Rom

7 Questions
2456 Answers

+9

1225

8

+6251

is there any point to answering these anymore?

Does anyone even look at the answers given?

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Rom Mar 3, 2020

+1

1761

9

+6251

latex delimiters

Is there a way of embedding LaTex into posts w/o using the LaTex button and dialogue?

Other boards have $$, [tex][/tex], [math][/math]
read more ..

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Rom Aug 8, 2019

+6

1805

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+6251

You know what guarantees I won't look at your problem?

Using the words ASAP, or fast, or now, or anything similar in your title.

You're all quite fortunate to have the group of us here that answer your questions.
read more ..

off-topic

Rom Jan 4, 2019

+2

1302

0

+6251

sub forums

It might be nice to have a few sub forums so we know better how to address given problems.

For example I suspect we sometimes use calculus to answer questions posted by people in pre-calculus classes.
read more ..

Rom Nov 27, 2018

+2

1465

8

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Why do sometimes we get the option to filter out answered questions but sometimes we don't?

Why do sometimes we get the option to filter out answered questions but sometimes we don't?

off-topic

GingerAle ●●●●●●●●

Rom Nov 15, 2018

+26

3062

18

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I'm concerned that we are just doing people's homework for them. That's no way to encourage people to actually learn the math.

I'm concerned that we are just doing people's homework for them. That's no way to encourage people to actually learn the math.

Thoughts?

CPhill ●●●●●●●●●●●●●●●●●●

Rom Oct 16, 2015

+2

1699

1

+6251

help file?

Is there a help file somewhere on how to use the forum tools to get a decent math output display?
Does this board support LaTex?

Rom Jan 30, 2014

+6251

0

Quote:
25x^2-16y^2

you should recognize this as the difference of two squares

(a ² - b ²) = (a + b)(a - b)

here a=5x, b=4y so

25x ² - 16y ² = (5x + 4y)(5x - 4y)

RomFeb 11, 2014

+6251

0

Quote:
Factor: 6x^2-13x-5

this doesn't quickly factor on inspection so I'd use the quadratic formula to solve for it's roots, r1 and r2.

Then the factors will be (x-r1)(x-r2) or something equivalent

here

a=6, b=-13, c=-5 so

r1,r2 = (13 +/- sqrt((-13) ² - 4(6)(-5)))[size=150]/[/size](2*6) =
(13 +/- sqrt(169 + 120))/12 =
(13 +/- 17)/12 = (30/12, -4/12) = (5/2, -1/3)

so 6x^2-13x-5 = 0 ==> (x-5/2)(x+1/3) = 0
we can rewrite this as (2x-5)(3x+1) = 0 and these are the two factors we are looking for.

So 6x^2-13x-5 = (2x-5)(3x+1)

RomFeb 11, 2014

+6251

0

Quote:
Solve The System Of Equations :3x+4y=11
x-2y=-3

3x + 4y = 11
x - 2y = -3

from the 2nd equation x = 2y - 3

plug that into the first

3(2y-3) + 4y = 11 ; multiply out
6y - 9 + 4y = 11 ; combine terms
10y = 20 ; divide both sides by 10
y=2
x = 2y-3 = 2(2)-3 = 1

(x,y) = (1,2)

RomFeb 11, 2014

+6251

0

Quote:
The speed of sound is 330m/s. The speed of light is 3x10^8m/s.

If the time between thunder and lightning is 3.5s, how far away is the storm?

You may as well assume that light is instantaneous so that the moment the lightning occurs you see it.

Then the distance from you to the bolt is the distance sound travels in 3.5s

That's just 330 m/s * 3.5 s = 1155 m

Just to show the assumption about light speed is ok the time that light take to travel this distance is

1155 / 3x10 ⁸ = 3.85 microseconds which is insignificant compared with the 3.5s it takes sound

RomFeb 11, 2014

+6251

0

Quote:
Construct the confidence interval for the population mean u.
c=0.90, x (it has a line over it)= 15.1, s=7.0, and n=100
A 90% confidence interval for u is (__,__). (Round to one decimal place as needed)

with n=100 your sample variance s' = s/sqrt(n) = s/10 = 7/10 = 0.7

so your sample distribution is Normal(15.1, 0.7)

c=.90 you need the lower tail to be at (1 - .9)/2 = 0.05

looking that up in your table you find that this corresponds to z = -1.64485

Your interval will thus be

(u + z s', u - z s') =
(15.1 - 1.64485*(0.7), 15.1 + 1.64485*(0.7)) =

(13.9, 16.3) to one decimal place.

RomFeb 11, 2014

+6251

0

google is your friend

1 mile = 5280 feet

RomFeb 11, 2014

+6251

0

You need to show that T and U have the same y coordinate.

T has y coordinate apq
U has y coordinate -apr

but if you look at the coordinates of P and Q and note that PQ is perpendicular to the axis of the parabola then it should be clear that q = -r

so both T and U have y coordinates apq and thus TU is horizontal and thus perpendicular to the vertical parabola axis.

RomFeb 11, 2014

+6251

0

Quote:
use special right triangles to write each trigonometric ratio as a simplified fraction . sin 30

a 30/60/90 triangle has legs

1/2a opposite the 30 (the short leg)
sqrt(3)(1/2a) opposite the 60 (the mid leg)
a as the hypotenuse (the long leg)

a is some positive number that represents how big the triangle is

so sin(30) = (1/2a)/a = 1/2

RomFeb 10, 2014

+6251

0

someone break your calculator fingers?

sqrt(20) = sqrt(4 * 5) = 2sqrt(5)

see if you can punch this in yourself

RomFeb 10, 2014

+6251

0

Quote:
TanA=1/2,tanB=3/4,TanC=1/2,show that tan(A+B+C)=4/7

from wiki

let tan(A) = a, tan(B) = b, tan(C) = c

then

tan(A + B + C) = [size=150]([/size](a + b + c) - abc[size=150])[/size][size=150]/[/size][size=150]([/size]1 - (ab + bc + ac)[size=150])[/size]

so

tan(A + B + C) = [size=150]([/size](1/2 + 3/4 + 1/2) - 1/2*3/4*1/2[size=150])/([/size]1 - (1/2*3/4 + 3/4*1/2 + 1/2*1/2)[size=150])[/size]

tan(A + B + C) = [size=150]([/size]7/4 - 3/16[size=150])/([/size]1 - (3/8+3/8+1/4)[size=150])[/size]

tan(A + B + C) = (25/16)/(1-1)

which tries to divide by zero and is thus nonsense

are you sure you have your numbers right?

RomFeb 10, 2014