Saturday
April 25, 2015

Posts by Steve


Total # Posts: 30,777

Calc
you can use partial fractions. (2x+1)/(x+1) = 2 - 1/x+1 so, the integral is 2x - ln(x+1) + C Note that my C is different from Jai's, because it includes the extra 2.
March 14, 2015

Calculus 2
tan^2 (sec^4) = tan^2(1+tan^2)sec^2 = (tan^2 + tan^4)(sec^2) dx Now note that if u = tanx, you have (u^2 + u^4) du See what you can do with the others.
March 14, 2015

Calculus
moving right when s is increasing. That is, when ds/dt > 0 a is increasing when da/dt is positive. That is, 48t-24 > 0 t > 2
March 14, 2015

Calculus
compare the graphs of x^2, x^3, x^4, x^5 Or, just consider the fact that an inflection point occurs when f"=0 and f' does not change sign.
March 14, 2015

Calculus
ever heard of the chain rule? y = 3/u y' = -3/u^2 u' Now just plug in u = sinx+cosx
March 14, 2015

Pre-Calculus
a does not change y-k = a(x-h) has vertex at (h,k) regardless of a.
March 14, 2015

Pre-Calc.
recall the basic definition of the logarithm: b^(logb(x)) = x logb(b^x) = x 5^x = 125 so, just take log5 of both sides: log5(5^x) = log5(125) x = log5(125)
March 14, 2015

Calculus check revised.
y = -1(x^2+1)^(-1/2) y' = 1/2 (x^2+1)^(-3/2) (2x) = x/(x^2+1)^(3/2) you are correct you can always check your answer at wolframalpha.com: http://www.wolframalpha.com/input/?i=derivative+-1%2Fsqrt%28x%5E2%2B1%29
March 14, 2015

Calculus
(1-3x) -> -11 (x-4)^2 -> +0 so, looks like D to me
March 14, 2015

Pre.Calc
you want e^10r = 2 10r = ln2 = 0.693 r = 0.0693 so, a rate of 6.93% will do the trick
March 14, 2015

math
.9982^-60 = 1.1142, so .9982^(x-60) = 1.1142*.9982^x So, just split 3.9657 into two parts, such as 1+2.9657: g(x) = f(x) + 2.9657/1.1142 f(x-60)
March 14, 2015

algebra - incomplete
Since I have no idea what the data were, I cannot tell which is the line of best fit. The $ number is the result you get when plugging some value into the equation. Presumably it is the price of some given quantity of gasoline.
March 14, 2015

Calculus
y' = 2cosx y" = -2sinx y' is max when y" = 0, at 0,π,2π y'(π) = -2 y'(2π) = 2 So, the point (2π,0) has max slope. y = 2(x-2π) Note that x=0 is not in the given domain. b is clearly not 4π See the graphs at http://www...
March 14, 2015

Vectors
3x-6y-9z = -5 x-2y-3z = -2 are clearly parallel planes.
March 14, 2015

Math
http://www.wolframalpha.com/input/?i=plot+2x%5E2+%2B+y+%E2%89%A5+2%2C++x+%E2%89%A4+2%2C++y+%E2%89%A4+1
March 14, 2015

math
T = (x,y) -> (x+4,y-5) so, do that to (-4,5)
March 14, 2015

math, scale drawing
the scale is 1.5cm/2ft = 0.0492 the area scales as .0492^2, so a = (120ft^2)(30.48cm/ft)^2 * .0492^2 = 270 cm^2
March 14, 2015

math
as written, there is no solution. If the product of some numbers is 0, then one of the numbers must be zero. 3.9657 ≠ 0 ln 0.9982 ≠ 0 0.9982^x is never zero Looks like you have written d/dx (3.9657 * 0.9982^x) care to clarify what you really want?
March 14, 2015

Math
tanθ = 395/148
March 14, 2015

maths
28 min = 1680 seconds 1.4 L/s * 1680s = 2352 L = 2352000 cm^3 so, the side of the cube is 133 cm
March 14, 2015

math
If there were x people in all, then men = (3/4)(2/5)x = 3/10 x 3/5 x = 140 + (1 - 3/5 - 3/10)x = 140+x/10 6x = 140+x 5x = 1400 x = 280 check: 3/5 of 280 = 168 3/4 of 280-168 = 84 women = 168-140 = 28 168+84+28 = 280
March 14, 2015

algebra2
see why you should wait for one question to be answered before posting another just like it? ∛(n+8)-6 = -3 ∛(n+8) = 3 n+8 = 3^3 ...
March 14, 2015

algebra
.07x + .15(9) = .13(x+9)
March 14, 2015

math
As you can see from the graphs at http://www.wolframalpha.com/input/?i=plot+y+%3D+sin+x%2C+y+%3D+cos+x the region is roughly triangular. The graphs intersect at x=π/4. Using vertical strips of width dx, you have the area a = ∫[0,π/4] sinx dx + ∫[π/4...
March 14, 2015

Physics
just solve for t in 5t^2 + 100 = 6t^2
March 13, 2015

Calculus
y = ab^x ln y = lna + x lnb 1/y y' = ln b y' = y ln b The instantaneous rate of change is just (ln b) times the current value. That is the very definition of exponential change. The rate of change is proportional to the current value.
March 13, 2015

math
a = 25 - 9t^2 v = 25t - 3t^3 + c v(0) = 4, so c=4 and v = 25t - 3t^3 + 4 now just find v(2)
March 13, 2015

math
I can't figure out what A,B,C have to do with P,Q,R. PR = r-p = 3q-p/2 - p = 3q - 3/2 p RQ = q-r = q-(3q - 1/2 p) = -2q + 1/2 p I don't see that they are collinear. If we let p = 2j q = i then p and q are not collinear, and r=3i-j is not collinear with either p or q. ...
March 13, 2015

Math
You quoted the wrong formula, but used the correct one in your calculations. Those give the future value, given her payments. But the question is, what amount will she receive to deplete the funds at age 80? So, use the formula in reverse to find the PV=0 at age 80. The ...
March 13, 2015

Math (Pre-Calc)
sinC/c = sinB/b = sin58/74 = .01146 sinC = 84*0.1146 = .9626 So, C=74.29 or 105.71 Since A+B+C=180, A = 47.71 or 16.29 Now use a/sinA = b/sinB = 1/.01146 = 87.259 a1/sin47.71 = 87.259 or a2/sin16.29 = 87.259 Don't forget your Algebra I now that you're taking trig...
March 13, 2015

physics(Please respond)
after t seconds, the rock has dropped 1/2 g t^2 Use the value of g for the units you desire.
March 13, 2015

Math - Geometry
Lilly, you are correct. "therom," you are out of order.
March 13, 2015

Math - Geometry
recall that the vertex (maximum height) of at^2+bt+c is at t = -b/2a it hits the ground when h=0, so just solve the quadratic as usual. h(0) = 20 while the function has domain (-∞,+∞), we have not yet achieved time travel, so in the real world, the domain is [0,&#...
March 13, 2015

Math
x/40 = sin 30°
March 13, 2015

Pre-Calculus
I mean, that for each value of c, there is a corresponding value of b. Since B can be either 88.26 or 13.74, b1/sin(88.26) = 54.0265, so b1=54.10 or b2/sin(13.74) = 54.0265, so b2=12.86
March 13, 2015

Pre-Calculus
sinC/c = sinA/a sinC/43 = sin39°/34 = 0.01851 sinC = .7959 so, C = 52.74° or 127.26° Since A+B+C=180, B=88.26° or 13.74° Now use those two values for B to get B, using b/sinB = 1/0.01851 = 54.0265
March 13, 2015

Math - Geometry
surely, giben the vertex form of the parabola, you can read off the vertex? for the zeros, just solve normally the quadratic -2(x+5)^2 + 4 = 0 the y-intercept is where x=0 The parabola opens downward, so there is no minimum The vertex is the maximum, which you have already found.
March 13, 2015

Algebra 2
if 1+i is a root, so is 1-i. So, the factors are (x+1)(x-(1+i))(x-(1-i)) (x+1)((x-1)^2 - i^2) (x+1)(x^2-2x+2) x^3-x^2+2
March 13, 2015

Math
f = 2log5(2y-8) + 3 f = log5(2y-8)^2 + log5 125 f-3 = log5((2y-8)^2) 5^(f-3) = (2y-8)^2 5^((f-3)/2) = 2y-8 2y = 8 + 5^((f-3)/2) y = 4 + 1/2 √(5^(f-3)) so, the inverse function is 4 + 1/2 √(5^(y-3)) logx(x/y) = logx(x) - logx(y) = 1 - logx(y) logy(y/x) = 1 - logy(x...
March 13, 2015

math
the sum of all 39 of the numbers is 39/2 (17+55) so, divide that by 39 to get the average.
March 13, 2015

Math
384/6 = 64 There are three terms, so r = 4 T6 = T4*r^2 = 6*16 = 96 r^3 = 8!/7! = 8 so, r=2 T1 = T5/r^4 = 7!/16 = 315
March 13, 2015

Statistics - Can anybody help me?
after t hours, starting with A mg, the amount remaining is A*.76^t So, to find the original dose, solve A*.76^5 = 74 To get to 25%, you want .76^t = .25
March 13, 2015

Steve - Stat
9.0508% 2250 * 1.0905077^33 = 39258 showing the proper growth rate. Maybe they don't want a percent, but a factor?
March 13, 2015

Math
128/32 = r^2 r=2, so y=32*2=64 Or, evaluate the logs. The sequence is thus 5,log2(y),7 so, log2(y) = 6, and y=64 log a^2b^3 = 2loga + 3logb log a/b = loga - logb 2loga + 3logb = x loga - logb = y 2loga + 3logb = x 2loga - 2logb = 2y 5logb = x-2y logb = (x-2y)/5 solve for loga ...
March 13, 2015

math
% means per 100, so 34.6% = 34.6/100 = 0.346
March 13, 2015

Stats - Please help me
Since it grows by a factor of 2 every 8 days, the population is 2250 * 2^(t/8) In 33 days there will be 39258 The growth factor for each day is 2^(1/8) = 1.0905, for a 9.05% per day growth rate
March 13, 2015

Science
well, it combines CO2 with H2O to make sugars, storing energy. When this happens, heat is absorbed to drive the reaction and store energy in the sugar molecules.
March 13, 2015

Check My Answers Math
#9 eh? t=9, so d = t/3 = 3 km How did you get 12? That's d = t+3 #10 Did you check your answer? Note that y increases by 15 for each x, and starts at 14. So, y = 14+15x #11 Oh, please. Do you just pick a letter and hope? The first two, maybe you were just careless. But ...
March 13, 2015

Algebra
.20x + .50(30-x) = .30(30) x=20 So, 20ml of 20% and 10ml of 50% Note that 30% is 1/3 of the way from 20% to 50%, so 1/3 of the acid is the higher concentration.
March 13, 2015

math
2/5 of the height of the cone is missing. The complete cone would have a slant height of 100. The lateral area of a cone is πrs, so what we have is π(35)(100) - π(14)(40) = 2940π The hemisphere has area 2πr^2 = 2π(35^2) = 2450π The bottom of ...
March 13, 2015

Pre ALGEBRA
Since 1(1-2)-3 = -4, (b) is certainly the only possible choice, since the others don't start with -4. Luckily, the other values also work, so (b) it is.
March 13, 2015

Pre ALGEBRA
add 11 each time. You are correct.
March 13, 2015

Math Check My Work Please
#?: y=2x+1, not 2x-1 #6: The sequence starts with n=1 #7: 3.60 * 18 = ?
March 13, 2015

math
no way to make a square out of 120 blocks If you had 121, the square would be 11x11. (so, you could make a square if you left the center block out)
March 13, 2015

Calculus 1
y = e^(4t sin2t) y' = e^(4t sin2t)(4sin2t + 8tcos2t)
March 13, 2015

Calculus 1
you can factor out the 2(2x+1)^4 (x^4-3)^5 and you have 2(2x+1)^4 (x^4-3)^5 (5(x^4-3) + 12x^3(2x+1)) = 2(2x+1)^4 (x^4-3)^5 (29x^4+12x^3-15)
March 13, 2015

maths
1.4 L/s * 28s = 39.2L = 39200 cm^3 so, the side is ∛39200
March 13, 2015

Math 2
6/x = cos 61°
March 13, 2015

vectors and geometry
correct. You didn't even have to find a+b.
March 13, 2015

INT. Algebra
since WV is constant, 63*9 = W*81
March 13, 2015

Math
#1: (4p-1)-(6p) = (p^2-1)-(4p-1) #2: (y+6)/3y = -3 y = -3/5 (z+1)/(y+6) = -3 Now plug in y and solve for z
March 13, 2015

Mathematics
a + a+d = 4 a+9d = 19 so, find a and d, and then you want a+4d + a+5d
March 13, 2015

Geometry
Pythagorus won't help here. Your ladder must reach up 26 ft. That means that the ladder's length x is given by 26/x = sin 68°
March 13, 2015

math
each equation must be of the form y = mx+b Since they are parallel, they all have the same slope. So, just pick any value for m, and write four equations using the same m, and different values for b. I assume you can graph such lines.
March 13, 2015

Math Triangles
google is your friend. Go to http://www.authorstream.com/Presentation/ramarao.velury-1400926-7similartriangles-rev1/ and skip to page 12. The problem is explained.
March 13, 2015

math
another way. You do not need to find k at all. You know that f = k/g, so fg = k, a constant. That means that 20*4 = f*10
March 12, 2015

factorise fully
rearrange a bit and you have px(p-2q) - qy(p-2q) (px-qy)(p-2q)
March 12, 2015

factorise fully
difference of cubes, so (5x-4y)((5x)^2+(5x)(4y)+(4y)^2) . . .
March 12, 2015

factorise fully
difference of squares, so ((a+b)+x)((a+b)-x) ...
March 12, 2015

Algebra
clearly you want y >= 0 -0.1x^2+12 >= 0
March 12, 2015

factorise fully
(a-2b)^2 - 16x^2 now you have a difference of squares (a-2b+4x)(a-2b-4x)
March 12, 2015

algebra
.08(21000) + .04x = .05(21000+x)
March 12, 2015

Love Math
(28/4).5-6 + 4^2 powers first. so (28/4)*5-6+16 Inside parens, (7)*5-6+16 Now no parens, 7*5-6+16 Now multiply, 35-6+16 Now add/subtract, left-to-right: 29+16 45
March 12, 2015

Algebra u rgent
Odd, how you got #2 ok, but got stuck on #1 x increases by 1, and y increases by 1, so the slope is 1/1 = 1
March 12, 2015

Math
You start by (a) noticing that you misspelled too (b) reviewing your text so you know what the different words mean: sum, product, term, etc. A sum is two terms separated by a + or - sign (a) 56xy + 5 is a sum 5 - 6x is a sum (b) Terms are separated by + and - signs. So, the ...
March 12, 2015

Math
the map circle has radius 2 in. So, that represents a land circle of radius 120 mi. So, what's the area of such a circle?
March 12, 2015

Math
well, you can surely see that you want the part in the first quadrant. Then you an consider the line 3x+2y=6 Obviously, any x or y less than what's on the line will satisfy the inequality. SO, you want the region below the line, in QI: http://www.wolframalpha.com/input/?i=...
March 12, 2015

geometry
The median from A goes to the midpoint of BC at (6,3) Its slope is 3/8, so its equation is y = 3/8 (x+2) The bisector of BC also goes through (6,3) with slope -2/5, so its equation is y-3 = -2/5 (x-6)
March 12, 2015

Math
5-2=3 2+3=5 so, which is greater, 3*3 or 2*5?
March 12, 2015

algebra--1 question
Neither. It is (x+3)(x+4) (x-3)(x-4) = x^2-7x+12 (x-3)(x+4) = x^2+x-12
March 12, 2015

Math
1 large bag is 2/(5/6) = 12/5 small bags So, 5 large bags = 12 small bags
March 12, 2015

Math
draw the road, and label the houses DM=4 MC=1 So, DC = DM+MC = 5 Randy does not matter in this calculation.
March 12, 2015

7th grade geometry
if the prism has dimensions x,y,z, then if each dimension is increased by 2.5, we have 2(xy+xz+yz) = 2((3.5+2.5)(1.5+2.5) + (3.5+2.5)(2+2.5) + (1.5+2.5)(2+2.5)) = 138 ft^2 But, I doubt that is what happens. The question now is, how wide is the paper, and which dimension(s) get...
March 12, 2015

algebra
Just use your distance formula: d^2 = (7+9)^2 + (-6-5)^2
March 12, 2015

periodic functions(math)
(a) see http://www.wolframalpha.com/input/?i=plot+2.5sin%280.523t%29%2B2.9+for+t%3D0+to+24 (b) since sin(kt) has period 2π/k, sin(.523t) has period 2π/.523 = 12.01 That is, the tide cycles every 12 hours. (c) look at the graph and see where d(t) >= 1.3 You want ...
March 12, 2015

Math
6b+3o = 10 3b+5o = 12 12b+6o = 20 9b+15o = 36 21b+21o = 56 b+o = 56/21 = 2.67
March 12, 2015

math
If she saves for n days, she will need n(n+1)/2 >= 7000
March 12, 2015

math
3C1 * 7C3 * 3C1 = 3*35*3
March 12, 2015

physics
.35 ton * 2000lb/ton * 1N/.2248lb = 3113.88 N
March 12, 2015

algebra
I find it helps to have the highest powers first: -2x^2+7x-6 -(2x^2-7x+6) -(2x-3)(x-2)
March 12, 2015

alg. Compounding periods.
#1) how many months in 5 years? #2) 11000(1+.035/365)^90 = 11095.34
March 12, 2015

math
the wheel has a diameter of 30 ft So, its circumference is 30π ft That means that 4 trips around = 4*30π = 120π ft
March 12, 2015

Math
Assuming the three angles are listed in order, you have to remember that consecutive angles are supplementary opposite angles are equal. So, 5x-2 + 8y+2 = 180 5x-2 = 3x+22 So, x = 12, making y=15
March 12, 2015

calc
Been there, done that. 1st related question below: http://www.jiskha.com/display.cgi?id=1425923355 Always check the related questions when you have posted one. Yes, it's not often easy to find the ones you want before.
March 12, 2015

linear equation and one variable
If the pencil costs x, then the pen costs 7x The rest of the posting makes no sense. I think you left out an amount somewhere.
March 12, 2015

Physics
v = √(1.8^2 + (9.8*3)^2) = 29.45 If θ is the angle from the vertical, tanθ = 1.8/(3*9.8) h = 4.9*3^2 = 44.1 m distance from base = 3*1.8 = 5.4 m
March 12, 2015

Math
there are initially 2 yellows out of a total of 10 marbles. chance of yellow on 1st draw: 2/10 with that yellow gone, there is now only 1 yellow out of 9 total, so the chance of a yellow on the 2nd draw is 1/9 So, the total probability is 2/10 * 1/9
March 12, 2015

chemistry
3g C = 1/4 mole 8g O2 = 1/2 mole So, you have CO2
March 12, 2015

factorise fully
Do you mean (p^2)(x) or p^(2x) 2q^y or 2q^2 y The mixture of exponents and multiplication seems unlikely. I will assume you meant p^2 x - 2q^2 y - 2 pqx + pqy = (p-2q)px + (p-2q)qy = (p-2q)(px+py)
March 12, 2015

maths
the area of the tank is 220m^2 So, you want to have a volume of 220*.21 = 46.2 m^3 15 km/hr = 4.167 m/s The area of the pipe is pi*.07^2 = 0.01539m^2 So, the water is flowing in at 4.167*0.01539 = 0.06414 m^3/s 46.2 m^3 / (.06414 m^3/s) = 720 s = 12 min = 0.2 hr
March 12, 2015

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