Thursday
July 30, 2015

# Posts by steve

Total # Posts: 32,528

Algebra
If there are 3n with nuts, there are only n w/o nuts. n + 3n = 24
July 25, 2015

maths
if the base of the ladder is x from the wall, and the height up the wall is y, then we have x^2+y^2 = 25^2 so, when y=20, x=15. Taking the derivative wrt t, we have x dx/dt + y dy/dt = 0 Now just find dy/dt, knowing that dx/dt = 0.3 Note that dy/dt will be negative, since the ...
July 24, 2015

Appositives Redux
So, how do you parse this sentence? It is the responsibility of every patriotic citizen to protect and defend the constitution. Do we not have an appositive? How "next to" its noun must it be?
July 24, 2015

Grrr.
Hmmm. A little research has (mostly) convinced me that Ms. Sue is right, as usual.
July 24, 2015

English Grammar - Function of an Infinitive
I see the infinitive phrase as an appositive to the subject: it.
July 24, 2015

math
a/b/c = a/(bc) so, we have (3y-5)/5/(14/10 + 7/2 y) = (3y-5)/(5*7(1/5 + 1/2 y)) = (3y-5)/(35*(2+5y)/10) = 2(3y-5)/(7(2+5y)) Now subtract that from y and you have 7y(2+5y) - 2(3y-5) ----------------------- 7(5y+2) (35y^2+8y+10)/(35y+14)
July 24, 2015

math
since I = k/d^2, I*d^2 = k, a constant. So, just set it up: 85*5^2 = I*2^2 Now just solve for I.
July 24, 2015

math
inverse variation means that RT = k, a constant. So, just set up things which are both equal to k: 35*6 = R*5 now just find the R value.
July 24, 2015

math
since distance is proportional to t^2, then since 12 = 6*2, the distance fallen in 12 seconds will be 36 times the distance fallen in 2 seconds.
July 24, 2015

math
since distance = speed * time, 480t = 440(t + 1/2) 40t = 220 t = 5.5 So, it took 5.5 hrs at 480 mph, and 6 hrs at 440 mph. I figure you can do the rest now.
July 24, 2015

maths
let the boat have speed x and the river have speed y. Since time = distance/speed, 30/(x-y) + 44/(x+y) = 10 40/(x-y) + 55/(x+y) = 13 Just looking at the equations, I expect we will find that (x+y) = 11 and (x-y) is a multiple of 5. Doing the actual solutions, we find that ...
July 24, 2015

Trigonometry
well, 632° = 360°+272°, so it's the same as 272°. Was there something in particular you wanted to let us know about it?
July 23, 2015

math
If 1999 is a root of x^3 - 1999x^2+x-1999=0 then a root of (x-1)^3-1999(x-1)^2 +(x-1)-1999=0 is a value of x so that x-1 = 1999 In other words, x=2000
July 23, 2015

math
If the legs are a and b, and the hypotenuse is c, then a+b=50 ab=282 c^2 = a^2+b^2 = (a+b)^2 - 2ab = 2500-564 = 1936 so, c = √1936 = 44 1 2 3 6 47 94 141 282
July 23, 2015

math
there are 20 multiples of 5 between 1 and 100. Since 5^2=25, there are also 4 multiples of 5^2, so they have to be counted twice.
July 23, 2015

math
since 5^3 = 125 = 1.25x10^2 any power of 10 will do, as long as it is 2 more than a multiple of 3. That's because each 3 added to the power is the same as multiplying by 1000, which is 10^3.
July 23, 2015

math
Can you find the slope of a line joining two points? Assuming the vertices are listed in order around the figure, then the diagonals are lines between (-2,3) and (-1,4) and (3,1) and (-6,6) One of those lines should have a slope listed in the choices. If you can't figure ...
July 23, 2015

math
if two roots are equal, so are the numbers. So, since √(a+b) = √8 a+b=8
July 23, 2015

well, 2^48-1 = (2^24-1)(2^24+1) Both of those are way too big, so 2^24-1 = (2^12-1)(2^12+1) still too big, so 2^12-1 = (2^6-1)(2^6+1) = 63*65 So, 2^48-1 = 63*65(2^12+1)(2^24+1)
July 23, 2015

Algebra 2
#1 since you know that y = -x^2, just plug that in: x^2 - (-x^2-6)^2 = 36 This has no real solutions. If you graph the hyperbola and the parabola, you will see that they do not intersect. http://www.wolframalpha.com/input/?i=plot+x%C2%B2+-+%28y+-+6%29%C2%B2+%3D+36+%2C+y+%3D+-x...
July 23, 2015

math
This problem is poorly worded. The total sales if x new people are hired is (50000-1000x)(30+x) Find the vertex of that parabola to determine how many new people should be hired, to produce maximum total sales. But clearly, the average sales do nothing but decrease, since each...
July 23, 2015

algebra
If \$x is at 6%, then the rest (50000-x) is at 8%. So, just add up the interest: .06x + .08(50000-x) = 32000 Now just solve for x.
July 23, 2015

basic math
1/4 of 12 is 3
July 23, 2015

Computer
no flowcharts here. So, the flow of logic is just prompt for n1 read n1 since n1+n2=150, n2 = 150-n1 Also, n2 = 2*n1 - 40 You need to solve n1 + (2*n1-40) = 150 n1 = (150+40)/3 n2 = 150-n1 print n1 and n2 (with labels)
July 23, 2015

math
as usual, A = 1/2 bh = 1/2 (5y-2)(4y-7) m^2 can you multiply those two binomials?
July 23, 2015

physics
you know that the height h = 128t - 16t^2 = 16t(8-t) so, note that it hits the ground when h=0. now just do the math.
July 23, 2015

College Algebra
Let x be the middle number x-1 + x + x+1 = 966 3x = 966 ...
July 23, 2015

Unisa
You know that s = rθ. So, solve for θ in 20π = 24θ
July 23, 2015

Physics
Just use the formula F = GMm/r^2 Disregard the data about the sizes of the bodies. You have their masses and the separation, and G. So, plug in the numbers.
July 23, 2015

Calculus
I assume you mean ∫ cos(x)/√(sinx) dx let u^2 = sinx 2u du = cosx dx Now the integral is ∫ 2u/u du = 2∫du = 2u+c = 2√(sinx)+c
July 23, 2015

Calculus
Maybe this discussion will help. http://math.stackexchange.com/questions/359023/using-the-limit-definition-to-find-the-derivative-of-ex
July 22, 2015

Algebra 1
just count the ways the event can happen even: 11 13 15 22 24 26 31 33 35 42 44 46 51 53 55 62 64 66 So, there are 18 ways to roll an even. There are 4 ways to get a five: 14 23 32 41 So, P(even or 5) = 20/36
July 22, 2015

h(x) = ax^2+bx+c h(142) = 0, because at that distance the ball hits the ground h(0) is the initial height when the ball was hit (it has not traveled any distance yet). So, 0.6 <= h(0) <= 1.5
July 22, 2015

ALGEBRA
If the truck has speed x, then the car has speed x+20 since time = distance/speed, 350/(x+20) = 350/x - 2 Now just solve for x, and figure x+20
July 22, 2015

calculus
The region bounded by y=√x y=0 x=3 has its "vertices" at (0,0), (3,0), and (3,√3) To rotate it about the line x=9, it's best to think of flat discs with holes in them. So, since the volume of a thin disc of thickness dy is πr^2 dy, and we need to...
July 22, 2015

Math
well, consider the fact that 6x^2-7x-5 = (3x-5)(2x+1) ...
July 22, 2015

Mathematics
well, consider the fact that 6x^2-7x-5 = (3x-5)(2x+1)
July 22, 2015

math
Assuming you meant 51x+24y = 75, you can divide by 3 to get 17x+8y = 25 So, 17x+8y = C will be parallel, regardless of the value of C. (except C=25) So, pick (B) because (D) is the same line as the original (obtained by multiplying through by 2/3).
July 22, 2015

math
an odd number of them must be negative. So, I pick (B)
July 22, 2015

math
do you know what a reciprocal is? If not, you cannot pick the right answer.
July 22, 2015

math
0 = -1 + 0 + 1 n + n+1 + n+2 = 3n+6 so it must be a multiple of 3.
July 22, 2015

math
XY = 1/4 AB altitude of CXY is 3/4 the altitude ABC. So, CXY has area 1/3 * 3/4 * 21 = 21/4
July 22, 2015

Math Check
(x^2+3)^2 = x^4 + 6x^2 + 9 so, x^2+3 = √(x^4+6x^2+9) But, √(x^4+6x^2+9) = (x^4+6x^2+9)^1/2 so, (x^4+6x^2+9)^1/2 = x^2+3
July 22, 2015

Algebra
since area = width*length, w(2w-2) = 222 Now solve for w, and get the length.
July 22, 2015

Algebra
If the cork costs, c, then the bottle is c+1. So, adding them up, c + c+1 = 2 2c = 1 c = .50 cork: \$0.50 bottle: \$1.50
July 22, 2015

chem
Oh, yeah: 22.4L at STP, not 1L. (1*22.4)/(273*1) = (1.2*5.25)/(299n) n = 0.256 My 273 is included in the .08026 factor you inserted.
July 22, 2015

chem
Since PV=nRT, we have PV/nT = R is constant. So, use STP and your given numbers: (1*1)/(1*273) = (1.2*5.25)/((273+26)n) Just solve for n.
July 22, 2015

Urgent math
the quotient is indeed 2x^2 + 3x There is a remainder of 9. So, P(x) = (5x-7)(2x^2+3x) + 9 Not sure why your answer is marked incorrect, since you have the quotient right. Maybe you had to supply both Q and R. P(x)/(5x-7) = 2x^2+3x + 9/(5x-7)
July 22, 2015

Urgent math
as x→∞, -x^5 becomes more and more negative: it falls to the right: y→-∞ Similarly, as x→-∞, -x^5 rises to the left: y→∞ Since x^5 becomes so much greater than any lower powers of x, only the highest power needs to be considered...
July 22, 2015

maths
a+2d = 12 a+6d = 72 I think you can now easily find a and d and find other terms, right?
July 22, 2015

math
54 * 2/3
July 22, 2015

Math
Assuming that the pipes are to be straight from M to A and B (that is, the pipe does not go to some other point P and then divide), then let's add a couple more points to the diagram: P: the point on the river bank closest to A Q: the point on the river bank closest to B ...
July 22, 2015

math
See http://www.wolframalpha.com/input/?i=maclaurin+series+1%2F%281%2Bx%29
July 22, 2015

math
Since the series is x - x^2/2 + x^3/3 - x^4/4 + ... That would be ∞ ∑ (-1)^(k-1) x^k/k k=1
July 22, 2015

Urgent math
you can see all the details of long division by entering your polynomials here: http://calc101.com/webMathematica/long-divide.jsp
July 22, 2015

Urgent math
f(x) = x^2-8x+8 complete the square, by adding and subtracting 16, so things are unchanged: = x^2-8x+16 +8-16 = (x-4)^2 - 8
July 22, 2015

College Alg
You can see the steps here: http://www.emathhelp.net/calculators/algebra-1/synthetic-division-calculator/?numer=5x^5+%2B+10x^3+%2B+x+%2B+1&denom=x%2B2&steps=on But you will need to practice some of these on your own.
July 22, 2015

College Alg
You will have to do this graphically, since it's an algebra problem. There are lots of online graphing utilities. A good one is http://rechneronline.de/function-graphs/ You can set the domain and range and the grid resolution. Reading off the extrema will be easy.
July 22, 2015

English
(A) is the right idea: What unusual recipes it has! (B) could be expressed somewhat unusually as How unusual are its recipes!
July 22, 2015

Math
If I parse things correctly, we have πz^2rh = 2(.064^2)πr+.064*2πr z^2πr^2 = .064*2πr πr^2h = 1567.8 I get r=7.77 h=8.27 z=0.128
July 22, 2015

maths
note from #2 that x = 21y/(2y+1) put that into #1 and you have 3*21y/(2y+1) + 14y = 5y*21y/(2y+1) 63y + 14y(2y+1) = 105y^2 77y^2-77y = 0 77y(y-1) = 0 Now you have two solutions for y. Use them to get associated solutions for x.
July 22, 2015

math
There is an excellent G-J calculator here: http://www.gregthatcher.com/Mathematics/GaussJordan.aspx You can set the size of the matrix and enter the coefficients. Then it will show all the intermediate steps of the solution.
July 22, 2015

Urgent math
f(x) = 450+95x f^-1(x) = (x-450)/95 and so on
July 22, 2015

College Algebra
y = x^2+11x for inverse, switch names and solve for y: x = y^2+11y y^2+11y-x = 0 y = (-11±√(121+4x))/2 with the original domain restricted to x >= -11/2, that means y = -11/2 + √(121+4x)/2 or, consider that y = x^2+11x = (x+11/2)^2 - 121/4 restricting the...
July 22, 2015

College Algebra
x 5x 5x+9 (5x+9)^5 inverse: x = (5y+9)^5 5y+9 = x^(1/5) 5y = x^(1/5)-9 y = (x^(1/5)-9)/5
July 22, 2015

Math
1/4 * 2/3 = 2/12 = 1/6
July 22, 2015

Finite Math
well, A^5 = A^4 * A So, A = A^5 * (A^4)^-1 (A^4)^-1 = 5 -4 4 -3 So, A = 4 -5 * 5 -4 5 -6 4 -3 = 0 -1 1 -2
July 21, 2015

Math
4*5*6 = 120 = 5^3-5 -6 * -5 * -4 = -120 = -5^3 + 5 I suspect a typo in the problem.
July 21, 2015

Math
There are only 3 ways to get 3 or less: 1,1 1,2 2,1 So, there are 33 ways to get more than 3.
July 21, 2015

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

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