Thursday
April 17, 2014

Posts by steve


Total # Posts: 21,724

Math
y = 1/2 x - 4 has x-intercept at (8,0) 3x - 4y + 4 = 0 has slope 3/4 so, your line is (using point-slope form) (y-0) = (3/4)(x-8)

math
if sold at price p, we need the revenue from 90% of the 600 lbs to be 1.60 times the cost of 600 lbs at $5.59: 600(1-.10)p = 600*5.59*1.60 p = $9.94

Algebra
if you mean (fg)(x) that would be f(x)*g(x) = (x-11)(2x+12) = 2x^2-10x-132

College Mathematics
For any set with n elements, there are 2^n subsets. But A is not a proper subset of itself, nor is Ø, so that leaves just 2^4-2 = 14. By the way, "the number" is singular, not plural.

Math
Ya got me On Monday there was 1/2 bag left. That means 7/14 are left. If he is to eat a few more, then that means there are only 7/14 - 5/14 = 2/14 left after Tuesday's chow-down. But, the next largest candy leaves 1/3 of the bag full. 1/3 > 2/14, so eh? is that 1/3 of ...

math
I'll use the more common ^ instead of •, which is often used for simple multiplication. 10^5 = 10*10*10*10*10 = 100,000 it's a simple power. 3^2 = 3*3 2^6 = 2*2*2*2*2*2 = 64 and so on.

algebra - questions
What, are we playing Jeopardy?

geometry
What, no ideas? A simple review of the properties of the named figures should provide the answers. Or at least allow you to eliminate some possibilities.

Pre-Algebra
1:20

GEOMETRY
I'd say they are 1/66 times the lengths of AB,BC,CA respectively.

algebra
Hmmm. What is f(5)? 7 or 8?

algebra
as long as no two distinct pairs have the same 1st element, it is a function. So, what do you think?

Alg/Trig
well, you know that h/x = tan 39.8° h/(x+51.7) = tan 19.7° Now eliminate x and solve for h: h/tan39.8° = h/tan19.7° - 51.7 1.2h = 2.8h - 51.7 h = 32.3 check my math, but that's the method to my madness.

Algebra
Note that each tree costs the same as 2 bushes. Nick can buy 2-6 trees and 0 bushes, or 4-12 bushes and 0 trees. Each tree can be replaced by two bushes, so it's fairly easy to see how to keep within budget by replacing each tree by 2 bushes.

ap calculus.linear
earnings = 0.05 A•f A+f is meaningless, since you can't add ft^2 and n. A•f computes the total ft^2 mowed. For various earnings, you'd also need a vector of rates. Not sure how to do that with just vector operations. Say the rates were 0.05, 0.10, 0.07, 0.12,...

College Algebra
depends on the configuration of the pens. A longs skinny corral with 4 pens in a row? Or a rectangular corral with a 2x2 arrangement of pens? If the first, then we have two lengths and 5 widths. 2x+5y = 200 area = xy = x(200-2x)/5 = -2/5 x^2 + 40x the vertex of the parabola is...

algebra
apparently an = (-1)^n + 1/2^n as in -1/2, 5/4, -7/8 ... but I could be wrong...

Maths
.6b + .9g = 3/4 (b+g) .9g = .6b + 12 Now just solve for b and g

Math
Look up in your Z table for the upper tail at 20% You can play around with this at http://davidmlane.com/hyperstat/z_table.html where you can set the mean and variance and explore various properties of the normal distribution

Math
LCM(a,b) = a*b/GCF(a,b) so, 36 = a(a+6)/6 a^2 + 6a - 216 = 0 (a+18)(a-12) = 0 a = 12 So, the two numbers are 12 and 18

Math
60*5 = x(x+5) x^2 + 5x - 300 = 0 x = 15 The two numbers are 15,20

Math
if there are n even numbers (starting at 2, and not skipping any), then n/2 (2*2+(n-1)*2) = 420 n = 20 So, the largest is 40

math
AD/AB = DE/BC AD/6 = 20/8 AD = 15

algebra
factor it and set each factor to zero.

Algebra
You can get excellent graphing help at http://rechneronline.de/function-graphs/ You can plot up to three functions at the same time, and set the x- and y- boundaries as desired. I expect that you plotted the points wrong, if it didn't look like a parabola. Your tables look...

algebra
6x-4<-34 or 3x+10>10 6x-4<-34 6x < -30 x < -5 or 3x+10>10 3x > 0 x > 0 You can see the solution graphed at http://www.wolframalpha.com/input/?i=6x-4%3C-34+or+3x%2B10%3E10

algebra
5r+4 < 5 5r < 1 r < 1/5

algebra - an attempt
s = 5rt t = s/(5-r) t = 25r/s t = r^2-5s t = s/(5r^2) I get t=s/(5r) which is not any of the choices listed. If you want to repost using similar notation, maybe we can help more.

functions
lots of rules will produce that, but the easiest is f(x) = x-1

math
h/150 = sin 45°

Math-simplify
(2x/15)^2 / (.15-x/15)(.2-x/15) (4x^2/15^2) / (x^2-5.25x+6.75)/15^2 The 15^2 cancel out, and we have 4x^2/(x^2-5.25x+6.75) 16x^2/(4x^2-21x+27)

math
well, there are 5280 ft/mi, so 15*5280 feet

trigonometry
better just stick with "trig" One of the first things to do is to learn the special angles with easy trig values: 0,π/6,π/4,π/3,π/2 Knowing those, you will see that sin π/3 = √3/2 You have -√3/2, so that means that your angle is i...

Math
original fraction: n/(2n+4) modified fraction: (n+6)/(2n+4+6) = 7/13 13(n+6) = 7(2n+10) 13n+78 = 14n+70 -n = -8 n=8 So, the original fraction was 8/20 and the new value is 14/26 = 7/13

math
2/8 * 1/7

help
The month must begin on Monday, so there are 2 full weeks ending on Sunday. The 15th is thus the 3rd Monday.

chemistry
you know PV=kT solve for V, then use density = mass/volume

math
ab:xy = 10:11 So, other sides are in the same ratio ac/xz = 10/11 14/xz = 10/11 xz = 15.4

Calculus
we know that ∫cos(u) du = sin(u) ∫tan(u) du = -log cos(u) So, what we get here is (-1/3)sin(2-3x) - (-1/3)(-log cos(5-3x)) = -1/3 (sin(2-3x) + log cos(5-3x)) + C

Math
y = a(x-(-1+√5))(x-(-1-√5)) = a(x^2+2x-4) the one passing through (0,-32) is y = 8(x^2+2x-4) Similarly for the other root pair.

Quick math help
I only see one variable: x Factored it is -7(x-1)(2x+3)

Math
I'd say 8 8 balls and 8 straws for the base 1 ball and 8 straws for the edges

Math
well, it would have to be (2x-7)(2x+3)(x-2) = 117 4x^3 - 16x^2 - 5x - 75 = 0 (x-5)(4x^2+4x+15) = 0 ...

Math
2/(2/3) = 3 So, 3 people, each with 2/3 extra bag makes 2 extra bags.

Algebra 2
The second formula is correct The games played are 32,16,8,4,2,1 a1=32, r = 1/2 and there are 6 rounds played. 32(1 - 1/2^6)/(1 - 1/2) = 32(63/64)/(1/2) = 63

Math
2pi(21-14)

Math
if the cost is c, then c(d,v) = 8d + 6v c(5,3) = 8*5 + 6*3 = 58

Math
if it doubles at a constant rate, it's exponential growth.

calculus
check your graph against this one: http://www.wolframalpha.com/input/?i=tan%28x%29+for+5pi%2F3+%3C%3D+x+%3C%3D+3pi

Algebra 1
pick any x, say 5, and plug it in: 4*5 + 3y = 14 now solve for y 20 + 3y = 14 3y = -6 y = -2 So, (5,-2) is a solution Now just do some more. You can also pick a y value and then solve for x.

math
p - .20p = 56 .80p = 56 p = 70

math
1.5/w = 5/19

Geometry
Not sure where the typo is, but assuming you meant 7 and not 12, your reasoning is correct. You can do it the way you did, subtracting the larger from the smaller, or you can do |7 - (-15)) = |7+15| = 22 Personally, I prefer subtracting the smaller, but...

calculus
for even values of n > 0 f has a min for odd values of n > 1, inflection

math
not sure of your notation. try using ^ for exponents, as in x^2 or y^3 If you want a root, try using the special characters √ ∛ ∜ or use fractional exponents: x^1/2 for square root, etc. or, use a recognizable function name such as sqrt(x) cuberoot(x) 4throot...

Math
.04x + .03(15000-x) = 550

math
h/200 = tan 60°

math
94 - 40

algebra
2(26+h) < 180

math
that would be 28.05/3 kg

math
x/32 = 3/4

math
check the differences: 3,6,9,12,15 ... Now it should be clear.

math
18/12 s/s t^5/t^3 = 3t^2/2

math
4y + xy = 2 4y' + y + xy' = 0 y' = -y/(x+4) Now you can use the quotient rule or another implicit differentiation. 4y" + y' + y'^2 + xy" = 0 So, now just plug in (-3,2) to evaluate it there.

Calc Help :(((((
why would I want to help so you "can't do the rest"? I'd hope you can do the rest! Anyway, we all know that 1/∞ = 0 (or that the limit if 1/x as x->∞ is zero), so divide both polynomials by the highest power of x in either, to get (a + b/x^2) /...

Chemistry
the molecular mass in grams is the mass of mole. For example, since C has mass 12 amu and O has mass 16 amu, one mole of CO2 has mass of 12+2*16 = 44g 1M solution is 1 mole/1 liter

HELP
since 4B = A with a carry, B > 2 and A is a multiple of 4. Since 4A plus the carry generates no carry, 4A < 9 or A <= 2 So, I'd say A=2 and B can be 3 or 8, but 4*28 is 3 digits, so we have 23+23+23+23 = 92

calculus
r = ln (x+2)/(x-1) (x+2)/(x-1) = e^r x+2 = e^r x - e^r x(2-e^r) = -e^r x = e^r/(e^r-2)

math
Since there are 4 colors, even if the 1st 4 marbles are all different, the 5th marble must be the same color as one of them.

Mat/116
ummm. all points (x,y) where y=2x-3.

math
.035 * 200 = ?

algebra
just do the steps normally taken to solve equations -2 < 2x-4 < 4 add 4 throughout to get 2 < 2x < 8 now divide by 2 to get 1 < x < 4

English
#2 haven't forgotten (didn't forget would have been correct) The others are ok.

algebra
assoc prop of mult. Also, it's commutative, not communicative!

math
1.5 * 1.1^n is NOT 1.65^n That's like saying 2*3^2 = 5^2 Also you are saying that 1.5(-1) = .5 The correct algebra is 100=1.5((1.1^(n) - 1))/(1.1-1) 10 = 1.5(1.1^(n) - 1) Now divide by 1.5 20/3 = 1.1^n - 1 23/3 = 1.1^n n = log(23/3)/log(1.1) = 21.37 or 22 if you round up t...

add maths
as you know, the vertex of a parabola is at x = -b/2a. In this case, that will be at x = 12/6 = 2. So, find f(2)

Probability
Consider the AB combination as a single letter. Then there are 4!=24 ways to arrange the letters AB,C,D,E. Since A-B can be arranged in two ways, there are 2*4! = 48 ways.

Math
not sure what "this" refers to. Radicals and linear equations are separate topics. First step: google the terms you are interested in. You will find a wealth of discussions, far beyond you will find here.

Math
5040 + .30p = p p = 5040/.7 = $7200

math
I'd say 48000 * (.18+.124+.029) / 4 = 3996

algebra
-2(2x+9)>-4x+9 -4x-18 > -4x+9 -18 > 9 what do you think?

Math
you have correctly determined that y = -(x-2)^2 (x+2) You know the graph crosses the axis at x = -2 and that it just touches the x-axis at x=2 (because of the double root) Since for large negative values of x, all 3 factors are negative, y > 0 for x < -2 So, y < 0 for...

Physics
a = (110-77)/16 = 33/16 m/s^2 displacement during that time is s = 77*16 + 33/32 * 16^2 = 1496 m

Math
72 = 2^3 3^2 99 = 3^2 11 54 = 2 3^3 LCM(72,99) = 2^3 3^2 11 = 792 LCM(72,54) = 2^3 3^3 = 216

Algebra
you are correct as you surely verified, by using the values in the equations ???

Algebra
I think you must have meant -13 and 16. If so, then your algebra isn't entirely useless.

Algebra
no ideas at all? Let the numbers be x and y Now, what do you know about them?

Math
how does the heart shape relate to the circle and square?

Math
Eh? 72 - 5(13+2)*5 72 - 5(15)*5 72 - 75*5 72 - 375 -303

alg 2
I can only assume you mean (m•n)^-1 = 1/(m•n)

Maths
Yeah, it's kind of tricky. Using 6,1 for factors will make things kind of lop-sided, so I'd go with 2 and 3. (5x-2)(x+3) = 5x^2 + 13x - 6 Nope (5x+3)(x-2) = 5x^2 - 7x - 6 Nope I think we're out of luck. The discriminant is 64+120 = 184, which is not a perfect squar...

Math
well, 4,000,000 has 6 zeros. 40 has 1 zero. So, if you need to add 5 more zeros, which multiplier has 5 zeros?

Algebra
If the 1,2,3 pointers are in amounts of x,y,z, then x+2y+3z = 95 x+y+z = 54 y = x+16 (x,y,z) = (17,33,4)

math
33.60/4 * 1000

algebra
12n ≤ 15

Algebra 1
initial velocity v is zero - it just fell initial height is 16 feet, so h = -16t^2 + 16 So, you want to find t when h=0 (apple hits the ground) -16t^2 + 16 = 0 -16 (t^2-1) = 0 -16(t+1)(t-1) = 0 So, the apple's height is zero when t=1; that is, one second after being dislod...

Algebra 1
Ahem. h = -16(2)^2 + 47(2) + 3 You do not have -(16*2)^2, you just have -16 * 2^2 = -16*4 So, h(2) = -64 + 97 = 33 Ball hits the ground when h=0, so -16t^2 + 47t + 3 = 0 -(t-3)(16t+1) = 0 t = 3

Algebra 1
your answer is right, but your units are not The volume is 2500 ft^2 * 10 ft = 25000 ft^3 25000 ft^3 * 1gal/(0.134 ft^3) = 186567 gal

Algebra 1
If the moat has width m, castle area = 45*60 = 2700 castle+moat area = (45+2m)(60+2m) since there is moat on both sides. moat area = (45+2m)(60+2m)-2700 Now plug in your value for m, and recall that volume is area * depth

Math
so, area = x^2 + 4x(v/x^2) = x^2 + 4v/x Now just find when that is a minimum

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