Wednesday
March 29, 2017

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Posts by STEVE

Total # Posts: 49,706

Mathematics
You know nothing about MN, except that it bisects PQ. It could have a long piece on one side of PQ, and be short on the other.
March 16, 2017

Math Algebra
recall that for y = ax^2+bx+c the axis and vertex always lie on the line x = -b/2a
March 16, 2017

Math
If the AP has 1st term=x difference=y a = x+(p-1)y b = x+(q-1)y c = x+(r-1)y Now just plug and chug ... and chug ... and chug
March 16, 2017

Maths
since the speed (km/hr) is constant, 240/2 = 600/x
March 16, 2017

calculus
The asymptote is y=0 So, revolving the area around the x-axis, and using symmetry, v = 2?[0,?] ?y^2 dx = 2?[0,?] ?(1/(x^4+1))^2 dx = 3?^2/(4?2) It looks hard, and it is complicated, but you can start off by noting that x^4+1 = (x^2+1)^2 - 2x^2 and then factor that as the ...
March 16, 2017

Math
x(x-2p)=3(x-p) x^2-2px = 3x-3p x^2-(2p+3) + 3p = 0 for rational roots, the discriminant must be a perfect square. That is, (2p+3)^2-12p = 4p^2+12p+9-12p = 4p^2+9 must be a perfect square. p=2 is one solution check: x(x-4) = 3(x-2) x^2-7x+6 = 0 (x-1)(x-6) = 0 Not only rational...
March 16, 2017

math
18(2+5) = ?
March 16, 2017

math
Lat a = 2^(x-2) b = 5^(y-2) Then you have 4a-25b = 3 a+b = 2 Hmmm. I suspect a typo, since the results are strange.
March 16, 2017

maths
Draw a radius perpendicular to the chord. Draw a radius to the end of the chord. Now you have a right triangle where x^2+6^2 = 8^2
March 16, 2017

Math
so, divide the annual rate by 12 to get the monthly rate.
March 16, 2017

Math
well, how many months in a year?
March 16, 2017

MAth
so, multiply the daily rate by 365 to get the annual rate.
March 16, 2017

MAth
well, how many days in a year?
March 16, 2017

Maths
B is the midpoint of AC. So, its coordinates are the average of the endpoints. So, if C=(x,y) we have (x+4)/2 = 1 (y+5)/2 = -1 Now just solve for x and y.
March 16, 2017

calculus
Just use the product rule y = ?x lnx y' = lnx/(2?x) + 1/?x y" = 1/(2x^(3/2)) + lnx((-1/4)x^(-3/2)) + (-1/2)x^(-3/2) = -lnx/(4x^(3/2))
March 16, 2017

Maths
P = 2(4+6) A = 4*6
March 16, 2017

algebra
Just add up the acid content: .45x + .90(120-x) = .60(120)
March 16, 2017

Series
clearly, 1,3,5 are an AP 2,4,8 are a GP Now just plug in your formulas for partial sums.
March 16, 2017

algebra
0.95x = 4.75
March 16, 2017

@Elsa
I like your 25 stones.
March 16, 2017

Mathematics
I like Elsa's proof, using Heron's formula. Works for me.
March 16, 2017

Mathematics
The line containing (a,0),(0,b) has equation x/a + y/b = 1 This is called the intercept form of a line. Clearly, (1,1) lies on that line if 1/a + 1/b = 1
March 16, 2017

Math, Series
well, just plug and chug 1/(2y) - 1/(y-x) = 1/(y-z) - 1/(2y) (x+y)/(2xy-2y^2) = (y+z)/(2y^2-2yz) (x+y)/(x-y) = (y+z)/(y-z) (x+y)(y-z) = (y+z)(x-y) xy+y^2-xz-yz = xy+xz-y^2-yz y^2-xz = xz-y^2 y^2 = xz y/x = z/y Thus x,y,z form a geometric progression
March 15, 2017

Math, Series
Do you mean 1/(y-x), 1/(2y), and 1/(y-z) or 1/(y-x), (1/2)y, and (1/y)-z ??
March 15, 2017

Math
Again, the curve is unbounded. If you mean y=(x^3/3)+x^2+x+1/(4x)+4 then here is the graph: http://www.wolframalpha.com/input/?i=(x%5E3%2F3)%2Bx%5E2%2Bx%2B1%2F(4x)%2B4 So, which part of the curve do you want?
March 15, 2017

Calculus
Consider the interior of the bowl as a stack of thin circles. At height h, the circle has area ?r^2 = ?(16(h+1)) So integrate that from 0 to 2
March 15, 2017

Math
If there are no correct answers, then the possible scores are 0,2,4,...,24 If 1, then 5,7,9,...,27 If 2, then 10,12,14,...,30 I think you can see the pattern here. Just make a 12x12 table and fill in the scores. Then cross them off a list of values from 1-60. Those remaining ...
March 15, 2017

math
If she travels x minutes at 70m/min, then the distance is 70x meters. It takes her 2 minutes longer at 60m/min. 70x = 60(x+2) x = 12 So, the distance is 840 meters. Her normal speed takes her 22 minutes, so she leaves at 7:38
March 15, 2017

maths
http://formulas.tutorvista.com/math/orthocenter-formula.html This will give you the orthocenter, if you have the vertices of a triangle. If you set up your right triangle with the right angle at C=(0,0) then let the other two vertices be at A=(a,0) and B=(0,b). Then the right-...
March 15, 2017

math
I think that the ? is just a way of giving us the slope of the ladder. If the firefighter has climbed a distance z to a height h, then we have x^2+y^2 = 29^2 w^2+(y-h)^2 = (29-z)^2 when ?=?/3, x = 29/2 and y=29?3/2 w = (29-z)/2 and h = z?3/2 when z=6, then, w = 23/2 and h=3?3 ...
March 15, 2017

math
they are the same. 10/10, 5000/5000, ...
March 15, 2017

Math
any plane intersection with a sphere is a circle.
March 15, 2017

Algebra
What were you expecting it to "add up" to? -4b * (1-b)/b = -4b(1-b)/b = -4(1-b) = 4b-4
March 15, 2017

algebra, series
The n'th term is ar^(n-1) Sn = a(1-r^n)/(1-r) = 1/4 4a(1-r^n) = 1-r 4a - 4ar^n = 1-r 4a - 4ar^(n-1)*r = 1-r ar^(n-1) = (1-r-4a)/(4r) I can't see how you can solve for r and a. There are many possible solutions. n=1: a=1/4 n=2: a(1+r) = 1/4 a = 1, r = -3/4 a = -1/3, r...
March 15, 2017

Pre-Algebra
12 is 3/7, so 4 is 1/7 Now how much would you pay?
March 15, 2017

sir damon steve damon damon help maths
That is correct. The average value of a function over an interval if ?[a,b] f(t) dt ------------------ b-a
March 15, 2017

Algebra
You know the factors will be (3n-?)(n+?) or (3n+?)(n-?) where the ?? pairs are 1,4 or 2,2 So, just poke around a bit and you will soon find that (3n-4)(n+1) works
March 15, 2017

Math
12/28 as much time, so 28/12 as many workers. 28/12 * 3 = 7
March 15, 2017

Math
distance = speed * time Since their distances are the same, if Jim's speed is x, then x(1/4) = (12)(1/3) x = 16 mi/hr Or, you can consider it like this. Jim takes 3/4 as long, so his speed must be 4/3 as great. 4/3 * 12 = 16
March 15, 2017

english
8 - 10 paragraphs on The Odyssey part 1. PLEASE, I WONT TAKE THIS FOR GRANTED. god bless. i tried but i cant read it very well
March 15, 2017

Math
The curve is unbounded. Also, there appears to be a typo. Why the +x+14x? As with any curve, its length over a given interval [a,b] is s = ?[a,b] ?(1+y'^2) dx
March 15, 2017

Math1
(a) do not know the formula (b) your text formatting sucks. try writing fractions as 3/4 and sequence terms as t7 or t20
March 15, 2017

Math! Help Hurry!
each small block has a volume of (1/4)^3 so the whole lot has a volume of 576 * (1/4)^3 = 9 ft^3
March 15, 2017

Math! Help Hurry!
I thought you said these problems were all different. They look exactly the same to me. Figure the volume of one of the small blocks, and use that to divide into the whole volume. 3 1/4 = 13/4 so the box has a volume of 13/4 * 3 * 1 = 39/4 ft^3 each small block has a volume of...
March 15, 2017

Math and Hurry Please!
2304 * (1/4)^3 = 36 cm^3
March 15, 2017

Math
the new mix of 32+8=40 oz contains 4+8=12 oz of cream 12/40 = 30%
March 15, 2017

Caclulus
#1 I assume that x,y,z are integers, or there is no maximum sum. The minimum sum would be 3?500 ? 23.811 500 = 2^2 5^3 so its factors are 1,2,250 1,4,125 1,5,100 1,10,50 1,20,25 2,2,125 2,5,50 2,10,25 5,5,20 5,10,10 5,25,4 Now pick the largest and smallest sums. #2 v = ?r^2h...
March 15, 2017

Mathematics
Take a look at the distances for each stone, numbering them outward. I'm assuming that we only include the distances actually carrying stones. The actual distance walked would be twice that. # d 1 10 2 20 3 30 ... n 10n So, after collecting n stones on each side, the ...
March 15, 2017

Mathematics
In that case, you must have forgotten your Algebra I. Look at what you know: a+7d = 2(a+2d) 8/2 (2a+7d) = 39 or, massaged a bit, a = 3d 8a+28d = 39
March 15, 2017

intermediate algebra
-2x - 5 < -2 -5 < 2x-2 -3 < 2x -3/2 < x or, x > -3/2 do the others similarly.
March 15, 2017

intermediate algebra
add 3 to each part
March 15, 2017

mat222
your copy/paste skills are severely lacking. What's so hard about this? You have the function pieces and their domains. Just plug in your numbers for the proper part.
March 15, 2017

Algebra
since ?WED ? ?FRI, ?R ? ?E So, solve for x.
March 15, 2017

Mathematics
consider the top of a large cone which has been cut off to leave the frustrum. Draw a side view. Using similar triangles, we know that the top of the bucket is 3/4 as high as the uncut cone. So, the piece that was cut off has an altitude of 15 cm. Subtract the small top of the...
March 15, 2017

maths
This should help a lot. You can construct the vectors u and v for the two orthocenters, and then just get the magnitude of |u-v| http://mathforum.org/library/drmath/view/70440.html
March 15, 2017

maths sir damon reiny or steve help!steve see
surely you know about the chain rule. ?u/?r = ?u/?x ?x/?r + ?u/?y ?y/?r = 2x sin(t) + 2*0 = 2x sin(t) similarly for ?u/?t
March 15, 2017

calculus
f = (6-x)e^-x f' = (x-7)e^-x f" = (8-x)e^-x f"=0 at x=8 f(8) = -2e^-8 so (x,y) = (8,-0.00067) See http://www.wolframalpha.com/input/?i=(6-x)e%5E-x+for+6+%3C%3D+x+%3C%3D+11
March 15, 2017

calculus
(a) [?[0,?] (10 sin(x)-5sin(2x)) dx]/(?-0) = 20/? (b) 10sin(c)-5sin(2c) = 20/? c ? 1.238 or 2.808
March 15, 2017

calculus
well, the weight is 44-0.2t now integrate that over the required distance.
March 15, 2017

maths
AC = AB+BC = a+b and so on. Of course they sum to zero, since that is a closed path.
March 15, 2017

Trig
so, think back to your Algebra II days and finish it up. What you have is correct, but make it look good: x^2-4x + y^2+4y = 0 x^2-4x+4 + y^2+4y+4 = 8 (x-2)^2 + (y+2)^2 = 8 http://www.wolframalpha.com/input/?i=r%3D4cos%CE%B8+-+4sin%CE%B8
March 15, 2017

math
unchanged
March 14, 2017

physics newton
F = ma
March 14, 2017

Math
log2(2?3/5)) = log2(2) + 1/2 log2(3/5) = 1 + 1/2 (log2(3)-log2(5))
March 14, 2017

math
try n=5 1+4*5 < 2^5 -- true So, what about n+1? 1+4(n+1) = 1+4n + 4 Now just show that it is less than 2^(n+1)
March 14, 2017

MATH AGAIN
surely by now you could have figured this out. Since ?ABC is isosceles, ?A = ?B = 30° Therefore, ?BMC is a 30-60-90 right triangle, with ?MCB = 90° So, BC = 12?3 Now drop an altitude from C to AB and use BC to find AB.
March 14, 2017

physical science
work = PE = mgh
March 14, 2017

Math
$80
March 14, 2017

math
Cool. Now where the heck is PR? Get with it, ok?
March 14, 2017

help
force is N = kg-m/s^2 work is J or N-m
March 14, 2017

Math
I hope you are not the one who has already posted this several times, receiving an answer each time. It is (11+9)/2 * 6 * 16/12
March 14, 2017

algebra
multiplying by 10, we have -2x+25 = 22 ...
March 14, 2017

Math
17000*1.03^5
March 14, 2017

algebra 2
x = (6+y)/(2y) 2xy = 6+y y = 6/(2x-1)
March 14, 2017

math
Note that ?MQP = ?MPQ so ?QMP is isosceles. MQ = MP = 18 ?MRQ is 30-60-90, with a hypotenuse of 18 RQ = 9?3
March 14, 2017

math
and PR is where?
March 14, 2017

math
where is M?
March 14, 2017

Math
well, the area is (11+9)/2 * 6 = 60 m^2 How many boxes is that? So, how much cost?
March 14, 2017

Math
you cannot simplify the log of a sum. Since there are no common factors to remove, this is as simple as it gets. Unless you mean log 6(7m+3q) = log 6 + log (7m+3q)
March 14, 2017

Math
Since 100 = 10^2 take the square root of both sides, and you have 10 = 100^(1/2) x = 1/2
March 14, 2017

science
PE is measured in J or N-m PE = mgh
March 14, 2017

algebra
V=kT/P so PV/T = k, a constant. You want T such that 10*74/T = 8*42/84 also, "cm to the 3" is written cm^3
March 14, 2017

algebra
3x+10 >= 4 3x >= -6 ...
March 14, 2017

Algebra 2
(x+2)(x-3) --------------- (x+2) This is equal to (x-3) for every value of x except -2, where it is undefined.
March 14, 2017

Math
recall that (a+b)^2 = a^2+2ab+b^2 so, take 1/2 of the middle coefficient and square it.
March 14, 2017

Math
since the center is at y=5, and it is tangent to the x-axis, the radius is 5. Now, what is the standard equation for a circle?
March 14, 2017

Math
well v increased by 3 m/s in 8 seconds. now, what is the definition of acceleration?
March 14, 2017

Math
figure the lengths of the sides. Then use the law of cosines. c^2 = a^2 + b^2 - 2ab cosC
March 14, 2017

Math
x^2?6x+9+y^2+2y+1 = 25 (x-3)^2 + (y+1)^2 = 5^2 Look familiar?
March 14, 2017

math
Draw a diagram, where a radius bisects the chord. You will see that the arc is subtended by the angle ?, where sin(?/2) = 9/14 The arc length is then s = r?
March 14, 2017

Rox
yes
March 14, 2017

math
top is 14 left is 12 right is 10 bottom is 20 If the figure is a trapezoid, then 144-x^2 = 100-(6-x)^2 x = 20/3 The height h is h^2 = 144-(20/3)^2 h = 8/3 ?14 So, the area is a = (14+20)/2 * 8/3 ?14 = 136/3 ?14
March 14, 2017

Maths
what is the shape of the rope? straight lines? parabola? catenary?
March 14, 2017

Science
1 and 2 are ok. On #3 you confuse frequency and wavelength. (and that's "greater")
March 14, 2017

Physics
conserve momentum: 5v = (8000+5)*0.50
March 14, 2017

Maths
(15 km/hr * 10^5 cm/km) * (49? cm^2) * x hr = (50m * 44m)(100cm/m)^2 * 21cm x = 2 hr
March 14, 2017

algebra
you don't say whether the values given are opposite or adjacent angles. So, you have one of two cases: x+40 = 3x-20 x+40 + 3x-20 = 180 Pick the one you want, solve for x, and then you can answer the questions.
March 14, 2017

math
pair them up 2,2n 4,2n-2 6,2n-4 ... What is the average of each pair? Or, consider their sum: 2+4+...+2n = 2(1+2+...+n) = 2*n(n+1)/2 = n(n+1) So, what is the average of that sum?
March 14, 2017

math
(a + b+10)/2 = (a+b)/2 + 5
March 14, 2017

maths
N arctan(8/5)° E
March 14, 2017

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