Friday

September 4, 2015
Total # Posts: 33,290

**calculus**

A. Geez, the trapezoids all have height 1, so the area of each is just the average of the two y-coordinates. B. think of the units on the axes: v * t = distance C. avg speed is totaldistance/totaltime
*August 21, 2015*

**Algebra**

Try again. I think you'll have √5 x (5x)^5/2 (5x)^-3/2 = (5x)
*August 21, 2015*

**Algebra**

see related problems below
*August 21, 2015*

**Algebra**

I'd do it like this. Start by simplifying the numerator into a single fraction. You wouldn't have any trouble combing 2/3 - 7 would you? [-x^3/√(1-x^2) - 2x√(1-x^2)]/x =[(-x^3 - 2x(1-x^2))/√(1-x^2)]/x =(-x^3-2x+2x^3) / x√(1-x^2) = (x^3-2x) / x&#...
*August 21, 2015*

**Algebra**

Take a look at what wolframalpha got: http://www.wolframalpha.com/input/?i=2x+%28x-5%29^-3+-4x^2+%28x-5%29^-4
*August 21, 2015*

**Algebra**

you have t^2/√(t^2+1) - √(t^2+1) ---------------------------- t^2 Combine the terms in the numerator and denominator t^2 - (t^2+1) --------------------- t^2 √(t^2+1) -1/(t^2 √(t^2+1))
*August 21, 2015*

**Trigonometry and Analysis**

Hmmm. How did you get through this step? (.01)(D*2)+(.10)(D)=.84 .01D+.02+.10D=.84
*August 21, 2015*

**Math**

Sounds to me like the stock bottle's date will be in the future. If it's more than two years away, your item must still be labeled to expire in a year. If it's less than two years away, your item's date will be midway between today's date and the stock ...
*August 21, 2015*

**Math**

Assuming some of each coin must be used, I get 1 quarter 2 dimes 2 nickels 45 pennies Otherwise, you could also have just 2 dimes 8 nickels 40 pennies
*August 21, 2015*

**Algebra**

I disagree, if you interpret the expression as 5^-1/2 * (5x)^5/2 * (5x)^-3/2 as he apparently did. I must say though, in Damon's defense, Stephen's wily (wildly?) and inconsistent use of parentheses left things open to misinterpretation. Actually, even that is wrong, ...
*August 21, 2015*

**Algebra**

you are correct.
*August 21, 2015*

**Geometry**

as with the single dimension, the coordinates of the midpoint of a line in the plane is the average of each coordinate: ((-1+5)/2 , (0+2)/2) = (2,1)
*August 21, 2015*

**Geometry**

the midpoint is halfway between the two ends. That means it is the average of the two values: (-2+12)/2 = 5 5 is 7 above -2, and 7 below 12
*August 21, 2015*

**math**

I suspect that the pond is 12 ft longer than it is wide. 12 cm is a ridiculous amount. Assuming that, we have the dimensions of w and w+12. Then we are told that (w+4)(w+12+4) - (w)(w+12) = 160 Solve that and you find w=12. So, the pond is 12x24 16*28 - 12*24 = 160
*August 21, 2015*

**Mathematics**

well, just pick any 2-digit number, uv The 2nd number will be (9-u)(10-v) so, these are also good: 22 78 88 12 ...
*August 21, 2015*

**Mathematics**

Some candidates are 36 64 53 47 ...
*August 21, 2015*

**Mathematics**

first thing I want to know, is: which pairs?
*August 21, 2015*

**Trigonometry**

If you meant sinx + √3 cosx = 1 then try this √3 cosx = 1-sinx 3cos^2x = 1-2sinx+sin^2x 3(1-sin^2x) = 1-2sinx+sin^2x 4sin^2x - 2sinx - 2 = 0 2(2sinx+1)(sinx-1) = 0 sinx = -1/2 or 1 x = 90 or 210 or 330 But 210 does not work in the original equation, so throw it out.
*August 21, 2015*

**mathmetic**

If you mean x^4 = 3.125 then just take the 4th root to get x = 1.339 verify with any calculator. Or did you have something more in mind?
*August 21, 2015*

**Integration help**

let u = 2x-1 Then du = 2 dx the integrand then becomes 1/2 u^(-1/2) du Now it's a cinch.
*August 21, 2015*

**algebra**

n = d^2-7 (n+6)/(d+6) = 2 I suspect a typo. wolframalpha gets 8+2√14 ----------- 1+√14 However, if 1 is added to the denominator, then the fraction is 2/3 http://www.wolframalpha.com/input/?i=solve+n+%3D+d^2-7%2C+%28n%2B6%29%2F%28d%2B6%29+%3D+2
*August 21, 2015*

**alliance**

Can't tell without more information. Pick any speed for the lorry, say 70 km/hr Then the time for the lorry is 4 hr Then the car moves at 98.8 km/hr You can pick any other value for the lorry's speed and find a corresponding speed for the car.
*August 21, 2015*

**Algebra**

Hard to say; the parentheses are unbalanced. It could be t^2/√(t^2+1) - √(t^2+1) ------------------------- t^2 Then you could proceed like this t^2 - (t^2+1) ------------------ t^2 √(t^2+1) . . . -1 --------------- t^2 √(t^2+1)
*August 21, 2015*

**Algebra II**

If the shortest side is x, then we have x + (x+4) + 3x > 39 5x > 35 x > 7 By the way, longer implies only two items. You want to use longest here, since a triangle has three sides. Especially, since without knowing the value of x, maybe x+4 is bigger than 3x. The ...
*August 21, 2015*

**Math**

60/40 = 3/2, so the 60lb child should sit 2/3 as far from the fulcrum.
*August 20, 2015*

**Algebra**

I have a hard time parsing the factors, since you eschew parentheses. Why don't you enter your expression at wolframalpha.com and confirm your work. I tried to get it right at http://www.wolframalpha.com/input/?i=5^%28-1%2F2%29+x+%285x%29^%285%2F2%29+%285x%29^%28-3%2F2%29 ...
*August 20, 2015*

**Algebra**

Looks good to me.
*August 20, 2015*

**Calculus 1**

what's the trouble, forgot your Algebra I already? f(4+h) = 1+2(4+h)-(4+h)^2 = -7-6h-h^2 f(4) = 1+2(4)-4^2 = -7 f(4+h)-f(4) = -6h-h^2 Now divide all that by h and you have -6-h
*August 20, 2015*

**Calculus 1**

g(h) = 3h = 3(x-5) = 3x-15 f(g(h)) = g(h)+9 = 3x-15 + 9 = 3x-6
*August 20, 2015*

**Calculus 1**

just try the steps. (d): -2f(x) reflect about the x-axis stretch the graph vertically by a factor of 2 the order does not matter here (e): f(6x) stretch the graph horizontally by a factor of 6 6x changes 6 times as fast as x, so x only has to be 1/6 as big to get the same ...
*August 20, 2015*

**Math**

x^2+12x+27 try a number. If x=1, does (1+3)(1+9) = 1^2+27 ??
*August 20, 2015*

**Math**

Use the distribute property. (x-1)(x-8) = x(x-8) - 1(x-8) = x^2-8x - x + 8 = x^2-9x+8 At least check you answer using a numeric value for x to see whether it works.
*August 20, 2015*

**Calculus 1**

(a) stretch the graph vertically by a factor of 7 (b) shift 4 units to the right (c) reflect about the x-axis You offered no ideas here or on your next post. If you truly are lost, you will do well to review your text, and google examples and explanations.
*August 20, 2015*

**math**

Ignoring the factor of pi/3, we have 3/4 * 4^2 * 10 = (5/9 h)^2 * h Now just solve for h
*August 20, 2015*

**Physics**

see related questions below
*August 20, 2015*

**maths - garbage**

try using (a+b)/(x-1) for division. Use * for multiplication is you want to use x for a variable. I have no idea what your multi-line formatting is supposed to convey.
*August 20, 2015*

**math**

depends on whether they are hung as landscapes or portraits. Either way, just draw a diagram, and add up the needed heights and spaces!
*August 20, 2015*

**The Chemistry of Life Quiz // Just Answers please**

I can see why you're having trouble - you can't read...
*August 20, 2015*

**The Chemistry of Life Quiz // Just Answers please**

#1. Carbon is an element, not a complex molecule. Lipids and proteins fit the bill #2 Adhesion sticks stuff to each other cohesion makes stuff stay together #3 looks ok
*August 20, 2015*

**math**

since the diameter has been reduced by half over a height of h, it will shrink to zero (the tip of the cone) in another h. So, the cone's height is 2h. Or, using a ratio to find the cone's height H, H/2r = (H-h)/r H = 2(H-h) H = 2h
*August 20, 2015*

**chemistry**

4Al + 3O2 = 2Al2O3 2KClO3 --> 2KCl + 3O2 5.1g Al2O3 = 5.1/101.96 = 0.050 moles Al2O3 So, you need 3/2 * 0.050 = 0.075 moles of O2. Thus, you need 2/3 * 0.075 = 0.050 moles KClO3 to produce that needed O2.
*August 20, 2015*

**algebra**

regardless of the typo, it's -1/2 I find it hard to understand the difficulty in finding the "m" in y = mx+b to get the slope.
*August 20, 2015*

**algebra**

Ok. I'll show some maybe-not-so-divine mercy and help you out. (x+y+z)/3 = 6 (x+y+z+t+u+v+w)/7 = 9 x+y+z = 18 x+y+z+t+u+v+w = 63 18+t+u+v+w = 63 t+u+v+w = 45 (t+u+v+w)/4 = 45/4
*August 20, 2015*

**Test Post?**

why indeed? It depends on what "+" is. in binary, 1+1 = 10 in logic, 1+1 = 1 if + joins strings, then 1+1 = 11 I suspect a test posting.
*August 20, 2015*

**modular arithmetic**

10
*August 20, 2015*

**Math**

m/w = 6/4 (m-5)/(w-5) = 5/3 (m,w) = (30,20) m-w = 10
*August 20, 2015*

**Physics**

Draw a diagram. You want the hypotenuse of a 3-4-5 right triangle.
*August 20, 2015*

**The polythecnic Ibadan**

since PV is constant under these conditions, (300)(900) = 600V
*August 20, 2015*

**Algebra**

-4-4-4+9 = -3 so, they wound up with a loss of 3 yards or, 3(-4)+9 = -3 for the sub, you want -125 + 3(-50) = -125-150 = -275 Your setup yields -125(-150) = 18750 ft in the air! 220-4(35) or, 220+4(-35) Your final answer is correct, though, which shows that you not only don&#...
*August 20, 2015*

**algebra2**

first, use the point-slope form: y+2 = 6(x+1) Now move stuff around till you have y = mx+b y+2 = 6(x+1) y+2 = 6x+6 y = 6x+4
*August 20, 2015*

**Math**

use your calculator or, just type that into google's search box
*August 20, 2015*

**algebra2**

you want y all by itself on the left: y = mx+b So, start moving stuff around. x-y = -7 x = -7+y x+7 = y or y = x+7
*August 20, 2015*

**Physics**

first, dodos do not fly. second, dodos are extinct. However, since time=distance/speed, if the bird flies back x km, then (4.9+x)/24.8 = (4.9-x)/6.2 x = 2.94 So, the bird flew 7.84 km
*August 20, 2015*

**Math - eh?**

you want to try that again in English?
*August 19, 2015*

**Math**

32% = 0.32 "of" means multiply: half of 6 is 1/2 * 6 = 3 So, you want 0.32 * 250
*August 19, 2015*

**Math**

3 of the fruits are not apple or peach. So, p=3/12
*August 19, 2015*

**Calculus**

while x < 2, -2 < 0, so, |x-2| = -(x-2) So, you have the limit of (3x(-(x-2)))/(x-2) = -3x You can cancel the x-2 since x is not actually 2. The limit is thus -6 The limit from the right, of course would be +6 See the graph at http://www.wolframalpha.com/input/?i=%283x+|...
*August 19, 2015*

**Solid Mensuration**

I suspect it will be 4x8, but let's see what the calculations show. If triangle ABC has vertices at (0,0),(16,0) and (h,8) then the sloping sides are lines with the equations y = 8/h x y = 8(x-16)/(h-16) Now, suppose the inscribed rectangle has height k. The the line y=k ...
*August 19, 2015*

**Trig**

2sinθ+1 = 0 2sinθ = -1 sinθ = -1/2 sin π/6 = 1/2, so using that as a reference angle in QIII and QIV, we get the solutions π + π/6 and 2π - π/6
*August 19, 2015*

**Geometry**

well, UV bisects STU, so 1/4 x + 8 = x+2 6 = 3/4 x x = 8 Now you know x, so you can figure STV=VTU, and STU = STV+VTU I get 20 How did you get 25?
*August 19, 2015*

**Math**

I think you mean (8 * 2^10)^2 * 3^7 (2^13)^2 * 3^7 2^26 * 3^7 67108864 * 2187 146767085568 Clearly I have misinterpreted your unusual syntax.
*August 19, 2015*

**Math**

36*10/24 = 15
*August 19, 2015*

**Math**

5n+10(8-n) = 65 -5n = -15 n = 3 she spent 3 nickels and 5 dimes. So, starting with N nickels and D dimes, 5N+10(20-N) = 140 -5N = -60 N=12 So, she is left with 9 nickels.
*August 19, 2015*

**Geometry**

since R is the midpoint of ST, SR is 1/2 ST, so 2(3x+3) = 30 3x+3 = 15 3x = 12 x = 4 not sure what you mean by x being 9 to equal 15
*August 19, 2015*

**Calculus 1**

the roots indicate that f(x) = a(x+1)(x)(x-2) Since f(1) = a(2)(1)(-1) = -2a = 8, a = -4
*August 19, 2015*

**algebra**

Or, using y(x) = -9/2 x + 3, y(-2) = 9+3 = 12 You want y(-2) = 5, so you have to subtract 7 from the given value, leaving you with y = -9/2 x - 4
*August 19, 2015*

**ethics**

google turns up http://www.studydroid.com/printerFriendlyViewPack.php?packId=373583 It would have worked for you, too.
*August 19, 2015*

**algebra**

type in your expression at wolframalpha.com It will show the graph. Play around there a while.
*August 19, 2015*

**Math-unit rate**

(1 1/2 mi)/(3/5 hr) = (3/2 mi)/(3/5 hr) = 5/2 mi/hr or, 2 1/2 mi/hr if you like mixed numbers
*August 19, 2015*

**algebra**

It always helps if you show your work. If it is wrong we can spot the error. Assuming the usual sloppiness with parentheses, I will assume you meant (44/9)x - 7/4 + (12/7)x + 1 = (44/9 - 12/7)x - 7/4 + 1 = (200/63)x - 3/4 I might have thought you were using x for ...
*August 19, 2015*

**algebra**

y = mx+b where m is the slope b is the intercept just plug in your values.
*August 19, 2015*

**pre algebra**

-|-16| = -16 since |-16| = 16
*August 19, 2015*

**MATH**

12/60 = 0.2
*August 19, 2015*

**algebra**

y=0 is the same as y = 0x+0 so, its slope is zero. 9x+2y = -8 is the same as 2y = -9x - 8 y = -9/2 x - 4 so its slope is -9/2 Try the others. Rearrange stuff to get y all alone on the left side, as I did above.
*August 19, 2015*

**algebar**

two lines are perpendicular if their slopes are negative reciprocals. That is, their product is -1. y = -x-3 has slope -1. So, its reciprocal has slope -1/-1 = 1
*August 19, 2015*

**math**

wow - at least you used "whom" correctly. If you are trying to find roots of cubics, you must have already studied quadratics and factoring, maybe even synthetic division. Can you find the roots of quadratics? Like x^2-x-2 = 0 If not, you can forget 3rd-degree ...
*August 19, 2015*

**Math**

eschewing all the words, we have 8^2 + 9(12/3 * 2) - 7 64 + 9(4*2) - 7 64 + 9*8 - 7 64 + 72 - 7 129 Now, since you were unclear about just what was being divided, you might have meant 8^2 + 9(12/(3*2)) - 7 64 + 9(12/6) - 7 64 + 9(2) - 7 64 + 18 - 7 75 Parentheses are your ...
*August 19, 2015*

**Math**

so, the ratio is 7:26
*August 19, 2015*

**Math**

well, how many total cubes are there? How many red?
*August 19, 2015*

**math**

there are only 2 numbers larger than 6, so p = 2/8
*August 19, 2015*

**math**

It's not at all obvious that you tried. I did the first one for you. Take a look at that one, and use the same method for the others. The chances are good that there will be at least one root that is easy to find. At least show what ideas you tried, which failed.
*August 19, 2015*

**math**

cubics are tough. Look for low-hanging fruit. Clearly there are no positive roots, since all the coefficients are positive. f(-1) = -1+6-12+8 = 1 f(-2) = -8+24-24+8 = 0 So, x^3+6x^2+12x+8 = (x+2)(x^2+4x+4) Now it's easy
*August 19, 2015*

**Algebra II**

looks good to me
*August 19, 2015*

**Math**

the ratio of height/shadow is the same for both objects. So, 51/48 = h/16
*August 19, 2015*

**Math**

the two angles must add to 180 degrees. So, to get <2, subtract <1 from 180 Complementary angles add to 90, so the complement of 2 is 90 - <2 Or to do it all in one step, if the measure of <1 is x, then the complement of <2 is 90-(180-x) = x-90
*August 19, 2015*

**math**

you have a problem with actual math symbols? 3/5 = 27/45 7/9 = 35/45 so, which do you think took less time?
*August 19, 2015*

**math, science, everything else for 10th grader**

secx = 17/8, so cosx = 8/17 sinx = 15/17 tanx = 15/8 Now just plug in your values: (3-4sin^2x)/(4cos^2x-3) = (3-4(15/17)^2)/(4(8/17)^2-3) = 33/611 (3-tan^2x)/(1-3tan^2x) = (3-(15/8)^2)/(1-3(15/8)^2) = 33/611
*August 19, 2015*

**Math**

Looking good. Nice work.
*August 19, 2015*

**Geometry**

the diameter is the distance between the two points: √((5-2)^2+(5-1)^2 = 5 Now it's a cinch, right?
*August 19, 2015*

**Algebra**

yes. commutative property of multiplication There is also a commutative property of addition, which could be written as (2 + p)(r + 9) = (p + 2)(9 + r)
*August 19, 2015*

**Algebra II**

transitive relates 3 values: a=b and b=c ==> a=c Clearly this is just a case of substituting z for y, since y=z.
*August 19, 2015*

**maths**

since r is constant, (1-t)/(2-5t) = (t+1)/(1-t) Solve that for t, and you will find that matching sequences are, with r=2 and r=1/3, 1/3, 2/3, 4/3, ... 9/2, 3/2, 1/2, ...
*August 19, 2015*

**physics**

Vy = 300-9.8t Vx = 519.6 So, at t=2, Vy = 280.4 Vx = 519.6 |v| = √(280.4^2+519.6^2) = 590.4 θ = arctan(280.4/519.6) = 28.4°
*August 19, 2015*

**Physics**

1.07 E = <1.07,0> .533 S = <0,-0.533> 4.62 @ W50.1°N = <-2.963,3.644> add them all up and you have a final displacement of <-1.893,3.111> = 3.642 @ N31.3°W now you can figure the velocity
*August 19, 2015*

**Math**

you are correct.
*August 19, 2015*

**Math**

well, 1364 = 14*93 + 62 17765 = 27*646 + 323
*August 19, 2015*

**math**

y = 3(x-2)^2+3 y' = 6(x-2) y" = 6 critical point is at x=2 minimum because y" > 0 there. http://www.wolframalpha.com/input/?i=3%28x-2%29^2%2B3 But then, you knew all that from Algebra I, right? Vertex of a parabola and all that.
*August 19, 2015*

**math**

the domain of rational functions is all reals except where the denominator is zero. x^2+8x+15 = (x+3)(x+5) So, I guess you can work it from there, right?
*August 19, 2015*

**math**

If you mean 10sin((x/4)-4π)-5 then that is 10sin((x-16π)/4)-5 period = 2π/(1/4) = 8π shift = 16π
*August 19, 2015*

**Algebra**

both right. good work. Of course, your nearest calculator could have confirmed your results...
*August 19, 2015*