Friday
July 25, 2014

Posts by Steve


Total # Posts: 23,952

geometry
You may not have seen it like this, but A = C/π

algebra
-3° is 18° less than 15° At 3°/hr that will take 6 hours, and happen at 6 pm. midnight is 12 hours after noon, so the temperature then will be 15-3*12 = -21°C Note that since 6pm is halfway between noon and midnight, since the temperature dropped 18° by...

science - not brilliant
The greater minus the lesser is -39 - (-98) = -39+98 = 59°C

math - typo?
since the diagonals are equal, 2(5a+1) = 2(a+1) 10a+2 = 2a+2 a=0 I don't think so...

maths - oops
oops - heh heh 3w = 12 w = 4

maths
length+width=9, so w + 2w-3 = 9 3w = 6 w = 2

math
r = 6w+1, so since r+w=50, 6w+1 + w=50 7w = 49 w = 7 r = 43

Math
the circumference is 20pi meters. So, the linear velocity is 60pi m/min. angular velocity is 2pi radians per revolution, so 6pi radians/min you know the circumference. Divide that by 8 to get the distance between seats.

new neutrich high school
depends -- do you want to know how many calories are burned as time passes, or do you want to know how long it takes to burn a calorie?

algebra
(f*g)(x) = f(x)*g(x) = (2x^2+7)(x-6) So, now just plug in x=1

Algebra
assuming you want to find the value(s) of s that make the equation true, place everything over the common denominator of (s^2-1) and clear fractions. Note that s=±1 are excluded, because that would involve division by zero. 3(s+1) + (s^2-1) = 12 s^2+3s-10 = 0 and I gues...

math
every time she works one more hour, how much more money does she get? That is the slope of the line.

Algebra
$2/item is the slope

Algebra
15000(1+r)^2 = 16099.44 (1+r)^2 = 1.0733 1+r = 1.036 r = 0.036

Math (Calculus)
The volume of a shell of radius r, height h and thickness dy (because revolving around the y-axis) is 2πrh dx Now, our plane region is symmetric about the y-axis, so revolving all of it it is the same as revolving only the part for x>=0. o, we'll take the volume to...

Math (Calculus)
v = ∫[0,4] 2πrh dx where r=5-x and h=y = 2π∫[0,4] (5-x)(4x-x^2) dx = 2π(x^4 - 3x^3 + 10x^2) [0,4] = 64π check using discs: v = ∫[0,4] π(R^2-r^2) dy where R=5-(2-√(4-y)) and r=5-(2+√(4-y)) = π∫[0,4] (3+√(4-...

Grade 12 Math
(2a-5b)•(3a+b) 2a•3a - 13a•b - 5b•b 6 - 13a•b - 5 1 - 13a•b Now |a+b| = √3, so using the law of cosines to get the angle θ between a and b, we have 1+1-2cosθ = √3 cosθ = 1-√3/2 Now, we know that since a and b are u...

math
divide the volume by the base area to get (40*pi*3.5^2)/(28*22) = 35/44 pi or 2.5

Calculus
#1 ok #2 dy/y = dx/x^2 lny = -1/x + c y = e^(-1/x + c) = ce^(-1/x) so, (B)

Algebra
They all look fine to me, though it took me a while to separate the problems from your answers. If they were marked wrong, then the key is in error. As you have presented them, your answers are all correct.

Math - Pleeeease
once you start tossing in angles, you'd better have some trig. Either that or know some basic facts about certain right triangles. I assume you have heard of the Pythagorean Theorem. For this problem, draw a right triangle with the hypotenuse going from the starting point ...

Math - Pleeeease
well, since plane #1 is rising at 45°, its ground distance is equal to its altitude, or 5600. The 2nd plane coves less ground than its altitude. It is 8200 cos 60° = 4100

Math
1 = (x+6)/(x+6) so, the right hand side becomes ((2x-6)+(x+6))/(x+6) = 3x/(x+6)

math
if there were x cardholders, there were 744-x others. Now add up the money collected for each kind. 1.75x + 2.25(744-x) = 1477.50 1674.00 - 0.5x = 1477.50 x = 393

math
if $x at 7%, then .07x + .10(3x+44000) = 41770 x = 101,000

math
1000(1+.03/12)^(12*10) - 1000

Math
w+4w = 15 w = 3 so the length is 12

math
50000(1+.025)^10

Algebra
pi r^2 h = pi r^2 * 25 so, r^2 = 225 Now you can find r easily.

Physics
starting at height 0, its height at time t is -5t - 4.9t^2 If we fudge a bit and approximate gravity with 5 instead of 4.9, then we have -5t-5t^2 = -5t(1+t) at t=2, that's -30

MATH PLS HELP CHECK ANSWERS
#3 since y increases by 3 when x increases by 1, the slope is 3/1 = 3. Only one choice has a slope of 3. And, as Leo said, you can just plug in the x's and see whether the y's match! #4 ok #5 ok #6 looks like A to me. Did you even try the given points? #7 ok #8 ok You ...

Algebra
what you have written is an assertion, either true or false, depending on the value of x. I suspect a typo or an unfinished question.

Math
since the volume is 1, and the height is now 1/8, the surface area of the two bases is 8 v = Bh = 8(1/8)

Math
It must gain 12 hours, at 1/3 hour per day. Looks like 36 days to me. (Assuming an analog clock -- a digital clock will take twice that long.)

Math
that would be f(6)-f(5) plug and chug

Math
divide 360 into 5 equal parts. What do you get? 72. But, that is angle AOB, the vertex of an isosceles triangle. So, each of the base angles (OAB and OBA) is (180-72)/2 = 54.

Math
why bother with all those decimals? 4/16 * 7/16 = 7/64 4/16 * 7/15 = 7/60 The fractions are exact; the decimals are usually only approximate.

Math
yeah - you have trouble multiplying fractions?

Math
(a) 4/16 * 7/16 (b) 4/16 * 7/15 (b) is different because there are fewer marbles to choose from on the second draw.

algebra 2
If you mean I = nE/R + nr then I-nr = nE/R R = nE/(I-nr) If you mean I = nE/(R+nr) then R+nr = nE/I R = nE/I - nr

Math Help!
#1 since (a+b)^6 = a^6 + 6a^5b + ... if we let a=2x and b=3y we get (2x)^6 + 6(2x)^5(3y) + 15(2x)^4(3y)^2 + 20(2x)^3(3y)^3 + 15(2x)^2(3y)^4 + 6(2x)(3y)^5 + (3y)^6 64x^6 + 576x^5y + 2160x^4y^2 + 4320x^3y^3 + 4860x^2y^4 + 2916xy^5 + 729y^6 #2 Hard to show. The bottom-line entrie...

Algebra 2
#1 4*2*5 #2,#3: visit calc101.com and click on the long division button. It will show you all the details of polynomial division. #4: (x+3)(x+1)(x-2) Now just expand that. again, calc101.com has a button for polynomial multiplication.

Algebra 2
#1 we have (x^4)/4 − 3x^3 + (23x^2)/2 - 15x Fractions are a nuisance, so I prefer x^4 - 12x^3 + 46x^2 - 60x = x(x^3-12x^2+46x-60) Cubics are tough, but a little synthetic division shows that we have x(x-6)(x^2-6x+10) So, we know we have at most 3 extremes for a 4th-degre...

math
if the boat's speed is s mi/hr, then since time=distance/speed, we have 24/(s-4) + 24/(s+4) = 5 s = 11.05

Math
1/5 scale is a reduction

Math
well, the new base:height ratio would have to be the same: 38/12 = 19/6 So, since all the choices have h=36, which is 6*6, we need a base of 6*19 = 114 Looks like A to me.

Math
DA/HE = AB/EF, so 19/133 = 8/EF EF = 56

math
the heights are in the same ratio as the shadows, so h/5 = 24/10 h = 12

Maths
since y=x-k, x^2 + (x-k)^2 + 2x - 4(x-k) - 1 = 0 2x^2 - 2x(k+1) + k^2+4k-1 = 0 x = [2(k+1)±√(4(k+1)^2-8(k^2+4k-1))]/4 now, that looks like a lot of complicated stuff, but notice that it's really (k+1)/2 ± some stuff So, (k+1)/2 is the midpoint coordinate

Math
not in any general way. If f(x) = x then that's true. For other functions, it will be true only sometimes, but mostly never.

Maths
f(x) = 3x^2-6x+k = 3(x^2-2x) + k = 3(x^2-2x+1) + k-3 = 3(x-1)^2 + k-3 The vertex is at (1,k-3), so k-3 = 7 k = 10

Maths
since the variance is a measure of the absolute differences from the mean, shifting the mean by 14 and flipping the difference does not affect the variance. (B)

Math
if we let the vertex be at (0,0), y = 4(x/6)^2 = x^2/9 so, what's y(3)?

math
If we let one force be (7,0) then the other is (9cosθ,9sinθ) where sinθ = 0.4 cosθ = ±0.92 (7,0)+(8.25,3.6) = (15.25,3.6) (7,0)+(-8.25,3.6) = (-1.25,3.6) The magnitudes are 15.67 and 3.81

Math
n = d-2 n/d + d/n = 2 4/35 substitute in for n and we have (d-2)/d + d/(d-2) = 74/35 d = 7 so, n=5 check: 5/7 + 7/5 = (25+49)/35 = 74/35

Math
If we call the two forces u and v, then we have (using unit vectors), u = 15(3/5i - 4/5j) v = 4√2(1/√2i + 1/√2j) so, u+v = 13i-8j I expect you can find the magnitude of that...

Math - Algebra
if the distance from the edges is x, (8-2x)(12-2x) = 45 x = 3/2 So, the hole is 5x9 with area 45

Math
5P5 = 4! = 120

math
it advances 1 in/move after 12 moves it has advanced 12 inches. On the 13th move it covers the last 3 inches to complete the lap.

Math - Algebra
if the garden is x by y meters, x+y = 10 and xy >= 24 so, x(10-x) >= 24 x^2 - 10x + 24 <= 0 (x-4)(x-6) <= 0 since the parabola open up, the graph is below the x-axis between the roots. the roots are at x=4 and x=6 So, we need x <= 4 <= 6 Since usually the len...

Math
first, bequest is a noun. The verb is bequeath. I know, I know -- in English any noun can be verbed, but why bother, when there is already a perfectly good verb available? This is a sure sign of an incompetent attorney! Anyway, if the estate has $x, the red cat gets x/2 -1000 ...

math
c'mon, guy -- just substitute in the values: a▲b = 2a-3b, so 2▲(-3) = 2(2) - 3(-3) = 4+9 = 13

alegbra - eh?
If you mean N = 2500 + 100 - lna Cm >= 1 I still don't know what the letters mean The "equation" makes no sense anyway.

ALGEBRA
Thanks for fixing the typos. (Except for persisting in writing "in" for "ln") #1 From the context, I assume you meant ln3 - 2ln(9+18) ln3 - 2ln27 ln3 - 6ln3 -5ln3 -ln 243 or ln 1/243 #2 ln3 - 2ln15 ln3 - ln225 ln (3/225) ln 1/75 or -ln 75 #3 ln3 - 2(ln4 + l...

calculus help
recall that sinhx = (e^x-e^-x)/2 coshx = (e^x+e^-x)/2 so, sinhx+coshx = e^x 2e^x/e^x = 2

algebra
I assume you mean the function representing the height of the ball, such that f(x) is zero at x=3 and x = -5 How about f(x) = a(x-3)(x+5) = x^2+2x-15 Without further information, we cannot determine the scale factor. There are many possible parabolas with those two roots. I as...

Math
First, write the clues in math symbols: p = 3h a = h+16 a+h+p = 86 Now just start substituting to get rid of all the letters but one, then go back and calculate the other two values.

algebra
by definition, log_10(10^n) = n so, log_10(10^-4) = -4 Or, you can recall that log x^n = n*logx Since log_10(10) = 1, we again have -4*1 = -4

algebra
but 25 is not (1/5)^2 (1/5)^2 = 1/25 25 = 1/(1/5)^2 = (1/5)^-2 So, log1/525 = -2 loga = c*logb regardless of base. Using b for the base, log_b(b)=1,so logba = c

Math 12
I assume you mean 6 blue marbles, making 14 in all. Looking just at the blues, P(0) = 8/14 * 7/13 * 6/12 = 2/13 P(1) = 6/14 * 8/13 * 7/12 = 2/13 So, P(>=2) = 1-(2/13 + 2/13) = 9/13

Math
total bands: 185 P(pink) = 95/185 P(brown) = 90/185 I expect you can reduce the fractions.

Geometry
as a block of water, the displaced fluid is 36*18*0.25 = 162 in^3

Algebra
call the classes p,h,a. The clues are: p = 3h a = h+16 p+a+h = 86 now start eliminating values: p = 3h, so 3h+a+h = 86 a = h+16, so 3h + h+16 + h = 86 5h+16 = 86 5h = 70 h = 14 so, there are 14 art history students 42 psychology students 30 algebra students

MATH
hint 197g * 1atom/1.6601*10^-24 g = ? atoms

MATH
well, we all know that the sun is 93 million miles away. So you'd better get something like 9.3*10^6 186300mi/sec * 8.32min * 60sec/min = 9.300096*10^6 mi ta-da!

Math 12
2598960/78 = 33320

Calculus, Riemann
you need to revisit your posts and type in the functions. This copy/paste stuff is getting mangled. Use ^ for exponents, like x^2 for x squared. I can guess that 3 means ∑.

Help w/ Math PLS
Looks good to me. That was going to be my approach until I saw it so ably demonstrated...

math
14 total fruits, so P = 2/14 * 2/13

MATH PLEASE HELP MRS.SUE!
#1 C add 10 to get next term #2 C multiply by 2 for next term #3 D is the only possible choice, since the first two terms are -5,-3 #6 C These seem pretty straightforward. What ideas do you have on the rest? I don't want to do all your assignment for you...

Calculus
you figured how much will be there in 30 years if 32400 is deposited now. You want A(1 + 0.0801/12)^(12*30) = 32400 A = 2953.95

math
12/20 * 8/13

Maths
1st place to start would probably be the Pythagorean Theorem. Check it out.

Math Question Please Help
just put the words into symbols: m = s+2 h = s/2 r = m+s h = 2 Now start substituting since h=2, s=4 since s=4, m=6 now we know that r = 4+6 = 10 Don't know what the (12) at the end means.

Math homework help
so, go find the appropriate half-angle rule. What do you get? Just to get you started, for that θ in QIV, sinθ = -1/√2 cosθ = 1/√2

calculus help
Just use Lebniz's Rule: d/dx ∫[a(x),b(x)] f(t) dt = f(b(x))b' - f(a(x))a' d/dx ∫[cosx,sinx] ln(8+3v) dv = ln(8+3sinx)(cosx) - ln(8+3cosx)(-sinx)

Calculus Help Please Urgent!!!
With 4 divisions, the boundaries are 0 pi/8 pi/4 3pi/8 pi/2 So, the midpoints are at pi/16,3pi/16,5pi/16,7pi/16 So, we have 4 rectangles with width dx=pi/8, and heights 2cos^3(pi/16),... Add up the areas of the rectangles. I get 1.3330 To check, ∫[0,pi/2] 2cos^3(x) dx = ...

math
42

Matrices
dilation takes (x,y)->(2x,2y) translation takes (x,y)->(x,y+5) rotation takes (x,y)->(-y,x) So, combining, we get (x,y) -> (2x,2y) -> (2x,2y+5) -> (-2y-5,2x) So, just apply that to each coordinate. For example, (4,3)-> (-11,8)

Algebra 2 help!!!
just read off the product: -7x - 2y = 14 15x + 8y = -8

Algebra help please!
just add the respective elements: (6+3,-5+3) = (9,-2) Looks like (A) without the typo

MATH
just put the clues into symbols. if there are d dollars and h halves, d = h+132 d/h = 5/2 clearing the fractions, we have 2d = 5h now substitute in for d and we have 2(h+132) = 5h 3h = 264 h = 88 so, d = 88+132 = 220 the reward is 1/4 (88/2 + 220) = 1/4 (44+220) = 11+55 = $66

Calculus (lim)
x^3-6x^2+11x-6 = (x-1)(x-2)(x-3) So, for all x≠1, f(x) = (x-2)(x-3) as x->1, f(x)->2 since both factors are negative we need to show that for every ϵ>0 there is a δ such that f(x+δ)-2 < ϵ we can dispense with the absolute value stuff, si...

Calculus Riemann sum definition etc
I'm stumped by the cryptic symbols. Try the notation integral[a,b] x_i or xi for x sub i Whatever the function, the Riemann sum is evaluated by approximating the actual area with a set of rectangles, whose upper corners are points on the curve. Review your text, and maybe ...

Trig
using the logic of the solution to your previous post, try this one yourself.

Trig
since no QIII angles, a is in QIV and b is in QI sina = -7/25 cosa = 24/25 sinb = -15/17 cosb = -8/17 now just evaluate sin(a-b) = sina cosb - cosa sinb

Trig
since cosb < 0, b is in QII, so sina = 4/5 cosa = 3/5 sinb = 5/13 cosb = -12/13 Now just evaluate ain(a+b) = sina cosb + cosa sinb

Algebra
what's the trouble? They actually give you the equations to solve. What do you get for answers?

trig
depends on the positions of the two named animals. It will between 8*360 and 9*360 degrees

math
there are 201 numbers from 50 to 250. So, clearly, if 202 people are polled, at least two of them must have the same number.

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