad[/imath] r = 8 + x

a[3] = a[2] - a[1]

The area of a semicircle is not pi*r^2.

Have you learned the Pythagorean Theorem? The radius is the hypotenuse of a right triangle whose other sides you already know.

?
 
pka said:
If one considers the distance, RRR, from the centre of the semicircle to the upper right-hand corner of the inscribed rectangle it should equal 82+62\sqrt{8^2+6^2}82+62. What quantity is that part of the first problem?
If rrr were the radius of the semicircle then would the shaded area be 12πr2−(16)(6) ?\frac{1}{2}\pi r^2-(16)(6)~?21πr2−(16)(6) ?
Click to expand...
Yes! This is exactly what I was looking for. I knew I missed something really simple haha. Thanks :)
 
You must log in or register to reply here.
Top