Sunday
August 2, 2015

Posts by Steve


Total # Posts: 32,558

Physics
well one lap is 500m.
July 27, 2015

math
or, we could convert to polar first: 2+j4 = √20 cis 1.107 -3-j4 = 5 cis 4.068 multiply and you get Reiny's value.
July 27, 2015

math
I assume each equation is separate, so we have x = 2/π 3x+2 = 5x+7-2x 3x+2 = 3x+7 No solution 6x+2-4x=5+2x-3 2x+2 = 2x+2 infinitely many solutions
July 26, 2015

chemistry
The mol mass of KI is 166, so 3.5g = 0.021 moles KI .021mol/.0275L = 0.767 M So, you need to dilute the original solution from 5.95M to 0.767M That's a dilution by a factor of 7.757 So, the volume must increase by that factor, so you need .047*7.757 = 365mL
July 26, 2015

math
You can check your calculations here: http://www.wolframalpha.com/input/?i=solve+{{1%2C-1%2C3}%2C{2%2C1%2C2}%2C{-2%2C-2%2C1}}*{{x}%2C{y}%2C{z}}+%3D+{{2}%2C{2}%2C{3}}
July 26, 2015

Physics
42
July 26, 2015

math- partial fractions
so, fix it and follow the steps. If you enter your formula at wolframalpha.com, it will show the decomposition, so you can check your work. Watch to be sure you include necessary parentheses. wolframalpha will show how it interprets your input.
July 26, 2015

math- partial fractions
If, however, you meant 1/((s^2)(s^2 +2s +3)) then that is A/s + B/s^2 + (Cs+D)/(s^2+2s+3) = A(s*(s^2+2s+3)) + B(s^2+2s+3) + (Cs+D)s^2 = As^3+2As^2+3As + Bs^2+2Bs+3B + Cs^3+Ds^2 = (A+C)s^3 + (2A+B+D)s^2 + (3A+2B)s + 3B all over s^2(s^2+2s+3) So, to make the two sides equal, we ...
July 26, 2015

algebra
I think that's the symmetric property. Transitive is A=B and B=C ==> A=C
July 26, 2015

Math 156
You know that √N * √N = N So, if you pick pairs of factors, one factor must be less than √N and the other must be greater than √N. So, if you have tested all possible factors less than √N and found none, you are done.
July 26, 2015

Math Functions
You know that y=e^x goes through (0,1) and has an asymptote at y=0, so, y = e^x + 3 has its asymptote at y=3. Further, 5e^x goes through (0,5), so one function would be 5e^x + 3 Now, you can pick any number greater than 1, and the above statements hold true, so 5*2^x, 5*10^x ...
July 26, 2015

math
plates: no repeated letters: there are 26 choices for the 1st letter, leaving only 25 for the 2nd, and 24 for the 3rd: 26*25*24 = 15600 repeated letters: 26*26*26 = 17576 matrix: If the matrix of coefficients is A, you want (x,y,z) such that AX = B where B = (2 3 2) That means...
July 26, 2015

MAth 109
I assume your formula is d = √(3h/2) If the person is 80' above the water, just plug it in: d = √(3*80/2) = √120 = 2√30 = 10.95 So, the person on the deck can see 10.95 miles.
July 26, 2015

Physics
PE = mgh 3800 = (mg)(4.42) His weight is mg
July 26, 2015

calculus problem I have tried 100 times
The radius of the surface of the chocolate at height y is 4y/5. So, the volume of a disc of thickness dy at height y from the tip of the cone is v = π(4y/5)^2 dy That makes the mass of the disc m = 16π/25 y^2 dy * 1080 kg = 691.2πy^2 kg The height that the mass ...
July 26, 2015

maths
could be anything, since 7≠56
July 26, 2015

Maths
1/a + 1/b + 1/c = 1/10 1/a + 1/b = 1/20 1/a + 1/c = 2/25 Now just solve normally use GJ, but use 1/a, 1/b, 1/c as your variables. When you get the results, the values for a,b,c are the reciprocals.
July 26, 2015

trig
or, you can proceed by noting that you have tanθ = (1-sin36)/cos36 = 0.509
July 26, 2015

St Kabir
sin(θ+36) = cosθ sinθ cos36 + cosθ sin36 = cosθ sinθ cos36 = cosθ(1-sin36) That's exact, but you can approximate sin 36 = 0.6 cos 36 = 0.8 You can change sin to cos bu squaring and remembering that sin^2 + cos^2 = 1
July 26, 2015

ssc..math
since the ratio of height:shadow is the same for both, 30/7 = h/5
July 26, 2015

src
well, clearly, the 1st term is 15, and the difference is 9.
July 26, 2015

Maths
5p + 2(p+10) = 370
July 26, 2015

Calculus
so, what formula did you use? was it 10*(1/2)^(t/30) ? If so, just recall that 1/2 = e^(-ln2), so that is the same as 10e^(-ln2/30 t) Now just plug in your various numbers.
July 26, 2015

Calculus
I assume you have been shown how to derive f' when f' = e^x. f(x) = 5^x f(x+h) = 5^(x+h) = 5^x * 5^h f(x+h)-f(x) = 5^x(5^h-1) dividing by h, we have 5^x (5^h-1)/h = 5^x (e^(h ln 5)-1)/(h ln5) * ln5 Recall than lim(u->0) (e^u-1)/u = 1, so we wind up with ln5 5^x x^2 ...
July 26, 2015

Math
the surface of the water is a circle of diameter 5m, so its area is 25π/4 m^2 Since it takes 4 hrs to fill the 1m, pool, the water comes in at a rate of 25π/16 m^3/hr So, after t hours, the volume of water in the pool is v(t) = 25π/16 t m^3
July 25, 2015

lesiba
Actually, it is not. The surface area of a sphere is 4πr^2, so the area of a hemisphere is 2πr^2. As to why, you can google the topic and find various ways to derive the formula.
July 25, 2015

Math
just put the product under the root symbol. √2 * √3 = √(2*3) = √6 √8 * √18 = 2√2 * 3√2 = 2*3√(2*2) = 6*2 = 12 (note that √(8*18) = √144 = 12) Did you have something a bit more complicated?
July 25, 2015

algebra - eh?
Some characters are missing. If I assume the missing symbols are + signs, and plot the resulting lines, the picture does not look much like a quadrilateral. Maybe you can fix things a bit? http://www.wolframalpha.com/input/?i=plot+2x%2B3y%3D2%2C+3x-2y%3D4%2C+x%2B2y%3D3%2C+2x-y...
July 25, 2015

Inverse Trigonometric Functions
use the sum of sines formula: sin(A+B) = sinA cosB + cosA sinB We have A = arcsin(x/a), so cosA = √(a^2-x^2)/a B = arcsin(y/b), so cosB = √(b^2-y^2)/b C = arcsin(c^2/ab) That gives us sin(A+B) = sinC (x/a)(√(b^2-y^2)/b) + (√(a^2-x^2)/a)(y/b) = c^2/ab ...
July 25, 2015

Math
m+c = 35 2m+4c = 114 ...
July 25, 2015

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

junior maths olympiad 2005
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

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

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