Thursday
August 27, 2015

Posts by STEVE


Total # Posts: 33,099

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

Math grade 11 u
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

Math Check
yes.
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

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

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