# Math Is Fun Forum

Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫  π  -¹ ² ³ °

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## #1 Re: Help Me ! » Vertices of Equilateral Triangle » 2024-04-12 08:54:55

Block him, Bob.

Isn't it nice that Bob gives people lots of chances before banning them?

## #2 Re: Help Me ! » Even, Odd or Neither Functions » 2024-03-24 14:06:15

FelizNYC wrote:

Determine if each function is even, odd or neither.

With poly's its really easy: just look at the powers

FelizNYC wrote:

1. g(x) = x^3 - 27x^1

All odd powers -> odd fcn

FelizNYC wrote:

2. f(x) = -x^3 + 12x^1

All odd powers -> odd fcn

FelizNYC wrote:

3. F(x) = -x^4 + 8x^2 + 8x^0

All even powers -> even fcn

FelizNYC wrote:

4. G(x) = -x^4 + 32x^2 + 144x^0

All even powers -> even fcn

## #3 Re: Help Me ! » Determine Local Minimum Value » 2024-03-24 14:03:01

FelizNYC wrote:

Given f(x) = -x^3 + 12x, a local maximum value of 16 is said to be at 2.
Determine the local minimum value.

since you can't use calculus then they probably wnat you to look at the picture
install the TI-84 emulator on your phone
plug -x^3+12x into [Y1=]
hit 'graph'
select 'calc'
choose 'minimum'

FelizNYC wrote:

Does the local maximum value of 16 at 2 mean point (2, 16)?

Yeh

FelizNYC wrote:

If so, how does the point (2, 16) help me find the local minimum?

I think youre supposed to assume mirrored symmetry
max at (2,16)
min at (-2,-16)?
this *is* the min but I don't know how you were supposed to know
THis mirroring doesn't always happen so you can't assume

## #4 Re: Help Me ! » Analyze f(x) » 2024-03-24 13:56:08

FelizNYC wrote:

Can you post the graph for me?

YOu can do the graph yourself in your phone
In 'search' box enter 'Graphing calculator plus 84 83'
Install app to get TI-84 emulator on your phone
TI-84 can do things like find the minimum on a graph
(and there's lots of tutorials, how-to's, etc online for Texas Instruments TI-84)

## #5 Re: Help Me ! » Vertices of Equilateral Triangle » 2024-03-24 13:54:24

FelizNYC wrote:

What is the purpose of this exercise [other] than algebra practice?

probably no other pt than to give you a chance to
(1) work some more with the fomrulas
(2) get practice seeing when formulas might be useful

## #6 Re: Help Me ! » Vertices of Equilateral Triangle » 2024-03-22 07:31:25

FelizNYC wrote:

Verify that the points (0, 0), (a, 0), and (a/2, sqrt{3}a/2) are the vertices of an equilateral triangle. Then show the midpoints of the three sides are the vertices of a second equilateral triangle.

1st part: Equilaterals have all sides the same length
so plug pairs of pts into Distance Formula
2nd part: Use Midpoint Formula to find midpts
Use Distance Formula to show all new sides have same length

## #7 Re: Help Me ! » Equilateral Triangle » 2024-03-22 07:29:22

FelizNYC wrote:

An equilateral triangle is one in which all three sides are of equal lengths.  If two vertices of an equilateral triangle are (0, 4) and (0, 0), find the third vertex. How many of these triangles are possible?

Equilaterals have all sides the same lenbth

Distance Formula:

so sides' lengths is 4
3rd pt will be 4 units from known pts

Both are equal to 4 so set them equal

Square both sides and solve

Now you need to find x
try with (0,0)

this means that there are 2 triangle that work
(draw the dots to see why this is so)

## #8 Re: Help Me ! » Find Coordinates of Point B » 2024-03-22 07:17:14

FelizNYC wrote:

Plot the points A = (-1, 8) and M = (2, 3) in the xy-plane. If M is the midpoint of a line segment AB, find the coordinates of B.

just plug into midpoint formjula

Set the x and y coords equal

Solve for x and y

## #9 Re: Help Me ! » Even, Odd or Neither Functions » 2024-03-22 07:13:28

FelizNYC wrote:

Are you saying that the cuberoot{-x} is not -x?

yes I'm saying they're not the same
eg cbrt{8} = 2, not 8
cbrt{27} = 3, not 27
cbrt{-64} = -4, not -64

## #10 Re: Help Me ! » Basketball » 2024-03-21 02:08:45

FelizNYC wrote:

Can you help me with Part B?

find 'v' for part A
plug that into the eqn they gave you
this is all they want for partt B

## #11 Re: Help Me ! » Even, Odd or Neither Functions » 2024-03-21 02:06:35

FelizNYC wrote:

what happend to the cube rt?

## #12 Re: Help Me ! » Basketball Foul Shots » 2024-03-21 02:03:11

FelizNYC wrote:

Can you set up the function for me?

They gave you

They ask if the equation works with

So see if it works

Simplify
does this equal 10?

## #13 Re: Help Me ! » Effect of Elevation on Weight » 2024-03-19 07:39:00

FelizNYC wrote:

If an object weighs m pounds at sea level, then it's weight W (in pounds) at a height of h miles above sea level is given approximately by W(h) = m[4000/(4000 + h)]^2. If Amy Weighs 120 pounds at sea level, how much will she weigh on Pike's Peak, which is 14,110 feet above sea level?

(dont round until the end!)

## #14 Re: Help Me ! » Basketball » 2024-03-19 07:25:51

FelizNYC wrote:

A. The center of the hoop is 10 feet above the floor and 15 feet in front of the foul line. Determine the initial velocity with which the ball must be shot in order for the ball to go through the hoop.

B. Write a function for the path of the ball using the velocity found in part A above.

C. Determine the height of the 84 after it has traveled 9 feet in front of the basketball.

The only instrutions Im' seeing are the 3 quoted
sorry

## #15 Re: Help Me ! » Find Domain & Range » 2024-03-18 10:08:49

Why did original link not work?
but if you right-click (on computer) and pick 'open image in new tab' you get different url
Put that url inside image tags and you get:

domain: They show which bits of x-axis count
range: They show which bits of y-axis count

range: Graph does not go up to y=2
It stops at y=0 (x-axis)

## #16 Re: Help Me ! » Use Graph to Find Domain and Range » 2024-03-18 09:57:28

FelizNYC wrote:

How does one use the graph of a function to find the domain and range?

domain: Look at where the graph goes from side to side
Does it quit (like with square roots) or have gaps (like with vert. asymps), or does it go everywhere?
Domain is wherever graph goes along x-axis
(not necessarily right next to the axis but you can trace up or down from the axis to the graph)

range: Look at where the graph goes from bottom to top
Does it quit (like with parabolas) or have gaps (like with hor. asymps), or does it go everywhere?
Range is wherever graph goes along y-axis
(not necessarily right next to the axis but you can trace right or left from the axis to the graph)

## #17 Re: Help Me ! » Find Domain of A » 2024-03-18 09:53:30

FelizNYC wrote:

Given A(x) = 4x•sqrt{1 - x^2}, find the domain of A.

Theres a way to do this so you dont have to try to go from 'x<=1' to '-1<=x<=1'

This gives you two sol'ns: x=1, x=-1

Also you know shape of quadratics like y=x^2-1:
<=0 between sol'ns (when its positive like this)

This lets you go to

## #18 Re: Help Me ! » Find Ground Speed of Plane » 2024-03-18 09:48:52

FelizNYC wrote:

Try desmos.com or mathway.com for graphing.

YOu can do graphing on your phone
In 'search' box enter 'Graphing calculator plus 84 83'
Install app to get TI-84 emulator on your phone
TI-84 can do things like find the minimum on a graph
(and there's lots of tutorials, how-to's, etc online for Texas Instruments TI-84)

## #19 Re: Help Me ! » Basketball » 2024-03-18 09:42:48

FelizNYC wrote:

...the path of the ball can be modeled by the function h(x) = -(136x^2)/(v^2) + 2.7x + 3.5, where h is the height of the ball above the floor, x is the forward distance of the ball in front of the foul line, and v is the initial velocity with which the ball is shot in feet per second.

Part B. Write a function for the path of the ball using the velocity found in part A above.

I need help for part B.

Once you get the number for 'v' from part 'A', plug that into the eqn they gave you
(and maybe simplify)
That's all they want for this part

FelizNYC wrote:

Part D. To find additional points, I must create a table in terms if x and h(x).

What were the instructions for this part?
(it's not in your first post, i don't think?)

## #20 Re: Help Me ! » Points On the Coordinate Plane » 2024-03-18 09:36:00

FelizNYC wrote:

Can you show me STEP BY STEP how to upload photos here using an android phone?

Select 'search'
Enter 'carbon browser'
Select and install
Open carbon brwoser
Enter url for image that you uploaded
Long-press image (hold you finger on the image until a menu pops up)
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 (back-space) from the end until you get to the .webp
Replace .webp with .jpg
Select 'go' at bottom of keyboard
Your image should disply alone on the page
Copy new url and paste between [ img] [ /img] tags (without the extra spaces of course)

i.imgur.io/7uB3NEl_d.jpg

I removed 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:

## #21 Re: Help Me ! » Intercepts of a Function » 2024-03-18 09:30:29

Pick any graph of any function
find where the grpah crosses y-axis: this is y-int
find where the graph crosses x-axis: this is x-int

## #22 Re: Help Me ! » Random Questions About Two Functions » 2024-03-14 01:11:58

FelizNYC wrote:

Given f(x) = (x^2 + 2)/(x + 4) and g(x) = 2x/(x - 2), answer the following questions.

A. The point (1, 3/5) lies on the graph of which function?

Plug x=1 into f and g
see which one gives you 3/5 for the answer

FelizNYC wrote:

B. If x = 4, what if g(x)? What point is on the graph of g?

Plug x=4 into g
See what g(4) equals
This is y
Point on g is (4,g(4))

FelizNYC wrote:

C. What is the domain of f and g?

Domains are different for f and g
f: solve x+4=0; everything else is domain
g: solve x-2=0: everything else is domain

FelizNYC wrote:

D. If f(x) = 1/2 and g(x) = 1, what is x for both functions?

f: set (x^2 + 2)/(x + 4) = 1/2 and solve
g: set 2x/(x - 2), = 1 and solve

FelizNYC wrote:

E. Graph the function of f. Graph the function of g.

graph vertical asymptotes
use the rules to find horizontal asymptotes
plot intercepts
make T-chart
graph a bunch of other points
then draw graph

FelizNYC wrote:

F. What is the range of f? What is the range of g?

like Bob said: look at the graph for the range

FelizNYC wrote:

G. List the x and y intercepts, if any, of the graph of f and graph of g.

y-int: set x=0 and solve
x-int: set y=0 and solve

FelizNYC wrote:

H. Find f(a + b) and g(a - b).

plug a+b in for each x in f
plug a-b in for each x in g
simplify if you can

## #23 Re: Help Me ! » Vertical Line Test » 2024-03-14 01:06:35

FelizNYC wrote:

Given a graph, how does one determine if it is a function using the vertical line test?

see if there is anywhere you could draw a vertical line and cross the graph more than 1 time
If yes, then not a fcn

## #24 Re: Help Me ! » Points On the Coordinate Plane » 2024-03-14 01:03:06

FelizNYC wrote:

A function has the following points:

(-6, -3), (-5, -2), (-3, 0), (0, 3), (2, 4), (4, 3), (6, 0), (8, -2), (10, 0), (11, 1)

A. Find f(0) and f(-6)

f(0) comes from pt (0,3)
f(-6) comes from pt (-6,-3)

FelizNYC wrote:

B. If f(3) positive or negative?

none of the pts has x=3
maybe f(-3)?
then use pt (-3,0)

FelizNYC wrote:

C. For what values of x is f(x) = 0?

f=0 comes from pts (-3,0),(6,0),(10,0)

FelizNYC wrote:

D. For what values of x is f(x) > 0?

f>0 comes from pts (0,3),(2,4),(4,3),(11,1)

FelizNYC wrote:

E. List the x and y intercepts.

use defs:
x-int: y=0, so pts (-3,0),(6,0)(10,0)
y-int: x=0, so pt (0,3)

## #25 Re: Help Me ! » Use Graph to Find Symmetry » 2024-03-14 00:58:33

FelizNYC wrote:

How does one use the graph of a function to find any symmetry with respect to the x-axis, y-axis, or origin?

Use def. of the symmetries
even: mirrored on each side of y-axis (like y=x^2)
odd: mirrored but upside down on other side of y-axis (like y=x^3)
origin: each pt matches another pt on th e other side of the origin (like y=x^3)