Sunday
January 22, 2017

Posts by Steve

Total # Posts: 47,949

geometry
see http://www.ask-math.com/constructing-triangles.html
January 10, 2017

Math science etc
google is your friend: http://www.ask-math.com/constructing-triangles.html
January 10, 2017

9th grade algebra (recursive formula)
You're welcome. As for the notation, I'm not sure it's "correct" or standard. I just thought of using it since making subscripts is a pain, and the parentheses sometimes get confused with function notation. You will also see An, An+1 (ambiguous: cf. (An)+...
January 10, 2017

9th grade algebra (recursive formula)
a<18> = a<1> + 17*200 = 3362 So, a<1> = -38 similarly, a<21> = a<1> + 20*0.6 = -1.4 now again, just solve for a<1> a<n> = a + (n-1)d
January 10, 2017

math
12c+b
January 9, 2017

Math
hint: a and w are times, and add to 12.
January 9, 2017

Math
You have a slight(!) error: R = 100/?q * q = 100?q Profit = R-2q-1200 = 100?q - 2q - 1200 maximum profit where dP/dq = 0 50/?q - 2 = 0 50 = 2?q q = 625 since P = R-C, dP/dq = 0 when dR/dq = dC/dq The price is 100*25 = 2500
January 9, 2017

Trigonometry
Just recall that C = 2pi * r
January 9, 2017

Math
the sides are equal, so 4a = 3b 4a = a+b+c c = 3a-b, so 4(3a-b) = 3b 12a-4b = 3b 12a = 7b subtracting, 8a = 4b or 4a = 2b But, 4a = 3b, so 2b = 3b b=0 You only supplied two equations for three variables, and 0 is not a likely solution. Check for typos and try again.
January 9, 2017

math
sin(theta) = y/r just to remind you, r^2 = x^2+y^2
January 9, 2017

algebra sir reiny sir steve&bob damon help
By inspection, it should be clear that 3*3^2 = 3^3 There is another solution, at about x = 0.4844 but you won't arrive at it algebraically. You can tell that 3 * 1/4 ? ?(1/2) 0.7500 ? 0.7071
January 9, 2017

MATHS
consult your trig text, or just google its images. sheesh ...
January 9, 2017

Math
since he wants 4 times the recipe, the cups turn to quarts: He will need 1.25 qt
January 9, 2017

Geometry
since BD bisects ABC, mABD = mDBC, and they add up to mABC: 9x = 2(4x+38)
January 9, 2017

MATH
rats: ?3y y^6 z -------------- x
January 9, 2017

MATH
?3 = 3^.5 z^0 = 1 So, we can write this as x^4 y^.5 z 3^.5 ------------------- = (y^6.5 3^.5/x) = ?(3y)y^6/x y^-6 x^5
January 9, 2017

math
3.5mi/22.25min = 0.157 mi/min
January 9, 2017

Math
84.06 m 8406 cm
January 9, 2017

math
48*8 + 54*9 = ?
January 9, 2017

Math
320rs / (5rs/m^2) = 64 m^2
January 9, 2017

math
well, he made 5.18-2.32 = $2.86 on each shirt, so ...
January 9, 2017

Math
the side length of the field is 32000/16 / 4 = 500 meters So, now you can get the area, and thus the cost.
January 9, 2017

Algebra
and did you check your answer? 2*4+2 = 10 4-3*2 = -2 yes, it works.
January 9, 2017

Math
huh? what are x and y?
January 9, 2017

AP Calculus
It depends on how far away B is when sighted. If it is k km north and west, then the distance z between the ships after t hours is z^2 = (k-3t)^2 + (k-8t)^2 = 73t^2-22kt+k^2 dz/dt = (73t - 11k)/?(73t^2-22kt+k^2) dz/dt=0 when t = 11k/73 so, the minimum distance is z = 5k/?73
January 9, 2017

Pre-Calculus
x(160-2x)
January 8, 2017

Math
as always, for y=ax^2+bx+c, the vertex is at x = -b/2a = -3 f(-3) = -(b^2-4ac)/(4a) = -4
January 8, 2017

calculus
You have to be kidding!! The entire area is only growing at 3 in^2/s. You need to learn to do a sanity check on any answer you get, especially in a new situation. Using the given equation and numbers, we have 3 = 2?*10 dr/dt dr/dt = 3/(20?) = 0.0477 in/s Your answer is 60?. ...
January 8, 2017

calculus
well, a = ?r^2 da/dt = 2?r dr/dt ...
January 8, 2017

MATH
well, the height y at time t is y = 33 + 64t - 16t^2 So, solve for t when y=48. The max height is of course, when t = 64/32 = 2. I expect you can determine the range... (restrict it to the domain involved.)
January 8, 2017

Math
There are 2^3-1 = 7 ways to choose at least one stamp.
January 8, 2017

Calculus
y = 1-x z = xy = x(1-x) now just use what you know about parabolas. No calculus needed here. Of course, you can verify that the max occurs at the vertex...
January 8, 2017

calculus
I'll do (b) to show the way. Of course, you probably already know the way... Assuming you meant f(x) = x^3+x-4, f(-2) = -14 f(3) = 26 slope of secant is 40/5 = 8 f' = 3x^2+1 3x^2+1 = 8 3x^2 = 7 ... clearly, ?(7/3) is in [-2,3]
January 8, 2017

Math
4" is 1/3 foot. So, (h - 1/3)^2 + 4^2 = h^2 Damon is correct. 24'2"
January 8, 2017

math
Let the plane be x west, and the jet be y south of St. Louis. Draw a diagram. Then the distance z between the two aircraft is z^2 = x^2+y^2 At the moment in question, 300^2 = 100^2+y^2 y = 100?8 z dz/dt = x dx/dt + y dy/dt 300 dz/dt = 100(-500) + 100?8 (-600) dz/dt ? -732 mi/hr
January 8, 2017

calculus
f(1) = -3 f(2) = 12f(1) = -36 ... Clearly, f(n+1) = -3*12^n
January 8, 2017

math
Draw a diagram. If the man is x feet from the tower, and his shadow is s ft long, then using similar triangles, s/6 = (x+s)/40 s = 3/17 x ds/dt = 3/17 dx/dt ...
January 8, 2017

Math
x^2y = 800 y = 800/x^2 c = 6*x^2 + 2*x^2 + 5*4*xy = 8x^2 + 1600/x dc/dx = 16x - 1600/x^2 = 16(x^3-100)/x^2 dc/dx=0 at x=?100 so, the shed is ?100 x ?100 x 8?100
January 8, 2017

Maths
(6-0)/(3-(-4)) = 6/7
January 8, 2017

math
22 > 6.3, right?
January 8, 2017

Trig
the period is 2?/n so, the solutions are ?/6n + k(2?/n) = ?/6n (12k+1) 5?/6n + k(2?/n) = ?/6n (12k+5) for all integers k.
January 8, 2017

math linear equation
If the larger is x, then x/5 = 8 + (110-x)/9
January 8, 2017

Math(simple interest)
.05(n-1)x = 736 .0375nx = 736 Now just solve for x, then double it.
January 8, 2017

Math
In a cyclic quadrilateral, opposite pairs of interior angles are always supplementary - that is, they always add to 180°. Now, what do you know about opposite angles of a parallelogram?
January 8, 2017

Geometry
well, heck - just draw one. What do you see?
January 8, 2017

Math
(10a+b)= 2(a+b)+2 b = 8a-2 So, what choices are there? a=1 b=6 a>1 : 8a-2 is too big for a single digit b. So, 16/7 = 2 r 2
January 8, 2017

Math
12+x + 345+x + 126+x = 975 Now just solve for x.
January 8, 2017

Math
Let the jugs hold x and y liters. x-1 = y y-2 = x/2 The jugs hold 6 and 5 liters.
January 8, 2017

Math
4" = 1/3 ft so, reviewing your diagram, (h - 1/3)^2 + 4^2 = h^2 h = 145/6 = 24'2"
January 8, 2017

Maths
well, the diagonals are equal, so 2x = 3x+1 I suspect a typo.
January 8, 2017

Algebra2
What is the simplest form of the quotient? ^4?810/^4?2
January 7, 2017

algebra
360 <= 87+96+91+x 86 <= x
January 7, 2017

maths
since the brick dimensions divide the road dimensions evenly, it does not matter which way the bricks are laid (assuming that the brick's edges are parallel with the road's). So, we can just divide the area of the road by the area of a brick: (100m * 20m)/(.25m * .10m...
January 7, 2017

science
so, how many moles of AgNO3 are needed? multiply that by 170 g/mol
January 7, 2017

math
.53x = .47x + 9600
January 7, 2017

Algebra2
there are none - it is negative. However, the real roots of 9/16 are +3/4 and -3/4
January 7, 2017

Algebra2
Find all of the real square roots of -9/16.
January 7, 2017

Maths
When the water has depth y, the surface has radius y/4 v = 1/3 Vy^2h = ?/48 y^3 dv/dt = ?/16 y^2 dy/dt Now use you numbers to find dy/dt
January 7, 2017

History
How did World War II change the population of Arizona?
January 7, 2017

algebra
3j(j^2-17j+70) = 3j(j-10)(j-7)
January 7, 2017

algebra
3(15g^2+4g-3) = 3(3g-1)(5g+3)
January 7, 2017

algebra
which factors of 54 add to 15? Just consider the pairs: 1 54 2 27 3 18 6 9
January 7, 2017

Math
so, where are E and F?
January 6, 2017

algebra word problem
the nice wikipedia article on trajectory gives the equation, including the angle involved.
January 6, 2017

Algebra
how can y be negative? x+y+z = 54000 .08x + .06y + .09z = 4260 .08x = 6*.06y x,y,z = 36000, 8000, 10000 ----------------------------------- So, where did you go wrong? 8x+6(9y)=0 Why do you think the interest sums to zero?
January 6, 2017

algebra
G <= 2
January 6, 2017

Math
come on, man! It's still ?2u^(2/3) du = 2 (3/5) u^(5/3) + C = 6/5 (x^2+2x-3)^(5/3) + C
January 6, 2017

Math
I suspect a typo. You probably meant ?(4x-4)(x^2-2x-3)^(2/3) dx or ?(4x+4)(x^2+2x-3)^(2/3) dx Assuming the first, Let u = x^2-2x-3 du = 2x-2 dx Then you have ? 2u^(2/3) du which is easy. ... right? If there is no typo, you are in deep trouble.
January 6, 2017

Math
1+i = ?2 cis ?/4 (1+i)^101 = (?2)^101 cis (?/4 * 101) = 2^50 ?2 cis (25? + ?/4) = 2^50 ?2 cis 5?/4 = 2^50 (-1-i) or -2^50 (1+i) There appears to be a typo.
January 6, 2017

math
what do you mean 4y=6y-2x+1 ?? Why not just say 2y = 2x-1 If that is the case, then we have 2(2x-1) + x+2x-1 = 28 Use that to find x, and then y. If there's a typo in the problem, fix it and use the same logic.
January 6, 2017

Math
8000 * 0.095 * 120/365
January 6, 2017

math - eh?
by "cover the entire room" do you mean all the walls, floor, and ceiling? Strange use for border.
January 6, 2017

maths
Not sure what you mean. The angle of reflection on the surface is always equal to the angle of incidence. The critical angle for total internal reflection decreases with increasing index of refraction.
January 6, 2017

More calculus
the fence length f = 2r + r? since the area is constant, 1/2 r^2 ? = A ? = 2A/r^2 so, f(r) = 2r + 2A/r Now just find r where df/dr = 0 Use that to get ?
January 6, 2017

Calculus
You have the right idea. But a must be chosen so that lim (ax-10) = 1 as x->3+ f(x) is defined every where except at x=3, so define it to be 1 there, since the limit from both sides is 1. That is, f(3) = B a = 11/3 B = 1
January 6, 2017

Math
true for any number except zero.
January 6, 2017

calculus
the points are (4,1) and (4,-1). -2x + 4yy'+3 = 0 y' = (2x-3)/(4y) So, now you have a point and a slope, and the lines are y-1 = (x-4) y+1 = -(x-4) See http://www.wolframalpha.com/input/?i=plot+-x%5E2%2B2y%5E2%2B3x%3D-2,+y-1%3Dx-4,+y%2B1%3D-(x-4)
January 5, 2017

Algebra2
rearrange things to 3x^2+6x-5 = 0 Now use the quadratic formula.
January 5, 2017

Algebra2
Which expression gives the solution -5+2x^2=-6x?
January 5, 2017

calculus
5y + 5xy' + 2xy + x^2 y' = 0 Now collect terms and solve for y'
January 5, 2017

Calculus
f' = 3h^2 h'
January 5, 2017

Math
.450km / 10km/hr = .045 hr
January 5, 2017

pre calc
do this just like your previous exercise.
January 5, 2017

math
They are separating at a rate equal to the slower truck's speed. Since It took 6 hours to separate by 204 miles, that is 204mi/6hr = 34 mi/hr So, the slower truck is going 34 mi/hr You found the faster truck's speed, but then botched it again since 2*8 ? 146 !!
January 5, 2017

pre calc
If x is at 6%, then the rest y=(3000-x) is at 7%. So, x+y = 3000 .06x + .07y = 194.00
January 5, 2017

Calculus
look up the arc length. The particle must move along a curve. At each small interval, the curve can be considered a straight line, with "arc length" ds^2 = dx^2 + dy^2 Thus, adding up all the tiny hypotenuses gives. s = ?ds = ??(dx^2+dy^2) = ??(1+(y')^2) dx
January 5, 2017

Math Calc
I assume you mean y = 3x^(1/3) + 6x^(4/3) = 3(2x+1) x^(1/3) y' = x^(-2/3) + 8x^(1/3) = (8x+1) x^(-2/3) y" = -2/3 x^(-5/3) + 8/3 x^(-2/3) = 2/3 (4x-1) x^(-5/3) y'=0 at x = -1/8 y"(-1/8) < 0 so y(-1/8) is a maximum y"=0 at x = 1/4 so that is an ...
January 5, 2017

math
double the 1st equation and you have 6x-2y = -6 It is clear to see that since -6 ? -8 the two equations cannot have a single solution. The lines are parallel, and do not intersect.
January 5, 2017

Pre calc
adjust things a bit to get 6x+12y = 57 -12x+12y = 12 subtract and you get 18x = 45 x = 5/2 Now use that to find y. Or, note from the 2nd equation divided by 3 that -x+y=3 y=x+1 Use that in the 1st equation to get 2x+4(x+1) = 19 2x+4x+4 = 19 6x = 15 x = 5/2
January 5, 2017

pre calc
add the two equations to get 0 = x-1 x = 1 now use that to get y.
January 5, 2017

Algebra
f+s = 106 f+3 = 2(s-4) now crank it out.
January 5, 2017

math
PV=kT So, PV/T = k a constant. So, you want T such that 48*1/T = 1*16/305
January 5, 2017

Math
Any line not in the plane of GH is skew to GH. Skew lines necessarily cannot intersect. Not having any details of your diagram, it's hard to say much more. Maybe google can provide you with further relevant examples.
January 5, 2017

math
Try this. I just googled ABCD is aparallelogram in which BCis produced to E such thatCE = BC and got this hit, among others: http://www.meritnation.com/ask-answer/question/abcd-is-a-parallelogram-in-which-bc-is-produced-to-e-such-th/areas-of-parallelograms-and-triangles/...
January 5, 2017

math
F=ma v = at = Ft/m so, t = vm/F = 2.8*10^3*7.9 /6.7*10^5 = 0.033 seconds
January 5, 2017

math
a = v^2/(2s) = 0.614/0.744 = 0.8263 m/s^2 F = ma = 61.0*0.8263 = 50.34N
January 5, 2017

math check my answer ?
as written, f(x) has a range of all real numbers. Pick any value for f(x), and you can easily find an x to produce it. For example, suppose you want f(x) = 11 -3x-1 = 11 -3x = 12 x = -4 So, you must have a typo. Your range of f < -1 could be produced with f(x) = -3x^2 - 1 f...
January 5, 2017

geometry
a = 1/2 r^2 ? Use that once you supply the missing data.
January 5, 2017

Science
google is your friend. Try it.
January 5, 2017

math
g = 12.50 r = 0.75g y = 2.5r = 2.5 * 0.75 * 12.50 = 23.4375 or, using mixed numbers, y = 2 1/2 * 3/4 * 12 1/2 = 23 7/16
January 5, 2017

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