Sunday
August 2, 2015

Posts by steve


Total # Posts: 32,558

math
53 is a prime, so it cannot appear in any factorial less than 53! I don't see how v can be anything other than 52, but that's not one of the choices. Hmmmm...
July 21, 2015

Algebra
that would be just how much g changed: g(9) - g(-6) just plug in the values for t and do the math.
July 21, 2015

MATH- URGENT!
If it wasn't urgent at 1:55, how come it was at 1:59? Not everyone is continuously monitoring the queue, so don't bother to cry URGENT! when posting a problem. We help with solutions because it's fun for us, and we like to help. Stamping your foot and shouting ...
July 21, 2015

math
if there are x footballs, then the rest (29-x) are basketballs. So, just add up the costs: 40x + 30(29-x) = 1000
July 21, 2015

calculus
well, you know that the surface has two circular ends, and a curved lateral surface. If you unroll the cylinder, the curved surface is just a rectangle as wide as the circumference of the cylinder (2πr) and height h. So, its area is 2πrh. Add that to the two circles ...
July 21, 2015

math
y = 5 - x + 2e^x sin3x y' = 2e^x sin3x + 6e^x cos3x - 1 y" = 12e^xcos3x - 16e^x sin3x 2y' = 4e^x sin3x + 12e^x cos3x - 2 y" = -16e^x sin3x + 12e^x cos3x 2y'-y" = 20e^x sin3x - 2 10y = 50 - 10x + 20e^x sin3x 2y'-y"-10y = -52+10x or, y"-...
July 21, 2015

ALGEBRA
If the faster pipe takes x minutes, then we have 1/x + 1/(x+10) = 1/12 x = 20 So, the pipes take 20 and 30 minutes, respectively.
July 21, 2015

URGENT MATH!!
How much of the job gets done in one hour by each person? Robert: 1/12 Dennis: 1/10 Vince: 1/9 So, in 2 hours, Dennis and Vince can do 2/10 + 2/9 = 19/45 of the job That leaves 26/45 for Robert to do. At his rate of 1/12 per hour, it will take him (26/45)/(1/12) = 6.933 hours ...
July 21, 2015

math
this should help 1/4 = 3/12 1/3 = 4/12
July 21, 2015

algebra
Let x = quantity of trouser material y = quantity of shirt material Then we are told that y/3 = x/2 or, y = 3x/2 cost of shirts: 50y cost of trousers: 90x sales of shirts: 1.12(50y) sales of trousers: 1.10(90x) total sales: 1.12(50y) + 1.10(90x) = 36600 Since 3y=2x, that means...
July 21, 2015

English grammar
I disagree. "Expensive" is an adjective, it can only be modified by an adverb. In this case, "too." The infinitive phrase is an appositive. There is no predicate noun; there is a predicate adjective (expensive) The basic sentence is It is expensive. The ...
July 21, 2015

Algebra
when does g(x)=20? When x=2 So, g^-1(20) = 2 Note that g(-10) = 20 as well, but that does not matter, since we have restricted our domain to x >= -4.
July 21, 2015

College Alg
consider the parabola y=36-x^2 Its vertex is at (0,6) So, restricting the domain to 0<=x<=6 means we only want the right branch of the function. SO, the inverse function is found the usual way, by switching variables and solving for y: x = 36-y^2 y^2 = 36-x y = ±...
July 21, 2015

Algebra
well, you surely know that revenue=price*quantity. That means R(x) = x(0.28-0.000002x) C(x) = 0.087x-0.0000005x^2 P(x) = R(x)-C(x)
July 21, 2015

physics
You want the ball to land 19.6m from the wall. So, how long does it take to fall 19.6m? That would be 2 seconds. So, what horizontal speed does it take to travel 19.6m in 2s?
July 20, 2015

Algebra
the average rate of change from x=2 to x=2+h is [f(x+h)-f(x)]/h = (4(x+h)^2-4x^2)/h = (4x^2+8xh+4h^2-4x^2)/h = (8xh+4h^2)/h = 8x+4h The net change is just f(x+h)-f(x) = 8xh+4h^2 At x=2, the net change is 16h+4h^2 and the average change is 16+4h
July 20, 2015

College Algebra
you need x when g(x) = 55 x^2+6x=55 x^2+6x-55 = 0 (x+11)(x-5) = 0 Since the domain is x >= -3, that means that g^-1(55) = 5 Note that specifying that x >= -3 means we have chosen only one branch of the parabola, whose vertex is at (-3,-9). Since g(x) = x^2+6x, x = -3 &...
July 20, 2015

Elementary statistics
you want Z such that P(Z>z) = 0.75 That means that Z >= -.674 .674*4.5 = 3.033 So, you want a score of at least 78-3.033 = 74.967 The 1st quartile ends at a score of 75% You can play around with Z table stuff at http://davidmlane.com/hyperstat/z_table.html
July 20, 2015

Elementary Statistics
.33 = .39-.06 = .39 - .04*1.5 so, that is 1.5 std below the mean. Now consult your Z table and find that P(Z > -1.5) = .9332 .9332*500 = 466.6
July 20, 2015

Math
Its length is 3 feet longer than its width. so, that would be x+3
July 20, 2015

Chemistry
40cm^3 * (1dm/10cm)^3 * .03mol/dm^3 = 0.0012 mol KOH Each mole of H2SO4 needs 2 moles of KOH to be neutralized. That means you had .0006 mol H2SO4 .0006mol/25cm^3 * 1000cm^3/L = 0.24mol/L = 0.24M H2SO4
July 20, 2015

Algebra1
It stays where it is. The vertex is at x=8, so a(x-8)^2 is always zero at x=8. The vertex stays at (8,9).
July 20, 2015

algebra 1
well, x^2-y^2 = (x-y)(x+y) That should help.
July 20, 2015

Algebra1
consider (x+2)^2 It is never negative, and is a minimum of zero when x = -2. So, (x+2)^2+7 has its minimum of 7 when x = -2. Read the choices carefully...
July 20, 2015

math
You have a 1/100 chance to win a $200 prize. So, your expected winnings are $2. Not much of a return on a $5 ticket. Still, it's for a worthy cause, right? . . .
July 20, 2015

Algebra
f^-1(x) = e^x g(x) = f^-1(x-2) So, reflect f(x) around the line y=x, and then shift it 2 to the right. In the graphs at http://www.wolframalpha.com/input/?i=plot+y%3Dln%28x%29%2C+y%3De^%28x-2%29%2C+y%3Dx%2C+y%3De^x you can see that f(x) is the blue curve the green curve is f ...
July 20, 2015

Algebra1
If a point (x,y) is on a graph of a function f, it means that y=f(x). That is true for both s and t in this case.
July 20, 2015

Algebra1
looks like it to me
July 20, 2015

Algebra
an even function has f(-x) = f(x) So, there are always two x's for each y. Consequently, there can be no inverse, since there will be two y's for the same value of x.
July 20, 2015

Algebra1
you are correct.
July 20, 2015

Algebra1
check to see whether 7 = (7/5)(5) what do you think?
July 20, 2015

Algebra1
well, check to see whether 9*9 + 5*5 = 0 doesn't look like it to me.
July 20, 2015

math
(7*12)(5*12)
July 20, 2015

math
6*3^2 = 54 Since the length is multiplied by 3, and the width is multiplied by 3, the area is multiplied by 9.
July 20, 2015

math
since each dimension is scaled, the area becomes (15/2.5)(25/2.5)
July 20, 2015

math
actually, since we're talking area, the new area is (1.5*7)(4*7) = ?
July 20, 2015

math
surely by now you have derived the desired equation of motion. h(t) = 7 + 85t - 16t^2 you know the max height is achieved at t = 85/32. So, is h at least 200 at that time? And why mention a speed of 150 ft/s if the upward velocity is only 85 ft/s? Do we need to assume an angle...
July 19, 2015

Geometry
the area of the base will be multiplied by 4, since it will be changed from LW to (2L)(2W) = 4LW So, apply that to finding the new volume.
July 19, 2015

@ Damon
I started reading your solution with trepidation. When I saw that we came up with the same solution, i breathed a huge sigh of relief!
July 19, 2015

physics(kinematics)
a = -8 v = -8t+c1 x = -4t^2 + c1*t + c2 x(4)=20, so -64 + 4c1 + c2 = 20 when v=16, -8t+c1=16, or t = (c1-16)/8 at that time, x=4, so -4((c1-16)/8)^2 + c1(c1-16)/8 + c2 = 4 Solve those two equations for c1 and c2, and you get c1 = 32 c2 = -44 That means that a = -8 v = -8t+32 x...
July 19, 2015

Math (Finite)
There are 15C2 ways to choose the couples. That uses up 4 people, leaving 26 individuals to make up the other 3 places on the committee. So, you have 15C2 * 26C3 = 105 * 2600 = 273,000 ways
July 19, 2015

Math
" means inches, not some weird "double prime." So, 6'3" = six feet, 3 inches, or 6.25 ft) Since the scale is constant, (3/8 ")/(1 ft) = x"/(6.25 ft) Now just solve for x: (3/8 ")/(1 ft)*(25/4 ft) = 75/32 "
July 18, 2015

Nice Save, Damon.
!!
July 18, 2015

Algebra
sometimes answer keys have errors. As far as I can see, Damon is right. 4 tests of 90 score a total of 360 points. The other test must be at least 50 to achieve the 410 points of 5 tests averaging 82 each. If any of the other high scores is less than 90, then the 4th test must...
July 18, 2015

Algebra
Here's an idea, Mr. Al. Why don't you try something else? Or, maybe you can find a flaw in Damon's logic, and get a better answer.
July 18, 2015

Math
since cos(x) starts at a maximum, you must have -cos(x) The radius is 35, so y = -35cos(x) It starts at y=2, so the axle is at y=37: y = 37-35cos(x) The period is 53, so y = 37-35cos(2pi/53 x) now just do what you need with that.
July 18, 2015

math
f is positive, increasing, and concave up. Draw such a curve, and you can see which approximations over- and under-estimate the value.
July 17, 2015

calculus
See related questions below.
July 17, 2015

calculus
well, just plug in the given condition C-cos(pi/2) = 1 C = 1 So, y = 1-cos(x)
July 17, 2015

adfaf
hint: who did the seeing?
July 17, 2015

mathematics
boats do not sail on bearings. They sail on headings. angle XYZ is 151° So, using the law of cosines, the distance XZ is z^2 = 6^2 + 7^2 - 2*6*7*cos151° If you draw the diagram, you will be able to figure all the angles needed to find the desired bearing.
July 17, 2015

maths
60 = 2*30 62 = 2*31 So, 31*60 = 30*62 That is the number of seconds that must elapse before they beep in synch again. How many seconds is that? Then convert that to a time since 10:00.
July 17, 2015

algebra
if there were x children, then the rest (2000-x) were adults. So, just add up the money: 2x + 4(2000-x) = 6000 and do the math
July 17, 2015

math
area grows by the square of the linear scale. That is because area = length*width so, if each of length and width are 1/2 as big, the area is (1/2)(1/2) = (1/2)^2 as big. So, the model is 1/4 the area of the enlarged patio.
July 17, 2015

Algebra 2
your steps and properties look good. Not sure about your initial mention of additive inverse. That appears nowhere here. a + (-a) = 0 uses additive inverse
July 17, 2015

maths
30-19 = ? assuming that you didn't eat any in the meantime... and that's how many, not how much.
July 17, 2015

math
Best guess: $2500 Not sure just what you're asking.
July 17, 2015

maths
3+1.5*5/60 = 5/60 * x
July 17, 2015

maths
since time = distance/speed, 2/(s-1.5) = 3 * 2/(s+1.5)
July 17, 2015

maths
add up the values of each component: 2.40*20 + 3.30x = 2.70(20+x)
July 17, 2015

Math
4*1500 + 12*2*120
July 17, 2015

algebra 2
recall that the sides of a 30-60-90 triangle are in the ratio 1:√3:2 You have a side of 200ft opposite the 30° angle, so it is the shortest side.
July 17, 2015

maths
31+x = 4(1+x)
July 17, 2015

maths
t=tens digit u=units digit t+u = 7 10u+t = 4(10t+u)-3
July 17, 2015

geometry
Two ways you can do this. Since ABC is similar to DEF, and DF/AC = 4/3, the other two sides are also 4/3 as big, making them each 16. So, the perimeter of DEF is 8+16+16=40 Or, since the scale factor is 4/3, the perimeter of DEF is 4/3 that of ABC. ABC's perimeter is 6+12+...
July 16, 2015

Math
this isn't so hard 7^2+5*7 = 49+35 = 84 < 100 8^2+5*8 = 64+40 = 104 > 100 So, any x, 8 or above, will satisfy the inequality. If any of your choices is less than 8 (or so), it won't work. Of course, if x is negative, there are other possibilities.
July 16, 2015

maths
1 dollar is 100 cents, so 4x dollars is 400x cents now add things up
July 16, 2015

careers
I am always amused by all you students who say what you're studying, and wondering what you can do with it. Seems to me like you're better off figuring out what you want to do, and then picking classes to help you prepare for that. In any case, your school counselor is...
July 16, 2015

math
b + b+5 = 49
July 16, 2015

math
just add up the value of the parts. They have to sum to the value of the whole. 8.00(20) + 6.00x = 7.00(20+x) Actually, this one is easy -- since 7.00 is the average of 6 and 8, you need equal amounts of the two kinds.
July 16, 2015

Algebra 2
what you have is a geometric series, with a = 20 r = 1/2 S2 = 20(1-r^2)/(1-r) S12 = 20(1-r^12)/1-r sigma(3,12) = S12-S2 = 20[(1-r^12)/(1-r) - (1-r^2)/(1-r)] = 20/(1-r) ((1-r^12)-(1-r^2)) = 5115/512
July 15, 2015

algebra
175e^5k = 181 so, k = .00674 P = 175 e^(.00674t) Now plug in t=25.
July 15, 2015

Math
r/80 = .20
July 15, 2015

Math
slope = ∆y/∆x = (2-14)/(10-2)
July 15, 2015

Calculus
(a+b)^4 is NOT a^4+b^4
July 15, 2015

Calculus
y=(x+λ)^4/(x^4+λ^4) y' = 4(x+λ)^3(x^4+λ^4) - (x+λ)^4(4x^3) ----------------------------------------- (x^4+λ^4)^2 = (4λ)(λ+x)^3(λ^3-x^3) -------------------------- (x^4+λ^4)^2
July 15, 2015

Math
and then multiply that by 4, since the square has 4 sides.
July 15, 2015

Math
or, since the ratio of lb/$ is constant, .99/3 = x/2
July 15, 2015

math
correct, but x is only halfway up the cliff . . .
July 15, 2015

Math
3.00 + 1.06(30/300 * 14.55)
July 15, 2015

Calculus
5th root of x^3 is (x^3)^1/5 = x^(3*1/5), not x^(3+1/5) So, you start out with y = x^(-1/2) - x^(-3/5) Now just use the power rule, to get y' = (-1/2)x^(-3/2) - (-3/5)x^(-8/5) If you insist on combining the fractions, then you wind up with 6 - 5x^(1/10...
July 15, 2015

algebra
The general solution to the quartic equation is very involved. Read the wikipedia article. This cannot seriously be a homework problem.
July 15, 2015

math
Let P be the base of the perpendicular from A, and Q the base of the perpendicular from B. APD is a 30-40-50 right triangle. So, CD=30, making AP=30 and QD=10. Triangle CQB thus has height 40 and leg CQ=50. So, tan(BCD) = 4/5
July 15, 2015

Math
factor it to get -16t(t-6) That should help
July 15, 2015

Math
C = T-S-H
July 15, 2015

Math
3*30 + (210-3*23)*.22
July 14, 2015

math
The mean is 20 + x/5 For that to be an integer, x must be a multiple of 5. The mean must be greater than 4, since the mean of 3,4,5,8 is already 4. For the mean to be 5, x=5 Also, the mode is 5 And the median is 5.
July 14, 2015

trig
Review what the grade is. It just means that tanθ = 0.1
July 14, 2015

Math
Sorry - not much TeX here. It appears that you mean H(x) = 120000*1.20^(1/2 x) That means that H grows by 20% every 2 years. But, if we want an annual rate, then we have to realize that this is the same as H(x) = 120000*(√1.2)^x √1.2 = 1.095 So, we wind up with H(x...
July 14, 2015

math
n is between 651 and 749 The last digit is between 0 and 4 Looks like we can choose from 650,652,654,...730,732,734
July 14, 2015

algebra
(fg-8)(f^2g^2 + 8fg + 64) This is just the difference of two cubes: (fg)^3 - 8^3 Recall that (a^3-b^3) = (a-b)(a^2+ab+b^2) You have a = fg b = 8
July 14, 2015

algebra
jeez - just plug in x=2! (4*2-2)^2 = 6^2 = 36 16*4-16*2+4 = 36
July 14, 2015

algebra
just square the binomial: (5m^2+7)^2 = 25m^4+70m^2+49
July 14, 2015

Sj
There are two branches: +√x and -√x Just pick one branch of the graph.
July 14, 2015

Maths
Of the 15 balls, 14 remain. P(red) = 2/7 means there are 4 red balls out of 14. So, the lost ball is red.
July 14, 2015

algebra
√(x^2+y^2+100x+2500)-√(x^2+y^2-100x+2500) = 60 (x^2+y^2+100x+2500)-2√((x^2+y^2+100x+2500)(x^2+y^2-100x+2500))+(x^2+y^2-100x+2500) = 3600 2(x^2+y^2+2500) - 2√(x^4+2x^2y^2+y^4-5000x^2+5000y^2+6250000) = 3600 √(x^4+2x^2y^2+y^4-5000x^2+5000y^2+6250000...
July 14, 2015

math
Just apply the chain rule y=sec^3(2x)-3sec2x y' = 3 sec^2(2x) * sec(2x)tan(2x) * 2 - 3sec(2x)tan(2x)*2 = 6sec(2x)tan(2x) (sec^2(2x)-1) = 6sec(2x)tan^3(2x)
July 14, 2015

interoduction of aeronautical engineering
the volume of an ellipsoid with semi-axes a,b,c is 4/3 pi*abc Your semi-axes are just 23/2, 7 and 7. Plug and chug.
July 14, 2015

math
If there are x lbs of $6.50 coffee, then the rest (140-x) of $2.50 beans. So, add up the total cost of the various amounts: 6.50x + 2.50(140-x) = 5.07(140) Now just find x and then 140-x.
July 14, 2015

algebra
that's the same as y = 3x If that still doesn't ring a bell, then write it as y = 3x+0 Compare that to y = mx+b
July 14, 2015

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