Wednesday

October 22, 2014

October 22, 2014

Total # Posts: 25,982

**math**

recall that ∫ du/(a^2+u^2) = 1/a arctan(u/a) now note that x^2+4x+13 = (x+2)^2 + 3^2 Nuff said? I get π/12
*August 23, 2014*

**equations**

1.25x = 3.5 - 0.4x 1.65x = 3.5 ok?
*August 23, 2014*

**maths**

Draw a diagram. If you draw a horizontal line from the top of the 6m pole to where in intersects the 11m pole, then you have a right triangle with legs 5 and 12. You should be able to recognize the ubiquitous 5-12-13 triangle. The tops are 13m apart.
*August 23, 2014*

**calc**

As usual, just use the chain rule: Let u = e^3x, and you have d/dx arctan(u) = 1/(1+u^2) * du/dx = 1/(1+u^2) (3e^3x) = 3e^3x/(1+e^6x)
*August 22, 2014*

**Algebra**

correct answer, but when typing online where there is no vertical fraction formatting, it's better to use 8/(x-m) That way it will not be confused with 8/x - m Normally, when evaluating expressions, multiplication is done before subtraction, unless parentheses indicate ...
*August 22, 2014*

**Algebra**

actually, you already have the difference. What you have done is find the quotient and then simplified it.
*August 22, 2014*

**college algebra**

If there are x kg of Brazilian coffee, then the rest (420-x) is Turkish. So, 10x + 13(420-x) = 12*420 x = 140 Note that 140 is 1/3 of 420, meaning that it drags the price down 1/3 of the way from 13 to 10, or $12.
*August 22, 2014*

**math**

you want to convert 100 pages to minutes. Your conversion factor is 20 minutes = n pg 20min/n pg = 1 Now multiply vy that to cancel the unwanted units: 100 pg * 20min/n pg = 2000/n min
*August 22, 2014*

**math**

Better take a look at http://mathmistakes.info/facts/CalculusFacts/learn/doi/doif.html So, what you have is √(1+(2x)^2)(2) = 2√(1+4x^2) at x=√2, that is 2√(1+8) = 2*3 = 6
*August 22, 2014*

**Algebra**

y = 3/(2x) so we want the minimum of 10x + 3/5 * 3/(2x) = 10x + 9/(10x) take the derivative and you have 10 - 9/(10x^2) set that to zero and you get 100x^2 - 9 = 0 (10x-3)(10x+3) = 0 x = ±3/10 So, at x = 3/10, y = 5 and 10x+3y/5 = 3+3 = 6
*August 22, 2014*

**math**

g'(1/2) = 4(1/2)(2-1/4) = 2(7/4) = 7/2 So, g is increasing at x = 1/2 Have you looked at the graph? http://www.wolframalpha.com/input/?i=4x^2+-+3x^4 Clearly only (b) is true
*August 22, 2014*

**math**

g' = 8x-12x^3 = 4x(2-x^2) g" = 8-36x^2 g' changes sign in x<1, so not (a) g'=0 and g"≠0 at x=0, so (b) g" changes sign, so not (c) so, (b) is the only true statement
*August 22, 2014*

**math**

you are correct
*August 22, 2014*

**math**

exactly 75%=3/4 implies the number is a multiple of 4, so the candidates are 40,44,48 exactly 1/6 implies it is also a multiple of 6, so 48 students
*August 22, 2014*

**Math**

9 clearly cannot be on a corner, so we have X9X X7X XXX Now, the only choices along the top are 1,2, so we have 192 X7X XXX 8 cannot be on a corner, because then we'd need 2,2 or 1,3 twice. It must be on one of the sides: 192 87X 3XX Now, 3+9=12 and 2+10=12 We still need ...
*August 22, 2014*

**Algebra**

(x-1)/(x-3) = √(17-x) (x-1)^2/(x-3)^2 = (17-x) x^2-2x+1 = -x^3+23x^2-111x+153 x^3-22x^2+109x-152 = 0 No rational roots here, so you will need to resort to a graphical or numeric method to get the desired accuracy. http://www.wolframalpha.com/input/?i=x^3-22x^2%2B109x-152
*August 22, 2014*

**math**

If the first basket has x and the second has y, x = 4/3 y x = y+3 x = 4/3 (x-3) x = 4/3 x - 4 1/3 x = 4 x = 12
*August 22, 2014*

**algebra**

P e^(.0855*(8+125/365)) = 225500 P = 110502.63
*August 22, 2014*

**algebra**

Assuming you want to factor it, grouping is probably the easiest way: 4ax+8a-10x-20 2(2ax+4a -5x-10) 2(2a(x+2)-5(x+2)) 2(2a-5)(x+2)
*August 21, 2014*

**Algebra**

sure. You can have any positive number of rows or columns.
*August 21, 2014*

**Math**

2 2/5 % = 12/5 % = (12/5)/100 = 12/500 = 3/125
*August 21, 2014*

**math**

(3/4 mi)/(9/8 mi/hr) = 3/4 * 8/9 hr = 24/36 hr = 2/3 * 60 min = 40 min
*August 21, 2014*

**Geomentry**

assuming RST are collinear, RT = RS+ST, so 8y+4 + 2x-2 = 64 2x = 64-8y-4+2 2x = 62-8y x = 31-4y Assuming the y is a typo, 8x+4 + 2x-2 = 64 10x = 62 x = 6.2
*August 21, 2014*

**math**

6/4
*August 21, 2014*

**Math**

Get the w stuff all alone G-4x-4/3 = 1/2 w Now multiply by 2 and you have 2(G-4x-4/3) = w
*August 21, 2014*

**math**

Because you have added 0 hudredths. Adding 0 of anything leaves the result unchanged. 10.6 = 10.60 = 10.6000000000000000000
*August 21, 2014*

**Math**

In that case, there is no way to tell. You must know how many rows, and how many seats in each row. And who cares which day it was?
*August 21, 2014*

**math**

Looks like $1.25 for the first 1.5 miles, and $.45 more for every 1/2 mile beyond that. So, since 2 5/8 = 1 1/2 + 1/2 + 1/2 + 1/8, the charge is $1.25 + 0.45 + 0.45 + 0.45 = $2.60 Now work on the other parts.
*August 21, 2014*

**math**

we know that (2x+12)^2 + x^2 = (2x+18)^2 expand all that and solve the quadratic, and you get x = 30 check: 30^2 + 72^2 = 78^2 That's just 6 times a 5-12-13 triangle
*August 21, 2014*

**math**

x^2-2x+1 - 4 x^2-2x-3
*August 21, 2014*

**Algebra**

correct!
*August 21, 2014*

**physics**

In terms of x & y, 186@E23°N = 171.21,72.68 327@N43°W = -223.01,239.15 Add them up: -51.80,311.83 That is 361.10 at 99.43° or, as a heading, 361.10@N9.43°W
*August 21, 2014*

**MAth**

Nope. Treat || like parentheses for grouping. Then, when everything inside has been evaluated, apply the absolute value: |13|-7x|-2+8|/6 13-7x|6|/6 13-7x6/6 13-7x1 6
*August 21, 2014*

**physics**

The swimmer's direction should be the hypotenuse of the diagram. Then, the current makes the resultant velocity perpendicular to the bank. The angle is thus upstream at an angle of arccos(1.5/3.76)=66.5° relative to the bank. That makes the speed relative to the shore...
*August 21, 2014*

**math**

For m minutes, A: 25.00+0.10(m-30) B: 20.00+0.12(m-30) So, just solve for m when A=B The language used for this problem is rather odd. Not at all what I'd expect from a school text.
*August 21, 2014*

**math**

since 7y=28x, y = 4x 6x+4(4x) = 40 22x = 40 x = 20/11 x^2 = 400/121
*August 20, 2014*

**Math**

just subtract his initial loss from the subsequent profit: 1580-415 = ?
*August 20, 2014*

**Algebra**

sounds good. You might also note that for an exponential function y = f(x), log(y) is linear.
*August 20, 2014*

**Geometry - eh?**

Hard to say. Just noting the degrees separating the hands tells nothing about the actual time. And, since you don't specify which hand is at 70 degrees, that's no help either. Want to rethink the question?
*August 20, 2014*

**Math**

If you mean (225-256)^2 that's just (-31)^2 = 961 If you mean 225-256^2 that's -65311
*August 20, 2014*

**Algebra**

easy. Note that y^3 / y^10 = y^3 / y^3*y^7 The y^3 factors cancel, and you are left with 1/y^7 Or, use the rule that in division, you subtract exponents, so y^3/y^10 = y^(3-10) = y^-7 = 1/y^7
*August 20, 2014*

**college algebra**

It's already factored! Want to rephrase the question?
*August 20, 2014*

**maths**

what do meters have to do with anything? If the equation is 3 cos x = 25x, that's one thing. If not, fix the equation, but leave the m^2 out of it.
*August 20, 2014*

**MATHH**

The slope of the line joining those two points is (4+7)/(3-2) = 11 But, you are supposed to find the slope of any perpendicular line. That is -1/11.
*August 20, 2014*

**math**

1. reflect through the x-axis 2. reflect through (0,0) 3. a translation, but you are missing a sign.
*August 20, 2014*

**math**

You have a/b = 4/5 a/c = 6/11 You want b/c = (b/a)/(c/a) = b/a * a/c = 5/4 * 6/11 = 30/44 = 15/22
*August 20, 2014*

**math**

B gains 100 yards every minute. So, after 10 minutes, B has lapped A once. C gains 100 yards on B every minute, so after 10 minutes C has lapped B. Thus, after 10 minutes, A has gone 7 laps, B has gone 8 laps, C has gone 9 laps, and all are even again.
*August 20, 2014*

**Math**

-8 is less than any of them. All the negatives come first. The || values are all positive. So, (C) is correct
*August 20, 2014*

**Geometry**

In an equilateral triangle, the median is the same as the altitude. If the side is s, the median is √3/2 s. Each median extends from a vertex to the midpoint of the opposite side.
*August 20, 2014*

**algebra**

I get this far √a-√b = √18-√6 and have trouble figuring out what "nd multiply root5" means. How about filling in the rest using math symbols?
*August 20, 2014*

**math**

None are. They are, however, supplementary.
*August 20, 2014*

**Maths**

that would be 645.7/8 Drag out your calculator of choice to evaluate that quotient.
*August 20, 2014*

**Algebra**

D = 1.2√H Now just plug in H=12000
*August 20, 2014*

**Trigonometry**

Looks like time to review the basic trig functions. It always helps to draw a diagram. (1) 12.75/x = sin 48° (2) sin x = 3.1/9.4 (3) 16/x = tan 9°
*August 20, 2014*

**Math**

mi/hr * 1hr/60min * 1min/60sec * 5280ft/mi Note that the units all cancel out, leaving ft/sec Actually all of the factors will work, if you divide by 1mi/5280ft. However, since one usually wants to multiply, I'd say (d) would not be used.
*August 19, 2014*

**math**

y = x^3 All of the odd powers look basically the same as x^3. Play around at wolframalpha.com to see.
*August 19, 2014*

**math**

hmmm. Is it 4? Is 4^2 = 36? Does 4 have 3 as a factor? Better read what I wrote, and this time pay attention.
*August 19, 2014*

**math**

I'd make that 6, since 81 = 3^4. p^2 must have some powers of 3 in it, else GCF(p^2,81) = 1. GCF(36,81) = 9 9 would be better, but we needed an even integer.
*August 19, 2014*

**English**

none that I know of, but there are plenty which will correct your spelling of "grammar."
*August 19, 2014*

**Physical Science**

The airspeed is the speed relative to still air. In the absence of other factors, the airspeed is the same as the ground speed. If the wind is blowing, the wind velocity must be added to the bird's velocity in still air (airspeed), to get the velocity relative to the ...
*August 19, 2014*

**physics**

total distance: 108+42 = 150km total time: 6hr avg speed: 150km/6hr = 25 km/hr
*August 19, 2014*

**math STEVE**

you could have appended the correction to the original post. Anyway, 783-500 = 283 Apparently he makes no commission on the first $100. Assuming that, he makes 0% on 100 = 0.00 5% on 400 = 20.00 10% on 283 = 28.30 Total = 48.30 If I made a mistake on the first $100, make the ...
*August 19, 2014*

**math**

read it. The last sentence makes no sense.
*August 19, 2014*

**math**

#2. Assuming all the rest tried out for pitcher, then we have 1/8 + 1/3 + 1/4 = 17/24 So, the remaining 7/24 must have tried out for pitcher. #1 is garbled.
*August 19, 2014*

**math**

I did it this way 20*34 = 680 (total of all 20 numbers) 4*45 = 180 (total of the 4 numbers with mean 45) 680-180 = 500 (missing total, due to the other 16 numbers) 500/16 = 31.25 Your final answer is so huge it should have been a tipoff. The mean of the other 16 should have ...
*August 19, 2014*

**math**

6(y-7)-6 = 6y-48
*August 19, 2014*

**math**

no. my typo of 41 is a boo-boo, but your answer is correct. You correctly answered the question that was asked.
*August 19, 2014*

**math**

looks good. Does it work? Jack is 45 5 years ago, he was 41 40 = 46-6 OK
*August 19, 2014*

**Science - go with DrBob**

Dang. I forgot about the molecules, not atoms.
*August 19, 2014*

**Science**

you know Avogadro's Number, AN=6.023*10^23 Also, 1 mole occupies 22.4L (22400 cm^3) at STP. (a) (50dm^3)/(22400cm^3) * AN = ? (b) (10cm^3)/(22400cm^3) * AN * 19 = ? (because F has 19 nucleons/atom)
*August 19, 2014*

**Math**

(a) note that as x increases by 4, y increases by 2. Then, as x increases by 2, y increases by 1. (b) and (c) work the same way. Starting at the first point, note that the changes in y and x have the same ratio. That is, the slope remains constant, and since the middle point ...
*August 19, 2014*

**Science**

well, they would be nice to know, but the crew of the carrier would presumably include a doctor and weather guy. I'd pick D over A. Modern ships have lots of computers on board, and a knowledge of physics would come in handy in handling the ship.
*August 19, 2014*

**math**

using substitution, 7/y = 31-5/x so y = 7/(31-5/x) = 7x/(31x-5) 7x+5y=29xy y = -7x/(5-29x) 7x + 35x/(31x-5) = 29x * 7x/(31x-5) 7x(31x-5) + 35x = 203x^2 14x^2 = 0 As Damon noted, x=0 is not allowed, so there are no solutions. If you plot the difference between the two functions...
*August 19, 2014*

**math**

looks like (b) to me (a) is distributive
*August 19, 2014*

**math**

assuming both values are -1, even powers of -1 are +1 odd powers are -1 so we have -1 - +1 = -2 Or, you could factor out (-1)^1988 and have (-1)^1988(-1 - 1) = (+1)(-2) = -2
*August 19, 2014*

**quadratic function**

let x be the time since midnight, and y be the water level. We have y(11.75) = 0.46 y(23.50) = 0.46 the vertex is thus (17.625,2.16) Now you have three points, so you can determine the parabola, and you want x where y=1.
*August 19, 2014*

**math**

If the length is x, the width is x-.5 so x(x-0.5)=3 Now just solve for x
*August 19, 2014*

**math**

Hmmm. If you had said three more than twice its width, I'd have immediately said the room was 5x13. But, now we have to use some algebra. w(3w+3) = 65 w = 4.1815 for the perimeter, we want 2(w+3w+3)=39.452
*August 19, 2014*

**algebra**

I'll take a stab at it. As written, it appears to be (-1^2+11^2)(11^2- -7^2) (-1+121)(121- -49) (120)(170) 20400 If we assume the usual carelessness with parentheses, per Damon, then we have ((-1)^2+11^2)(11^2- (-7)^2) (1+121)(121-49) (122)(72) 8784 I can't believe you...
*August 19, 2014*

**statistics**

better check your dairy almanac for stuff like this.
*August 19, 2014*

**Math**

why is google like a search engine?
*August 19, 2014*

**Math**

depends on whom you ask Most say 5 rounds up Some say 5 rounds to the next even digit, so 35 rounds to 40 45 rounds to 40 Better check with your instructor or text to see which answer will get you marked correct.
*August 19, 2014*

**Science**

weight(N) = mass(kg) * 9.81 m/s^2
*August 18, 2014*

**Advanced algebra**

looks discrete to me
*August 18, 2014*

**math**

15*5+2 = 77 15*6+2 = 92 So, only two of them
*August 18, 2014*

**Algebra 2**

midway between the two extremes is (32.85+31.15)/2 = 32.00 So, |x-32.00| <= 0.85
*August 18, 2014*

**Programming**

read amount, months; show_deposit(amount,months); function show_deposit(amount,months) { deposit = amount/months; print deposit; }
*August 18, 2014*

**maths**

Hmmm. you are mixing up price per kg and per cob, with no indication of how many cobs per kg.
*August 18, 2014*

**Maths**

50-y You can easily do stuff like this if you use an actual number, and then study how you solved it. Suppose you had R50 and spent R10. What is the change?
*August 18, 2014*

**Please Help ! Analytic Geometry**

try this solution: http://www.jiskha.com/display.cgi?id=1408162681
*August 18, 2014*

**Algebra**

Not bad, except that 6.5-4 ≠ 1.5
*August 18, 2014*

**Math**

assuming the 2300 included the 15% profit, the value was 2300(0.85) Now divide that by 100 to get the per-share price.
*August 17, 2014*

**Alegbra**

you are correct. To see its graph, type that in at wolframalpha.com
*August 17, 2014*

**math**

assuming the smaller rectangle is enclosed by the larger, we have small rectangle: w(2w-1) large rectangle: (w+2)(2w-1+2) Assuming the shaded region is the difference between the two rectangles, we have (w+2)(2w+1)-w(2w-1) = 86 w = 14 So, the smaller is 14x27, with area=378
*August 17, 2014*

**trig**

since the spring starts at (0,-17), we know that D(t) = -17 e^-at cos(kt) since the period is 1/13, k = 26π and we have D(t) = -17 e^-at cos(26πt) Now, we know that the amplitude has decreased to (16/17)^(t/3) That means that a = -1/3 ln(16/17) = .02, and D(t) = -17 ...
*August 17, 2014*

**geometry**

Of course the 3rd side can be 5 or 9. That just makes an isosceles triangle. So, you want all the numbers n such that 4 < n < 14: 5+6+7+8+9+10+11+12+13 = 81
*August 17, 2014*

**geometry**

as a hint, suppose you joined the two sticks at the end. Now consider rotating the smaller one, from being end-to-end with the larger one, to overlapping it. What's the max and min possible length for the third side? Now list all the integers in that range and add 'em up.
*August 17, 2014*

**geometry - again?**

another of these triangle problems? Have any ideas of your own on this one?
*August 17, 2014*

**physics - Go with Damon**

As usual, go with Damon. He tends to think things through more carefully.
*August 17, 2014*

**physics**

as usual, s = 1/2 at^2 Since g is acting downward, the net acceleration is 32-9.8 = 22.2 m/s^2 upward s = 1/2 * 22.2 * 4.1^2 = 186.6m Actually, the question is poorly worded, since it implies that the net acceleration is 32 m/s^2, even after including the effects of gravity. ...
*August 17, 2014*

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