Saturday

April 25, 2015

April 25, 2015

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*