Saturday
August 1, 2015

Posts by steve


Total # Posts: 32,558

Math
42
May 4, 2015

math
you need 2/x < x/22 44 < x^2 so, 6 < x Now, you need x/22 < 0.33 x < 7.32 So, we have x = 7 2/7 < 7/22 < .33 Do the other in like wise.
May 4, 2015

Algebra
what's the problem? Just start working out the values: a1 = -2 a2 = 2(a1)^2 = 2(-2)^2 = 8 a3 = 2(a2)^2 = 2(8)^2 = 128 ... a1 = ln(e^2) = 2 a2 = ln(e^4) = 4 ... b0 = 1 b1 = 2 b2 = 2(2)-1 = 3 b3 = 2(3)-1 = 5 ...
May 4, 2015

math
it will be a line sloping upward, passing through (0,-4)
May 4, 2015

Math
the intersection(s) will be where x^2 + (x+k)^2 - 25 has one solution. That is, where the discriminant is zero. x^2 + x^2 + 2kx + k^2-25 = 0 2x^2 + 2kx + (k^2-25) = 0 The discriminant is (2k)^2 - 4(2)(k^2-25) 4k^2 - 8k^2 + 200 = 0 k^2 = 50 k = ±√50 So, check out ...
May 4, 2015

Math
y = 4(x^2+6x)-5 = 4(x^2+6x+9) - 5 - 4*9 = 4(x+3)^2 - 41 The vertex is at (-3,-41), and the parabola opens upward, y cannot be less than -41. Did you actually try plugging in, say, 7=700 to see whether there was a solution there?
May 4, 2015

Math
correct
May 4, 2015

Algebra
do this just like the ellipse in your earlier post. That is, complete the squares, then review your text about hyperbolas. 36x^2-24x - (y^2-6y) = 41 36(x - 1/3)^2 - (y-3)^2 = 41 + 36/9 - 9 (x-1/3)^2 - (y-3)^2/36 = 1
May 4, 2015

Math
Switching dircetion is just a shorthand way of moving stuff from one side to the other: -4k > -36 add 4k to both sides: 0 > 4k-36 add 36 to both sides: 36 > 4k or, as you saw above, 4k < 36 k < 9 multiplying and dividing by a negative value change the direction...
May 4, 2015

Algebra
for this ellipse, the major axis is vertical. a = 3 b = 2 The vertices are at (-3,1±3) The co-vertices are at (-3±2,1) Looks like it's time to review your ellipses.
May 4, 2015

Algebra
rearrange stuff and complete the squares: 9x^2+54x + 4y^2-8y = -49 9(x^2+6x) + 4(y^2-2y) = -49 9(x^2+6x+9) + 4(y^2-2y+1) = -49 + 9*9 + 4*1 9(x+3)^2 + 4(y-1)^2 = 36 (x+3)^2/4 + (y-1)^2/9 = 1 Now answer the questions.
May 4, 2015

geometry - eh?
what is the "lip"? and where is your punctuation?
May 4, 2015

Math
F = ma
May 4, 2015

Math
so, if you have the answer, why are you posting the question? Check out the Pythagorean Theorem. x^2+y^2 = 1600 x+y+40 = 96.22
May 4, 2015

Math
2r+h = 25 a = πr(r+2h) = πr(r+25-2r) = π(25r-3r^2) da/dr = 0 when r = 25/3 d = 2r = 50/3 h = 25 - 50/3 = 25/3
May 4, 2015

Math
x+y = 37 x^2+y^2 = 765.5 x^2+(37-x)^2 = 765.5 2x^2 - 74x + 603.5 x^2 - 37x + 301.75 = 0 x = (37±9√2)/2 x = 12.1, 24.8 Hmmm. I don't get their answers either, but I'm a lot closer than you. What did you do?
May 4, 2015

geometry
the diameters are in the ratio 5:6 the larger is 12, so the smaller is 10 the smaller cone has height h=3, so the larger cone has height 3*(6/5) = 18/5
May 4, 2015

Math
Laid out on the x-y plane, the track's line can be described by y = 400 - 2/3 x So, if the rectangle has one corner on the line and the opposite corner at (0,0), its area is a = xy = x(400 - 2/3 x) = 400x - 800/3 x^2 This is just a parabola. Find its vertex, and that is ...
May 4, 2015

Calculus
all of them? f is concave down with a max at x = -3
May 4, 2015

math
divide the total amount by the amount needed for each batch, giving the number of batches: 6/(2/3) = 6 * 3/2 = 9
May 4, 2015

geometry
Recall your rotation matrix. (x,y) -> (x',y') where x' = xcosθ - ysinθ y' = xsinθ + ycosθ So, plug in your θ. You can easily check your work by noting that the point will rotate down to the x-axis.
May 4, 2015

math
300*1.04^5
May 4, 2015

alg
no ideas? Review your conic sections and show us whatcha got.
May 4, 2015

math
since the dice are independent events P(odd,odd) = 1/2 * 1/2
May 4, 2015

math
$5200 / $6.50/m = 800m of fence maximum area for a given perimeter is a square, so we have an isosceles right triangle with both legs 400m long.
May 4, 2015

math
#1 clearly the circle is of radius 5. So, since x^2+y^2 = 5^2, (0,5) lies on the circle. the center is the midpoint of AC: (0,0) so, the radius is 13. 0^2+13^2 = 13^2 7^2 + (2√30)^2 = 49+120 = 13^2 so, all vertices lie on the circle.
May 4, 2015

critical points
critical values are where f' = 0 or undefined. f'(x) = 18x^2-18 = 18(x^2-1) So, where is f' = 0?
May 4, 2015

math
a = s^2 da = 2s ds
May 4, 2015

trigonometry
You can expand both binomials, and watch things cancel out, or note that 2sin^2(45+A) = 1-cos(90+2A) 2sin^2(45-A) = 1-cos(90-2A) cos(90+x) = -sinx cos(90-x) = sinx Now just add it up.
May 4, 2015

math
v = (12-2x)(16-2x)x dv/dx = 4(3x^2-28x+48) set dv/dx=0 and solve for x.
May 4, 2015

math
it reverses direction when v changes from + to - v(t) = 3t^2-18t+24 = 3(t^2-6t+8) = 3(t-2)(t-4) So, where does v(t) cross the axis and become negative? Now use that value to find s(t) and a(t)
May 4, 2015

Physics
1/48 + 1/di = 1/110 M = 110/(110-48)
May 3, 2015

calc (please help)
I'm assuming that the angle between the planes is situated on the edge of the cylinder, so that the two planes intersect the cylinder in a circle and an ellipse. So, the ellipse has major axis of length 2r secβ, and the far side of the major axis is a distance 2r tan...
May 3, 2015

Math--ONE QUESTION
well, -14 = -9-5 0 = 8-8 So, what do you think?
May 3, 2015

Calculus max/min
If you walk directly to a point x feet from the bus stop, your walking distance is park: √(600^2+(2000-x)^2) sidewalk: x so, your time taken (distance/speed) is t(x,d) = √(600^2+(2000-x)^2)/(3.5+d) + x/(5.5+d) t(x) = √(600^2+(2000-x)^2)/4.267 + x/7.267 so, ...
May 3, 2015

Math Trigonometric Identities
if you set the left side over a common denominator of sinx, you have 1/sinx - sin^2x/sinx (1-sin^2 x)/sinx If that does not get you started, I don't know what will...
May 3, 2015

Math Trigonometric Identities
that is correct, but it would have been simpler when you got the LS expanded, to see that you had LS = sin^2x - 2sinxcosx + cos^2x = sin^2x + cos^2x -2sinxcosx = 1 - 2sinxcosx
May 3, 2015

Earth Science
the magnification of a telescope is changed by changing what? my answer is the eyepiece
May 3, 2015

Math
well, just plug in 180 = pi
May 3, 2015

Math
Since you are actually performing the action, I'd have to go with Experimental. If asked just to calculate the probability, then it would be theoretical. The actual observations might or might not agree with the calculation. In fact, for any finite number of trials, the ...
May 3, 2015

Math
why all those words? Try using a little actual notation: If tan A = a / b, a>0, b>0, and 0<A<pi/2, then what is cos A? a. a / b B. b / a C. a / √(a^2 + b^2) D. b / √(a^2 + b^2) E. √(a^2 + b^2) / b given tanA = a/b, you know that opposite side is a...
May 3, 2015

Algebra
add up the coins, and add up the values: n+d = 29 5n+10d = 230 Now just solve for n and d.
May 3, 2015

Algebra
done. see related questions below
May 3, 2015

Calculus 2
This looks suspiciously like 1/5 e^x which converges everywhere.
May 3, 2015

Calculus - more data
Is the intersection of the planes tangent to the curved edge of the cylinder? Which axis is the axis of the cylinder? the y-axis? If so, why mention it by name?
May 3, 2015

Calc 1
the base has area 2w^2 The volume is 10, so the height h=5/w^2 So, the cost is 13(2w^2) + 10(wh + 2wh) = 26w^2 + 10w(3h) = 26w^2 + 10w(5/w^2) = 26w^2 + 50/w
May 3, 2015

Math
cost: 4.50*14 revenue after spoilage: 10p we want 10p = 4/3 (4.50*14) p = 8.40
May 3, 2015

Calc 1
oh, please. Surely you can describe the diagram. As a calculus student, you have surely developed some skill with language as well.
May 3, 2015

Calc 1
no diagram. How about a description? I can guarantee that the maximum area is achieved when the fencing is divided equally among lengths and widths.
May 3, 2015

Math
Equal divisions: x receives $500 Proportional: x receives 4500/(4500+4500+1000) * 1500 = $675
May 3, 2015

Math
Just look at the ratios: 1/2 = 0.5 .5/1 = 0.5 .25/.5 = 0.5 ... So, the next number is .125 * .5 = .0625 It might have been easier using fractions. The sequence is thus seen to be 2, 1, 1/2, 1/4, 1/8, ...
May 3, 2015

math
I think the related questions below will provide the method of solution.
May 3, 2015

Math
a/b = 3/4 c/b = 1/2, so b/c = 2/1 and thus a/c = a/b * b/c = 3/4 * 2/1 = 3/2
May 3, 2015

Math. first and last repost. please help
done. see earlier post.
May 3, 2015

maths
8C5 = 8*7*6*5*4 ------------- 1*2*3*4*5 Note that this es equal to 8C3 = (8*7*6)/(1*2*3) because the 4*5 just cancels out. to figure nCm, just start with n, and count down for m factors in the top, and starting with 1, count up for m factors in the bottom. If m > n/2, you ...
May 3, 2015

Math please help.
Only the graph of a function has a slope. This and similar questions are extremely poorly worded. y has a greater rate of change. There is only one slope: that of the function. Its slope is 3. Only the function has a slope. x and y do not have slopes. They just have rates of ...
May 3, 2015

math
I only see one function: f(x) is (-1,0),(0,1),(1,2),(2,3) x and y change at the same rate. When x increases by 1, so does y.
May 3, 2015

trigonometry
120651/47 π = 2567.04 π So, tan(-120651/47 π) = -tan(120651/47 π) = -tan(2567π + 2/47π) = -tan(2/47 π) arctan(-tan(2/47 π)) = -2/47 π You are correct. x = a/√(25-a^2) son tan(arcsin(a/5)) = a/√(25-a^2) Always use the ...
May 3, 2015

mth121
2x+3y = 3 x-2y = 5 has solution (3,-1) This point is also on on the third line, so it is the solution to all three equations.
May 3, 2015

Math 222
a good place to start would be here. Does your text not have any examples of graphing functions? http://www.wolframalpha.com/input/?i=plot+y%3D-x%5E2%2C+y%3D%E2%88%9A%28x-1%29
May 3, 2015

math
y = -(10-x)^2+75 This is just a parabola with vertex at (10,75) So, the max height is 75 meters
May 3, 2015

Maths
The 4 points define a tetrahedron. What do you mean by "boxes" as related to the tetrahedron?
May 3, 2015

trigonometry
done. see earlier post.
May 3, 2015

trigonometry
just pull out your calculator. cos(1.50) = 0.07 Since cos x > 0 in QI and QIV, the other solution is 2π-1.50
May 3, 2015

trig
Trying to get past the copy/paste of strange fonts, I interpret the question as finding the trig functions of the angle whose terminal side is (√15,8) You have x=√15 and y=8, so r = √(15+64) = √79 Now just use the definitions sinθ = y/r cosθ...
May 3, 2015

Math
You don't need it. arctan(-x) = -arctan(x) So, now you want arctan(-tan(7/15π)) = -arctan(tan(7/15π)) = -7/15π
May 3, 2015

Math
tan(-22/15π) -tan(22/15π) -tan(π+7/15π) -tan(7/15π) not a recognizable value. As long as you have to use your calculator anyway, why nut just plug in the original value? You get -9.514 Or is there more to the question than what you posted?
May 3, 2015

math
Try this, which is a better rendering of the given statements: x+23 = 2y y+23 = 3z z+23 = 4x
May 3, 2015

Physics Help Please
just review your formulas. In particular, hi/ho = f/f-do 32mm/17m = 40mm/(40-do)mm 32/17000 = 40/(40-do) do = 21210mm = 21.21m
May 3, 2015

Math
let u = arcsin(x) then du = 1/sqrt(1-x^2) dx now your integrand is just 1/u du Think you can handle that one?
May 3, 2015

physics
since there is no friction, there is no horizontal force. Thus, no acceleration. So, think of Newton's 1st law of motion.
May 3, 2015

Chemistry
Given the very nature of the question, you must have studied some examples. Care to share your ideas on the topic?
May 3, 2015

Trigonometry - PS
However, since inverse trig functions have principal values (because they are multi-valued), you have to be careful. arctan(tan(3π/4)) = arctan(1) = π/4, not 3π/4. So, you need to reduce your fraction to see how many multiples of π you can discard, and then...
May 3, 2015

PHYSICS
That would be zero, of course. Care to rephrase the question?
May 2, 2015

algebra 1
with the exception of calling the vertex the axis of symmetry, yes. The axis always passes through the vertex, but it is not the vertex; the vertex is just a point. The axis has no minimum point; it is a line.
May 2, 2015

algebra 1
axis is the line x=0
May 2, 2015

algebra--1 question
recall that (a+b)^2 = a^2 + 2ab + b^2. So, (2√5+3√7)^2 = (2√5)^2 + 2(2√5)(3√7) + (3√7)^2 = 4*5 + 12√35 + 9*7 = 83 + 12√35
May 2, 2015

calculus
see related questions below
May 2, 2015

Optimization Calculus
so, now go for it. You know that 2x+y = 96, so y = 96-2x the area is xy = 2x(96-2x) = 192x - 4x^2 That's just a parabola; its vertex gives the maximal area.
May 2, 2015

math 1
42
May 2, 2015

Calculus
something wrong with Reiny's solution? See http://www.jiskha.com/display.cgi?id=1430504193
May 2, 2015

Maths(URGENT ANSWER please )
you have sum[1,∞] 2n/n! = 2 sum[1,∞] 1/(n-1)! = 2 sum[0,∞] 1/n! recall that e = 1 + 1/1! + 1/2! + 1/3! so, your sum is 2e
May 2, 2015

Calc 1
y' = 2(x-5) Let x0=1 x1 = 1 - y/y' = 1 - 16/-8 = 3 x2 = 3 - 4/-4 = 4 x3 = 4 - 1/-2 = 6 x4 = 6 - 1/2 = 5.5 and so on for six decimal places.
May 2, 2015

Maths(URGENT ANSWER please :
sum[1,∞] 2n/(n+1)! = 2 sum[1,∞] n/(n+1)! = 2 sum[1,∞] (n+1-1)/(n+1)! can you take it from there?
May 2, 2015

Algebra
recall that a^3-b^3 = (a-b)(a^2+ab+b^2) You have 3^3 - (m+2n)^3 = (3-(m+2n))(3^2 + 3(m+2n) + (m+2n)^2) = (3-m-2n)(9+3m+6n+m^2+4mn+4n^2) I think I like the original way more . . .
May 2, 2015

Calc 1 - ouch! (duh)
I sure flubbed that one. Your later solution was spot on, Reiny.
May 2, 2015

Calc 1
Naturally, the tangent with the largest slope will be the one closest to the origin. So, we want -6cosx = -6sinx/x x = tanx solve that using Newton's method, and you have x = 4.93 so, your line is y = -6cos(4.93)(x-4.93)+6sin(4.93) or y-5.98 = 0.52(x-4.93) See the graphs ...
May 2, 2015

Physics Help Please --- Urgent
since the rays from the building may be considered parallel, we have f = 24. So, to find the distance of the insect's image (from the lens), 1/16 + 1/x = 1/24 Use that to arrive at your final answer.
May 2, 2015

Math
since t=0 when y is a max, we will have y = a cos(kt) the radius is 5, so y = 5cos(kt) the period is 1/25 min, so k/2pi = 1/25 k = 2pi/25, and thus y = 5cos(2pi/25 t)
May 1, 2015

Math- Trigonometric Functions
since the curve starts at the top when t=0, y = a cos(kt) the diameter is 10, so the radius is 5: y = 5 cos(kt) The period is 1/25 min, so 2pi/k = 1/25, making k = 2pi/25 y = 5 cos(2pi/25 t) Not sure what you mean by the blade's distance from the center. I think you meant ...
May 1, 2015

Algebra
b + 2(2b-0.3) = 4.9 That gives the base; now figure the legs.
May 1, 2015

college precalculus
a = 1/3^6 r = 1/3^2 S = a/(1-r) = (1/3^6)/(1-1/9) = (1/3^6)(9/8) = 1/648 a = -100/9 r = -3/10 S = (-100/9)/(1+3/10) = -1000/117
May 1, 2015

Trigonometry
Assuming that the first-named point on the opposite side (P) is the point directly opposite from the point on his own side (Q), then we have, if the observer is point O, m<POQ = 28 m<OQP = 128, so m<OPQ = 24 Now, using the law of sines, if the width is w, we have w/...
May 1, 2015

math ( help please instantly )
just a little synthetic division trying to find a root. Cubics are not always easy to factor by inspection.
May 1, 2015

math ( help please instantly )
m^2-7m+12 = (m-3)(m-4) m^3-2m^2-2m-3 = (m-3)(m^2+m+1) so, LCM = (m-3)(m-4)(m^2+m+1) Now try the others. What do you get?
May 1, 2015

Maths
p = √(32/6)
May 1, 2015

Math
It's always easiest to convert mixed numbers to improper fractions. for adding, find the lowest common denominator for multiplying, just multiply/divide 9 9/10 × 8 8/9 = 99/10 * 80/9 = 88 15 11/15 + 14 5/9 + 7 3/5 = 708/45 + 655/45 + 342/45 = 1705/45 = 341/9 = 37 8/9...
May 1, 2015

Math
3^3 = 27, not 18 4 * 27 -54÷6+25 Just as multiplication/division are done left to right, so are addition and subtraction 108-9 +25 99+25 124 Besides the typo of 26, you did 72-(9+26), not 72-9+26 314-3 [2^5 -(9- 4 ) ^2 +3]^2 314-3 [2^5 - 5^2 +3]^2 314 - 3[32-25+3]^2 314...
April 30, 2015

Math
so, show us your work, and we'll check it.
April 30, 2015

Calculus
the area of a triangle of side s is √3/4 s^2 So, if the triangles have side x and the tent has length y, we have (√3/4)x^2 * y = 2.2 the area of cloth used is a = 2(√3/4)x^2 + 3xy and the cost c is c = 1.4(2(√3/4)x^2 + xy)+xy Now just find dc/dx, after ...
April 30, 2015

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