# Posts by STEVE

Total # Posts: 49,504

**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*

**mathematics**

remember the point-slope form of a line. The line with gradient m through (h,k) is y-k = m(x-h) Now just plug in your numbers.

*March 14, 2017*

**calculus**

y = -(x-3)(x-4) So, using discs of thickness dx, v = ?[3,4] ?r^2 dx where r=y v = ?[3,4] ?(x^2-7x+12)^2 dx = ?/30 Using shells of thickness dy, and taking advantage of the symmetry, v = 2?[0,1/4] 2?rh dy where r=y and h=?(1/4 - y) v = 2?[0,1/4] 2?y?(1/4 - y) dy = ?/30

*March 14, 2017*

**Math**

well, there are 10 choices for each digit, so ...

*March 14, 2017*

**math**

first step: what is the probability of rolling a 7?

*March 14, 2017*