Math Is Fun Forum
You are not logged in.
- Topics: Active | Unanswered
#151 Re: Help Me ! » Border of Circular Swimming Pool » 2023-11-10 07:07:55
Outline: 1. [The area A of a circle with radius r is given by] A = pi•r^2
yes
2. The expression that gives the outer radius is not too clear to me.
I think it is: A = pi•(2x + 10)^2
draw the circle for the pool
label the radius
draw the outer cricle for the border
label the width
label the radius
is the radius of the pool+border area equal to the whole diameter of the pool plus the border width on both sides?
3. A foot is 12 inches. How much of a foot is 3 inches? It is 3/12 of a foot.
3/12 = 1/4 = 0.25
4. Let A_b = area of border. I think it is pi(2x + 10)^2 - pi•(5)^2
no
5. Is the right equation the following?
27 = pi(2x + 10)^2 - pi•(5)^2, where x is the width of the border.
where does this use the thickness of the border?
#152 Re: Help Me ! » Completing the Square » 2023-11-09 11:50:14
the complete-the-squarr process is:
half of b/a is b/2a
square this to get the completed-square 3erd term
add this squared term to both sides
including any multiplier 'a':half of (pi)/2 is (pi)/4
square this to get ((pi)^2)/16
unless they tell you specifically to round to 4 decimal places you should do exact using pi
x^2 + (π/2) x + π^2/16 = -1 + π^2/16
(x + (π/4))(x + (π/4)) = 1.4674
like bob said: stop rounding
use exact values
(x + (π/4))^2 = -0.38315
where did -0.38315 come from?
all you did was change (expression)(expression) to (expression)^2
thats just a change of formatting
the value of the other side should not have changed
Stuck here....
follow the steps exactly as listed
including adding the (half of (middle coefficient))^2 to both sides
#153 Re: Help Me ! » Find Coordinates of Point A » 2023-11-09 11:41:54
amnkb wrote:open google play store
select 'search'
enter 'carbon browser'
select and install
open carbon brwoser
enter url for image
long-press image
select 'open image in new tab'
go to new tab
press url box (it should look like i.imgur.io/[bunch of characters]_d.webp?[query string]
note: [bunch of characters] in the new tab will NOT be the same as the [bunch of characters] in the original tab!!!
select edit (pencil icon)
erase from the end until you get to the [stuff]_d.webp
replace .webp with .jpg
delete _d
select 'go' at bottom of keyboard
your image should diaply alone on the page
copy new url and paste between [ img] [ /img] tags (without the extra spaces of course)This is too confusing.
which part? you installed carbon browser and then??
#154 Re: Help Me ! » Reducing Size of Candy Bar » 2023-11-09 11:38:59
A jumbo chocolate bar with rectangular shape measures 12 cm in length, 7 cm in width, and 3 cm in thickness. Due to escalating costs of cocoa, management decides to reduce the volume of the bar by 10%. To accomplish this reduction, management decides that the new bar should have the same 3 cm thickness, but the length and width of each should be reduced an equal number of centimeters. What should be the dimensions of the new candy bar?
This one through me into a loop.
I think this problem demands the use of the volume formula
V = length • width • height. The part about reducing the volume by 10% is confusing to me.Can someone explain what is going on in this problem and set up the right equation for me to use?
old length: 12
old width: 7
old thickness: 3
old volume: ___
new length: 12 - x
new width: 7 - x
new thickness: 2
new volume: ___
new volume is 90% of old volume
#155 Re: Help Me ! » Border of Circular Swimming Pool » 2023-11-09 11:36:14
A circular pool measures 10 feet across. One cubic yard of concrete is to be used to create a circular border of uniform width around the pool. If the border is to have a depth of 3 inches, how wide will the border be?
I know that 1 cubic yard is 27 cubic feet.
I say let x = width of the border around the pool
I don't know where to go with this information.
what is the formula for the area of a circle with radius r?
if x is the border width then what expression gives the outer radius of the border?
how much of a foot is 3 inches?
the area of the border is (outer circle - inner circle)
the volume is area times thickness
plug info into equation, set equal to 27
solve for x
#156 Re: Help Me ! » Find Coordinates of Point A » 2023-11-08 11:25:46
Can you send me step be step instructions in terms of uploading photos and images?
okay i can expand on what i said before
open google play store
select 'search'
enter 'carbon browser'
select and install
open carbon brwoser
enter url for image
long-press image
select 'open image in new tab'
go to new tab
press url box (it should look like i.imgur.io/[bunch of characters].webp?[query string]
note: [bunch of characters] in the new tab will NOT be the same as the [bunch of characters] in the original tab!!!
select edit (pencil icon)
erase from the end until you get to the .webp
replace .webp with .jpg
select 'go' at bottom of keyboard
your image should diaply alone on the page
copy new url and paste between [ img] [ /img] tags (without the extra spaces of course)
with your image from another thread i got this:
i.imgur.io/7uB3NEl_d.jpg
remove the '_d' to get i.imgur.io/7uB3NEl.jpg
putting it between the 'img' tags does this:
if you dont delete the underscore-d then you get a thumbnail (?) thats pretty small:
#157 Re: Help Me ! » Completing the Square » 2023-11-08 10:15:56
amnkb wrote:where did 1.4674 come from?
did you assign n the value of pi?
how did you get the square of n/4 being (n^2)/4?
shouldnt the 4 be squared too?
not understanding your results
sryLook:
-1 + π^2/4 = 1.4674 according to the calculator.
so n equals
?also the middle coefficient of your equation is (pi)/2
you're supposed to take half of this and then square it to get the third term to complete the square
the complete-the-squarr process is:
half of b/a is b/2a
square this to get the completed-square 3erd term:
half of (pi)/2 is (pi)/4
square this to get ((pi)^2)/16
unless they tell you specifically to round to 4 decimal places you should do exact using pi
#158 Re: Help Me ! » Find Value of a » 2023-11-08 09:51:00
(-1)^2 + 6(-1) = (1) - 6 = -5
(-5)^2 + 6(-5) = (25) - 30 = - 5
The correct of a is -5.
why do you say a = -1 is not a sol'n?
#159 Re: Dark Discussions at Cafe Infinity » Coney Island Parachute Ride » 2023-11-08 09:49:00
This is just a test. I want to know if anyone here can see the photo.
https://imgur.com/gallery/4Gh1VYy
i did copy n paste
is it supposed to be 'coney island parachute ride'?
#160 Re: Help Me ! » Find Intercepts & Test for Symmetry » 2023-11-07 07:37:09
Given 16y^2 = 120x - 225,
A. Find the intercepts.
B. Test for symmetry with respect to the x-axis, y-axis, and origin.
For A, I simply let x = 0 to find the y-intercept(s).
To find find x-intercept(s), I must let y = 0.
yes
Yes, it's symmetric with respect to the x-axis.
I say not symmetric with respect to the y-axis.
I say not symmetric with respect to the origin.
check your work with a graph
its a sideways parabola so its only symmetric abt the x-axis
desmos graph
#161 Re: Help Me ! » Testing for Symmetry » 2023-11-07 07:30:19
An equation is being tested for symmetry with respect to the x-axis, y-axis and the origin. Explain why, if two of these symmetries are present, the remaining one must also be present.
Does anyone know?
Reddit thread
if its symmetric about the y-axis then its even
if its symmetric about the origin then its odd
so the equation cant be a function
maybe theyr'e thinking of circles/ellipses?
symmetry PDF
#162 Re: Help Me ! » Name Another y-intercept » 2023-11-07 05:03:40
If the graph of an equation is symmetric with respect to the x-axis and 2 is a y-intercept, name the other y-intercept.
A graph is said to be symmetric with respect to the x-axis if, for every point (x, y) on the graph, the point (x, -y) is also on the graph.
I say the other y-intercept is the point (0, -2).
yes
#163 Re: Help Me ! » Name Another x-intercept » 2023-11-07 04:30:53
If the graph of an equation is symmetric with respect to the y-axis and 6 is an x-intercept of this graph, name another x-intercept.
I know that a graph is said to be symmetric with respect to the y-axis if, for every point (x, y) on the graph, the point (-x, y) is also on the graph.
I say another x-intercept is the point (-6, 0).
yes
#164 Re: Help Me ! » Find Value of a » 2023-11-07 03:54:05
If (a, -5) is a point on the graph of y = x^2 + 6x, what is a?
-5 = a^2 + 6a
a^2 + 6a + 5 = 0
(a + 1) (x + 5) = 0
a = -1
a = -5
I got two values for a. Which one is right? Are they both right?
quadratics usually have 2 sol'ns
to check your ans plug it back into the problme
what does (-1)^2 + 6(-1) equal
what does (-5)^2 + 6(-5) equal
#165 Re: Help Me ! » Find Intercepts Given Equation » 2023-11-07 03:49:48
Find the intercepts given the equation 5x + 2y = 10.
To find the x-intercept let y = 0.
5x + 2(0) = 10
5x = 10
x = 2
To find the y-intercept, let x = 0.
5(0) + 2y = 10
2y = 10
y = 5
you can check your work by graphing
y = -(5/2)x + 5
#166 Re: Help Me ! » Completing the Square » 2023-11-07 03:43:14
x^2 + (π/2) x + π^2/4 = -1 + π^2/4
(x + (π/2))(x + (π/2)) = 1.4674
(x + (π/2))^2 = 1.4674
I now take the square root on both sides. Yes?
where did 1.4674 come from?
did you assign n the value of pi?
how did you get the square of n/4 being (n^2)/4?
shouldnt the 4 be squared too?
not understanding your results
sry
#167 Re: Help Me ! » Find Coordinates of Point A » 2023-11-07 03:35:55
The midpoint of the line segment from A to B is (5, -4). If B = (7, -2), what is A?
Solution:
Let point A = (x_1, y_1).
5 = (x_1 + 7)/2
-4 = (y_1 - 2)/2
Is this the correct set up to find the coordinates of point A?
this is fine
you can check your work by using the distance formula
if |AB| is twice as long as |CB| (i'm naming the midpoint C) then your answer is right
#168 Re: Help Me ! » Graph of Equations » 2023-11-05 15:09:17
Plotting points tells me where the intercepts are located. Yes? Do you have an example graph for me?
make your own example (& look at the examples in the book)
like take (x - 2)(x + 3) = y
graph it & check that it crosses at x = 2, x = -3
#169 Re: Help Me ! » Completing the Square » 2023-11-05 15:07:14
Given (π/2)^2 = π^2/4, I now must add π^2/4 to both sides of the equation.
Here it is:
x^2 + (π/2) x + π^2/4 = -1 + π^2/4
Where do I go from here?
turn the left-hand side into perfect-square form
combine the right-hand side to being 1 fraction
take the square root of both sides
solve for x= on the left-hand side
#170 Re: Help Me ! » Factoring Equations With Decimals » 2023-11-05 15:04:50
Factor 2.3x^2 + 1.4x - 4.5 = 0 without a calculator.
What is the best method to use for factoring equations with decimals without a calculator?
i'd multiply thru by 10 to get rid of the decimal pts
then do the Quadratic Formula
answer is messy
#171 Re: Help Me ! » Find Number of Right Triangles » 2023-11-05 15:00:31
#172 Re: Help Me ! » Dimensions of A Window » 2023-11-05 14:56:34
The area of a rectangular window is to be 306 square centimeters.
If the length exceeds the width by 1 centimeters, what are the dimensions of the window?I think A = length • width is needed here. Yes?
Length = x + 1
Width = x
306 = (x + 1)(x)
(x + 1)(x) = 306
x^2 + x = 306
x^2 + x - 306 = 0
Is this the correct equation?
solve the eqn and check the sol'ns in the problem
you'lla get 2 sol'ns
ignore the negative sol'n
#173 Re: Maths Is Fun - Suggestions and Comments » SSL expired? » 2023-10-22 08:58:52
im stillgetting the 'not secure' message w/ https having a red strike-thru
maybe new ssl is still propagating
now its working!
#174 Re: Maths Is Fun - Suggestions and Comments » SSL expired? » 2023-10-22 02:44:22
I got a reply and the problem is solved by around GMT 4 AM.
im stillgetting the 'not secure' message w/ https having a red strike-thru
maybe new ssl is still propagating
#175 Re: Help Me ! » Quadratic equations. Solution for x. Is it AND, or, OR? » 2023-10-20 04:10:36
When we solve for x and get two answers do we state this as, for example, x = -2 OR x=3. Or do we state it as x = -2 AND x=3?
I'm new to quadratic equations, obviously, and I've heard someone say, 'Or', another say, 'And', and yet another just put a comma between the two answers.
both sol'ns work
but x cant be 2 values AT THE SAME TIME
so x = -2 OR x = 3
but both are valid sol'ns