Saturday
December 10, 2016

Posts by STEVE

Total # Posts: 47,054

G.p.
a = 1 r = 1/2 S12 = (1 - 1/2^12)/(1 - 1/2)
December 8, 2016

G.p.
b-a = c-b 1/a^2 - 1/b^2 = 1/b^2 - 1/c^2
December 8, 2016

Math
well, add 'em up: 2 4/8 3 3/8 1 2/8 ------- 6 9/8 = 7 1/8
December 7, 2016

math
(450-45)/450 = ? Or, you can reason that 45 is 10% of 450 that were used, so ...
December 7, 2016

Trigonometry
24.91 @ S36°W
December 7, 2016

MATH, please help
they are in proportion because 8*9 = 6*12 In a proportion a/b = c/d ad = bc
December 7, 2016

Math
12% is about 1/8 so, you need about 8 times the amount.
December 7, 2016

Math
There must be a typo. It is 2x^3+5x^2+x-7 So, (C) could be right, if it has the typo.
December 7, 2016

Math
the slope is -A/B So, of course, B cannot be zero. That gives the equation Ax=C which is a vertical line, so the slope is undefined.
December 7, 2016

math
3
December 7, 2016

Math
right.
December 7, 2016

Check Answer!!
That is right.
December 7, 2016

Math
linear: constant difference quadratic: constant 2nd differences exponential: constant ratio over equal intervals
December 7, 2016

Check Answer!!
4600(1+.025/4)^(4*8) = 5614.96 what formula did you use?
December 7, 2016

precalculus
well, you know it will be in QIV, so 270 < ? < 360 arctan(7/3) = 66.8014° But you want arctan(-7/3) = -66.8014°, in QIV. So, add 360 to that to get 293.19° Hmmm. Not one of the choices. However, arctan(-3/7) = 337° Looks like there was a typo in the problem.
December 7, 2016

precalculus
tan?/sec? = sin? Now do you have an idea?
December 7, 2016

Algebra
the 2nd is just the first, shifted down 9 That is, subtracting 9 from the y-values moves the graph downwards. Try it.
December 7, 2016

Geometry
yes.
December 7, 2016

Geometry
D is the biggest angle, so the opposite side (EF) is the longest side. Now do the others similarly.
December 7, 2016

Math
I can find no solutions.
December 7, 2016

Geometry
Draw a diagram. Note that AE is divided into two pairs of equal lengths. BD contains one of each pair. So, BD is half the length of AE. 2(3x+5) = 4x+20 x = 5
December 7, 2016

algebra 1
since the lines have different slopes, they intersect. Now just use the value of y from eq #2 and substitute it into eq #1 to get the value of x. Then you can get y.
December 7, 2016

Math
look for SSS in the lengths of the sides of the triangles formed.
December 7, 2016

precalculus
I doubt I can explain it any more clearly than (a) your text (b) the many discussions provided using google.
December 7, 2016

math
7(a+6d) = 11(a+10d) 7a+42d = 11a+110d 4a+68d = 0 a+17d = 0 T18 = a+17d = 0
December 7, 2016

analytic geometry
x and y have increased by 2. Extending the line 3 times more will increase each by 6. So, the desired point is (9,9)
December 7, 2016

duet
the terms are a, a+d, a+2d, a+3d so you want to show that a^2 - (a+3d)^2 = 3((a+d)^2 - (a+2d)^2) Now just verify that by expanding both sides.
December 7, 2016

math(A.P)
The sum of the 1st n odd numbers is n^2. So, n^2 > 5000
December 7, 2016

Maths
(25-2x)(30-2x) = 300
December 7, 2016

maths
Let AB=AC = x, and the base BC = 2y Then you have 2x+2y = 64 y^2 + 24^2 = x^2 (32-x)^2 + 24^2 = x^2 x = 25 You might have guessed this right off, since one of the basic right triangles with integer sides is 7-24-25 Of course, a 3-4-5 triangle scaled up by 6 would be 18-24-40 ...
December 7, 2016

math
just use the formulas you know, and write down the facts as given: S25 = 25/2 (2a+24d) = 200 S3 = 3/2 (2a+2d) = 4.2 Solve those two equations, and you get a = 4/5 d = 3/5 "larger" indicates only two items. I assume you mean the "largest" term, which is T25...
December 7, 2016

Geometric progression
1+2^1+2^2+...+2^n = 2^(n+1)-1 So, the sequence becomes 2^1-1 + 2^2-1 + 2^3-1 + ... + 2^n-1 = 2^1 + 2^2 + ... + 2^n - n = 2^(n+1)-1 - n-1 = 2^(n+1) - (n+2) check (n=5): 1+3+7+15+31 = 2^6-7 = 57
December 7, 2016

G.p.
same old same old, with a = 1 r = -1/2
December 7, 2016

G.p.
Sn = a(1-r^n)/(1-r) Just use your formula.
December 7, 2016

math
just plug and chug: a+8d = 0 25/2 (2a+24d) = 50 8d = -a, so 25/2 (2a-3a) = 50 a = -4
December 7, 2016

math
of course not. multiplying miles by miles gives you area: miles^2 Keep track of the units and all becomes clear: 1 km = 0.62 mi that means that 1km/0.62mi = 1 Now, you can always multiply by 1 and not change things. So, since you want to convert miles to km, 26mi * 1km/0.62mi...
December 7, 2016

G.p.
when x/(x-2) = (x+3)/x
December 7, 2016

math
the one rising from 270 with a slope of 80
December 6, 2016

physics
correct.
December 6, 2016

Math
so you want the left limit (as x->2 from below) Now, recall the definition of |u| |u| = u if u >= 0 |u| = -u if u < 0 When x < 2, x-2 < 0, so |x-2| = 2-x So, the limit is (2-x)/(x-2) -> -1 You can see this on the graph at http://www.wolframalpha.com/input/?i...
December 6, 2016

Math
(?(2x+3)-?(3x))/(x^2-3x) If you have l'Hospital's Rule as a tool, then you know that the limit is the same as (1/?(2x+3) - 3/(2?(3x)) / (2x-3) = (1/3 - 3/6)/3 = -1/18
December 6, 2016

Math
g(k) = -k^2 + 4k + 1 I suspect there is more to this question...
December 6, 2016

maths
both numbers are multiples of 7. 77 = 7*11, so you want two numbers which sum to 11, and have no factors in common. That would be 1,10: 7+70 = 77 2,9: 14+63 = 77 ...
December 6, 2016

Math liberal arts 2
yes! m is the slope. That's why y=mx+b is called the "slope"-intercept form of the line.
December 6, 2016

Algebra
what's the trouble? Each term, starting with the 3rd, is the sum of the two previous terms. Since the first two terms are 9,9 the sequence continues with 9+9 = 18 9+18 = 27 18+27 = 45 ... You might try writing the sequence as a_(n+1) = a_n + a_(n-1) saves using all those ...
December 6, 2016

Algebra
parent: y = ?x shift left 7.3 gives y = ?(x+7.3) stretch by 9 gives y = 9?(x+7.3) reflection changes the sign of the y-values, so y = -9?(x+7.3) square root is a particular function. cube root is not "^3 squareroot" Try saying cube root 4th root 5th root etc. instead...
December 6, 2016

Algebra
vertical asymptotes: 1/((x+2)(x-7)) root at x = -5: (x+5)/((x+2)(x-7)) horizontal asymptote. we need the degree to be equal, so try 7x(x+5) -------------- 2(x+2)(x-7) The problem here is that now we have another x-intercept at (0,0) So, let's work with 7(x+5)^2...
December 6, 2016

Algebra
vertex at t = -b/2a = 570/32 = 285/16
December 6, 2016

Fraction Test Question
4x8 = 8x4 4/4 = 8/8 4x8/8 = 4
December 6, 2016

math - bogus
ever actually read what you posted?
December 6, 2016

algebra
so, draw the graphs, or make a table. No problema, right?
December 6, 2016

Algebra 2
Think of moving the y-axis 4 units to the right. All the x distances would be 4 less than they are now. So, y = (x-4)^2 is just the parabola y=x^2, moved 4 units to the right! replacing x by (x-h) moves the graph h units to the right. you can see this here: http://www....
December 6, 2016

Pre-Calculus
clearly you need to review this topic e < 1 ellipse e = 1 parabola e > 1 hyperbola
December 6, 2016

Calculus
try this site: http://www.wolframalpha.com/input/?i=plot+r+%3D+cos+5%CE%98+%2B+n+cos+%CE%98,+0+%E2%89%A4+%CE%98+%E2%89%A4+%CF%80,+n%3D1
December 6, 2016

Trigonometry
3 rpm = 6? radians/min 2?*25*3 = 150? ft/min
December 6, 2016

Math
Not quite. ?(75p^3q^2) = 5?3 pq?p ?(p^5q^4) = p^2q^2 ?p divide and you end up with (5?3)/(pq) Hmm. I guess you could have meant 5?(3/(p^2q^2)) but that simplifies to my result above
December 6, 2016

Cal 3
critical points are where they are both zero. So, you need x^3+y^3-15x^2-6xy+18y^2+39x+138y 3x^2-30x-6y+39 = 0 3y^2-6x+36y+138 = 0 http://www.wolframalpha.com/input/?i=solve+3x%5E2-30x-6y%2B39+%3D+0,+3y%5E2-6x%2B36y%2B138+%3D+0 http://www.wolframalpha.com/input/?i=minima+x%5E3...
December 6, 2016

Algebra II
real: 4,2,0 Using Descartes' Rule of Signs, positive: 2 max negative: 2 max complex: 4,2,0 how come (a),(b),(c) are all the same?
December 6, 2016

Trigonometry
cot(x) has period pi cot(x/3) has period 3pi Now add in the rest.
December 6, 2016

Applied calculus
pi, not pie or pai or ... try typing your functions in here. http://www.wolframalpha.com/input/?i=plot+x%3D2cos(2t),+y%3D2sin(3t),+0%3C%3Dt%3C%3D2pi rather than expressing them as vector components, use parametric equations.
December 6, 2016

Algebra
keep track of the amount of antifreeze in each part, and the whole: .25x + .60*4 = .45(x+4)
December 6, 2016

CALC
google is your friend. Many of these problems have been solved before, or ones like them. www.math.umn.edu/~emanlove/2263sum11/HW%2034.pdf
December 6, 2016

precalculus
well, geez -- just look at the equations. Surely you can notice the +/- signs, axis lengths, etc.
December 6, 2016

Calc
dy/du = sec^2u du/dv = 1 + 1/v^2 dv/dx = 1/x dy/dx = dy/du * du/dv * dv/dx now just crank it out. It's just algebra from here.
December 6, 2016

math
is (2,1) supposed to end up at (-1,4)? If so, why the intermediate point? The final translation is just (x,y) -> (x-3,y+3)
December 6, 2016

Science. Answer Check
false. In a series circuit, one failure causes the whole chain to stop. Parallel means that the current flows through each light "in parallel" with the others -- the lights each get their own current. Better look at a circuit diagram again to refresh your memory.
December 6, 2016

math
Hmmm. The problem says 9 people. How do you justify your answer?
December 6, 2016

Algebra
6200 * 1.08^t = 8750 * 1.06^t (1.08/1.06)^t = 8750/6200 ...
December 6, 2016

elimination
rearrange things to a standard format: x - 2y = -7 8x + 5y = 7 multiply #1 by 8: 8x - 16y = -56 8x + 5y = 7 Now just subtract, and the x's are eliminated...
December 6, 2016

math
Nope. -5(8) = -40 Now subtract 4 Your answer is -4 -5(w-8)
December 6, 2016

math
a=7 d=3 ...
December 6, 2016

Math
If the distance is x, then we have for the area a = 15*4 = 8x
December 6, 2016

Maths
looks like 4.5 for depth, -4.5 for height
December 6, 2016

math
2?rh = 1760 ?r^2h = 12320 square the area equation, and now you have 4?^2 r^2 h^2 = 1760^2 ?r^2 h = 12320 Divide and you have 4?h = 1760^2/12320 ...
December 6, 2016

Math
Your equation just satisfies y varies directly as x. What about the rest? y = ax + b/x + c Now use the points to get 3 equations in a,b,c and solve them.
December 6, 2016

Calc
dy/dx = dy/dt / dx/dt = (3/(2?(3t+1))) / (3t^2-1) at x=1, that is (3/(2*2))/(2) = 3/8
December 6, 2016

Calc
plug in lnx for x and then use the chain rule. f(lnx) = 6(lnx)^3 - 4lnx
December 6, 2016

Calculus
The question is incomplete: smallest n for what? You can easily verify that y^(2) = -y y^(4) = y and the odd orders are plus/minus cosine.
December 6, 2016

Maths
see related questions below
December 6, 2016

Math
If the numerator is even and differs by 3 from the denominator, then the denominator is odd. (Thus, the prime 2 is ruled out.) At that point, saying that their product is even is redundant. odd primes are 3,5,7,11,13,... So, the fraction could be 2/5, 4/7, 14/11, ...
December 6, 2016

G.p.
again? ar^6 = 1/9 ar = 27 divide, and you have r^5 = 1/3^5 r = 1/3 So, a=81
December 6, 2016

maths
2*5 = 10 so its fractions terminate. Try using 3 and see what happens.
December 6, 2016

Meth
fix the typo. Then maybe we can pick an answer.
December 6, 2016

harmonic progression
since the reciprocals are in AP, yes, it is an HP.
December 6, 2016

Algebra
well just plug in t=6 into your somewhat awkward formula.
December 6, 2016

G.p.
is that 2^(2-b) or 2^2 - b?
December 6, 2016

math
x + x+2 = x+4 + 16
December 6, 2016

g.p.
ar^3/ar^11 = 1/r^8 = 1/2^8 so, r = 2 I expect you can take it from there...
December 6, 2016

Calculus
I'd say no. It's just an exponential function. No way any logs can creep in there.
December 6, 2016

Calculus
well, geez - did you try it to check? f = e^(1-x) = e*e^-x f' = e*(-1)e^-x = -f
December 6, 2016

Calculus
Just using the product, quotient, and chain rules, I'd say (u'v + uv')(w) - uvw' ---------------------------       w^2
December 6, 2016

Calculus
y = x + 4/x has a max at x = -2
December 5, 2016

Calc
v = x(6x)*y y = V/(6x^2) A = x*6x + 2xy + 2*6xy = 6x^2 + 14xy = 6x^2 + 14x(V/6x^2) = 6x^2 + 7V/(3x) Now just find where dA/dx = 0.
December 5, 2016

Alegbra
you have basically a = bR^3 R^3 = a/b = 15000/(4pi/3) = 45000/4pi = 11250/pi R = ?(11250/pi)
December 5, 2016

Pre Calculus
just solve for t when h(t) = 0.
December 5, 2016

Math
A better question might be how did you get yours? Did you draw a diagram? since sin(30) = 1/2, the pole is 15/2 meters tall. A 45-45-90 triangle has equal legs, so base of the 2nd wire is 15/2 meters from the pole. I'll leave the rest to you. The Pythagorean Theorem should...
December 5, 2016

Math
That's not what I get. I get (15/2)(?3-1) How did you get your answer (which is not exact, by the way)?
December 5, 2016

Algebra
the maximum profit is at the vertex of the parabola. As you know, the vertex of the parabola ax^2+bx+c is at x = -b/2a y = (b^2-4ac)/4a So, for -10x^2+100x-210 the vertex is at (5,40) Since x=5, the price is 10-x = 5 as well.
December 5, 2016

math
If their numbers are x,y,z, then we know x/y = 2/7 x/z = 2/3 z = y-8 x+y+z = 24
December 5, 2016

Science
Recall that F = ma Now just use your numbers.
December 5, 2016

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