Thursday

September 3, 2015
Total # Posts: 33,270

**pre-calculus**

112.5 = 5π/8 = (5π/2)/4 so, use your half-angle formula twice: cos(x/2) = √((1+cos(x))/2) cos(5π/4) = -√((1+0)/2) = -1/√2 since 5π/4 is in QIII sin(x/4) = √((1-cos(x/2))/2) sin(5π/8) = √((1-cos(5π/4)/2) = √((1+1...
*July 27, 2015*

**Math**

The triangular numbers are 1,3,6,10,... So, the nth tetrahedral number is the sum of the first n triangular numbers. The nth triangular number is the sum of the first n integers (1+2+3+...) = n(n+1)/2 It is clear that the nth tetrahedral number will be a cubic expression in n...
*July 27, 2015*

**pre-calculus**

well, you have tan^2 x = 1/3 see previous posting for solving it.
*July 27, 2015*

**English 9**

I get that the only correct answers are 5,6,8
*July 27, 2015*

**pre-calculus**

well, you have tan^2 x = 1/3 which angle does not have tan x = ±1/√3 ?
*July 27, 2015*

**Math**

call the solutions A and B. If there are x gal of A, then there are 7-x gal of B. So, if we keep track of the alcohol amounts, we have 4/5 x + 1/6 (7-x) = 1/2 (7) Now just solve for x, the amount of solution A.
*July 27, 2015*

**Algebra**

well, did you check your answer? money spent at store #1 = 3/4 * 51100 + 75 = 38400, leaving 12700 at #2, spends 3/4 * 12700 + 75 = 9600, leaving 3100. at store #3, spends 3/4 * 3100 + 75 = 2400, leaving 700 Looks like you are correct. It seems you need to learn how to check ...
*July 27, 2015*

**pre-calculus**

you know that sin 45 = √2/2 225 = 180+45, so sin(225) = sin(180+45) now just use your addition formula to get the above result.
*July 27, 2015*

**Math**

Hmmm. I see I was mistaken. You are correct. My equations add up the wrong stuff. I see I should have checked my answer.
*July 27, 2015*

**Math**

Hmmm. If 2 kg of alloy 1 are used, then that means there are 2 kg of gold 10kg of silver 6 kg of lead You are already over 10 kg of the mixture. Add in to that any amount of the other alloys and things are even worse.
*July 27, 2015*

**Math**

If there are x,y,z kg of the alloys, then we want x+5y+3z = 10 2x+3y+4z = 10 5x+2y+2z = 10 Just solve those to find x,y,z. Since the x value is from the 1st alloy, in the ratios 1:5:3, that is how many kg of that alloy we need.
*July 27, 2015*

**Pre-calc**

we have sin(u+v) = sinu cosv + cosu sinv sin(u-v) = sinu cosv - cosu sinv add them up and you have sin(u+v)+sin(u-v) = 2sinu cosv now just finish it up.
*July 27, 2015*

**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*

**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*