# Posts by STEVE

Total # Posts: 52,318

math
r = k1v^2 + 2v^3

Maths trigonometric
8sinx-cosx = 4 8sinx = cosx+4 64sin^2x = cos^2x + 8cosx + 16 64-64cos^2x = cos^2x + 8cosx + 16 65cos^2x + 8cosx - 48 = 0 (5cosx-4)(13cosx+12) = 0 cosx = 4/5 or -12/13 so, sinx = 3/5 or 5/13

algebra
6^2 + h^2 = 12^2 so, what is h?

Algebra
14 hours = 50,400 seconds 855 minutes = 51,300 seconds yes, they are all about the same, but which is the smallest amount of time?

Algebra
I assume it means you need to multiply b^2 by something. Since b^8 = b^2 * b^6 b^6 goes into the box. Or, it might mean that b^2 is to be raised to a power. Since 8=2*4, (b^2)^4 = b^(2*4) = b^8 This appears to be just an exercise in working with properties of exponents.

Maths
I assume you mean log(384/5)+log(81/32)+3log(5/3)-log9 =log(384*81*125)/(5*32*27*9) =log(3888000/38880) =log 100 = 2

Maths
If you let u=3^x then the equation becomes (using parentheses to clarify matters) 9^(x+2) - 6*3^(x+1) = 0 9^2*9^x - 6*3*3^x = 0 81u^2-18u+1=0 (9u-1)^2 = 0 u = 1/9 So, 3^x = 1/9 = 3^-2 x = -2

math
Not even sure what the question is. If you are trying to write a fraction, then I'd guess at 9(4+2)/(3-1) = (9*6)/2 = 54/2 = 27 If that's wrong, then try rewriting it so we can tell what you want.

Maths
well, just plug in your numbers. (a) (1-h)^2 = 16 1-h = ±4 h = -3 or 5 Do (b) the same way.

MATHS
surely your text covers these topics. Offering complete courses is beyond the scope of this web site.

Marh
If there are x in the box, then 5/12 x = 3/8 x + 24 Multiply by 24 and you have 10x = 9x+576 x = 576

pre algebra 1
Assuming she only mowed the three lawns, then her total time was 1 3/4 + 2*(1 1/5) + 3/4 = 4 9/10 hours. That's 4:54, so subtracting that from 4:15, we have a start time of (using the 24-hour clock) 16:15 - 4:54 = 15:75 - 4:54 = 11:21 You are correct. Good job.

Alegbra
you should know that vertical angles are congruent. Each angle and its adjacent angle form a straight angle. So, the adjacent angles are 55°. 125+55 = 180 55+125 = 180 ...

Math
I think you're stuck. There's just no way to get things to just a product. According to wolframalpha, the integral is not elementary. http://www.wolframalpha.com/input/?i=integral+log(1-cotx)+dx

Capleton
a+5d = 2(a+2d) a+5d = 2a+4d a = d So, pick a first term, and use that for the difference. The sequence is thus a,2a,3a,4a,5a,6a,... 6a = 2*3a

Math - oops
Better go with Scott. I seem to have lost a factor of 2 somewhere. 7 hours is clearly not long enough for a smaller crew to do almost the whole thing.

Math
11h 40min = 700 minutes So, each man does 1/5600 of the job in a minute 8 men working for 60 minutes complete 8*60/5600 = 3/35 of the job. The remaining 6 men have to do 32/35 of the job, so it will take 8/6 as long as the full contingent of 8 men. The time is thus 8/6 * 32/35...

Math
The angles are 7x and 11x Now you know that 7x+11x = 180 Now git 'er done!

Maths algebra
This one has no rational roots. Your only hope is a numeric or graphical method.

Math
You have it backward. If the original population was x, then 1.9x = 16359 x = 16359/1.9 = 8610

math
4^2-2(3*5+1) = 16-2(16) = -16

math
if you mean 4 + 2^2 - 2(3*5+1) then that is 4+4-2(16) 8-32 -24 If that's not what you meant, then try using real math symbols (including parens as needed!) ...

math
The bearing is 360-?, where tan? = 7/24

math
let's assume there are 100 shirts, with a cost of \$100 each. 17 are not sold: \$0 18 are sold for \$70 each: \$1260 65 are sold for \$150 each: \$9750 total income: 11010 profit is thus 1010/10000 = 10.1%

Maths
If the slower's speed is s km/hr, then their combined speed of approach is s+2s = 3s So, since distance = speed * time, 3s * 3/2 = 2420

Math
it will be in grams the same as the atomic weight. All those words, to write 6.022*10^23 !!

physic
1st: 49t-4.9t^2 2nd: 49(t-3)-4.9(t-3)^2 So, when are the heights equal? 49t-4.9t^2 = 49(t-3)-4.9(t-3)^2 t=6.5 Now just plug that in to find the height.

Math
the area of the room is two side walls and two end walls, so 2*15*10 + 2*20*10 = 700 ft^2 The windows occupy 2*5*4=40 ft^2 So the cost is (700-40)ft^2 * Rs20/ft^2 = Rs 13200

Calculus II
I assume you know the chain rule, and that d/dx e^u = e^u du/dx Now, for some other base, such as 5, recall that 5 = e^ln5 So, 5^x = e^(ln5 x) d/dx 5^x = ln5 e^(ln5 x) = ln5 5^x So we arrive at the fact that d/dx a^u = ln(a) a^u du/dx and your result follows.

math
5+2x=35 2x=30 x=15

Algebra
4! = 24

Algebra
there are 4 choices for the 1st letter since that letter is used, there are only 3 choices for the 2nd letter. So, extending that logic, the number of possible passwords is 4*3*2 = 24

math
(15/20)/(4/10) = 15/8 = 1.875 or 87.5% increase

trigonometry
The sum-to-product formulas will make this just drop out easily.

math
come on. a 10% discount means that the new price is 90% as much (100 - 10 = 90) similarly, a 14 2/7% discount means the result is (100 - 14 2/7)% = 85 5/7%

math
85 5/7 %

Maths
the height is at 40 when t^2-14t+40 = 0 (t-4)(t-10) = 0 SO, it is above 40 for 6 seconds (between t=4 and t=10) x(x+7)/2 = 60 x^2+7x-120 = 0 (x+15)(x-8)=0 The triangle is the familiar 8-15-17 right triangle.

Math222
The domain of rational functions is all reals except where the denominator is zero. If your denominator is 5w, then only w=0 is excluded.

Math
check the ratios. 12/8.5 = 141% 16/11 = 145% So, use 141% so the width will fit. If you are really doing this on a machine, I think you'll find 141% on the menu.

calculus
you'd have to use some numeric integration technique to get an approximation.

calculus
That antiderivative is not expressible in elementary functions. It is an elliptic integral.

Math
If x is the larger angle, then x-28 + x = 140 ...

algebra-math
10^1^-x = (10^1)^-x 10^1 = 10 so, you have 10^-x = 10^4 so, x = -4

singapore math
k+y = 500 k+m = y+220 y+m = k+140 Or, in more standard format, k+m = 500 k+m-y = 220 -k+m+y = 140 These are easy to solve.

Math Trigonometry
Learn to recognize the easy Pythagorean triples. One of these is 7-24-25 Or, if you want to figure it out, just work with k^2 + 24^2 = 25^2 Now you can find the angles.

Math
|3-7x|=-6 trick question. || is never negative 6w-1/5 -3w=12w-16/15 w = 13/135 (6w-1)/5 -3w=(12w-16)/15 w = 1/3 (x-3)^2-3=-5 (x-3)^2 = -2 No solution, since square are never negative (x+3)^2+4(x+3)-5=0 If u=x+3 then you have u^2+4u-5=0 (u+1)(u-5)=0 So, x+3 = -1 or x+3 = 5 x...

Algebra
y = kxz so, y/(xz) = k, a constant You want y such that y/(8*6) = 64/(4*8) y/48 = 2 y = 96

Maths
As you say, we need a•b = 0 2t+3d = 0 but b is also a unit vector, so t^2+d^2 = 1 Solving those two equations gives the values of t and d. Pick the solution where d>0.

Math
120° is 30° south of due east so, draw your triangle in standard position, and note that y/1260=sin30° (south of where he started).

math (sinusoidal functions)
see the graph at http://www.wolframalpha.com/input/?i=plot+y%3D29%2F2+-+25%2F2+cos(pi%2F3+t),+y%3D2,y%3D27+for+0%3C%3Dt%3C%3D12 use what you know about shifts, periods, and amplitudes to arrive at it.

math (sinusoidal functions
see the graph at http://www.wolframalpha.com/input/?i=plot+y%3D21-18cos(pi+t),y%3D3,y%3D39+for+0%3C%3Dt%3C%3D8 use what you know about periods, amplitudes and shifting to see how it works.

math
depends on how long the water runs, and how deep the water is. you're trying to convert ft^3/s to acres (ft^2) That means you're going to have to multiply by s/ft to make the units come out.

Geometry
6.3

Math
cosx+2sinx+1 = (cosx+sinx) + (sinx+1) So, your quotient can be written 1+(1+sinx)/(cosx+sinx) Now, since cosx < 1, cosx+sinx < 1+sinx So, (1+sinx)/(cosx+sinx) > 1 and the rest follows.

math
WZ corresponds to PL. WZ/PL=4 I have no idea what c is, but since XW corresponds to AP, XW/AP=4, so XW=64

math
the times are 80 seconds and 55 seconds 1mi/80s * 3600s/hr = 45 mi/hr 1mi/55s * 3600s/hr = 65.45 mi/hr Now just subtract

math
I'll assume you meant R = pl/A p=AR/l A=pl/R l=AR/p and that's "formula" with no "r" ...

Math
Oops. I see a big one! That 1/u factor makes it ?[?/6,?/4] ?2 a cos^2t/sint dt a?2 ?[?/6,?/4] (1-sin^2t)/sint dt a?2 ?[?/6,?/4] csct-sint dt a?2 (-ln(csc t + cot t) + cost) [?/6,?/4] = a?2 (-ln(?2+1)+1/?2)-(-ln(2/?3 + ?3)+?3/2)) = a?2 (1/?2+?3/2 + ln(5/(?3+?6))) Still nowhere ...

Math
Ok, let me check on that u^2 = x^2+a^2 2u du = 2x dx a^2-x^2 = 2a^2-u^2 and now ?[0,a] x?((a^2-x^2)/(a^2+x^2)) dx = ?[a,a?2] 1/u ?(2a^2-u^2) du You seem to have lost the factor of 1/u Now let u=?2 a sint 2a^2-u^2 = 2a^2-2a^2sin^2t = 2a^2 cos^2t du = ?2 a cost dt and the ...

Math
well, just looking at the calculations, they appear reasonable, so at the end you have ?2 a^2 [6-3?3+?]/12 <= ?-2 a^2 <= 12(?-2)/(?2 [6-3?3+?]) |a| <= ?(12(?-2)/(?2 [6-3?3+?])) = 1.567

math
(2n)(2n+2)(2n+4)=8n(n+1)(n+2) Now, if n = 3k, n+1 is even, and we have 8n*3k*2m(n+2)=48nkm(n+2) if n=3k+1, then n+2=3k+3=3(k+1) and n+1 is even. if n=3k+2, then n+1=3(k+1) and either n+1 or n+2 is even

Math
clearly, odd-numbered rows begin with red Not sure how a 3x3 array has a 13th row, however ...

Math
f(2a)=(2a)^2-1 So, now you just have to solve 4a^2-1=35 4a^2=36 a^2=9 a = ±3

Math
Well, you can evaluate y at several places and you know that if it is positive at x1 and negative at x2, there is at least one root in between them. This can be repeated to the desired precision. You can use Descartes' Rule of Signs to figure how many positive or negative ...

Math
This polynomial does not factor with rational coefficients, so you will need to use a numeric or graphical method. I'm not sure what tools you have at your disposal, but there are several good graphing calculators online, such as http://www.wolframalpha.com/input/?i=2x%5E4...

Computer Programming
income = 0 loop {    print "Income: "    read income   if income <= 0 exit loop   tax = (income > 100000) ? (6000+0.09*income-100000)     : (income >= 50000) ? (2500+0.07*(income-50000)   ...

math
the dimensions of the small stones must divide those of the courtyard. GCD(5750,2200) = 50 so, the largest stones can be 50x50 cm. Thus the area, in terms of stones is (5750/50) * (2200/50) = 115*44 = 5060

Differentiation
x^2+y^2+2gx+2hy=0 2x + 2yy' + 2g + 2hy' = 0 y'(y+h) = -(x+g) y' = -(x+g)/(y+h) at (0,0) y' = -g/h or x^2+y^2+2gx+2hy=0 (x+g)^2 + (y+h)^2 = g^2+h^2 2(x+g) + 2(y+h) y' = 0 y' = -(x+g)/(y+h)

Math
Actually, this is just a problem in geometry. I would not be surprised if Euclid did it 2000 years ago. Still, you could start here: http://mathworld.wolfram.com/Circle-CircleIntersection.html But using general circles in coordinate geometry, it will get messy!

Math
that's a whole different problem. You want to have two circles intersect so that they divide in half? Not nearly so easy, as I'm sure you can appreciate. (x + 1/4)^2 + (y+1)^2 = 1/16 (x+p)^2 + y^2 = p^2 x^2 + 1/2 x + 1/16 + y^2 + 2y + 1 = 1/16 x^2 + 2px + p^2 + y^2 = p...

Math
I think you lost a factor of 2 in your transformation. 2x^2+2y^2+x+4y+2c=0 x^2 + x/2 + y^2+2y = -c (x + 1/4)^2 + (y+1)^2 = -c + 1/16 + 1 For this to be a real circle, the right side must be positive, so c < 17/16 The only positive integer value of c is 1, so we have (x + 1/...

Calculus
read what Scott told you last evening: https://www.jiskha.com/display.cgi?id=1501461094 Recall the sum of an infinite geometric sequence is S = a/(1-r)

Math
well, you know there are 36 possible outcomes. How many add up to more than 9?

Math
clearly that is 20,000 * 0.075 = ?

Algebra1 Word Problem HELP#2
they intersect where the two functions are equal. That is, their difference is zero. You can draw the graphs and find their intersection. Or, using algebra, 2^x = 4^x - 2 4^x - 2^x - 2 = 0 Looks hard, but if you let u = 2^x, then 4^x = (2^2)^x = 2^(2x) = u^2 and you have u^2-u...

Algebra1 Word Problem HELP#3
The two lines are shown here: http://www.wolframalpha.com/input/?i=plot+y+%3D+2x-7,+y+%3D+-1%2F2+x+%2B+3 You want the area below the blue line and above (and including) the red line. So, does (3,-7) satisfy both inequalities? Is it in your shaded area?

Math-college
A = P((1+r/n)^(nt)-1) pick the one you want to leave unknown. See related questions for ideas on questions.

Marh
amount * 1.06 = 5000

Math
"combined" means to add them together: 54+x

Math
h/100 = sin 65°

maths
if simple interest, then 1+20r = 2 r = 1/20 = 5% if compound interest, (1+r)^20 = 2 r = .035 = 3.5%

Maths

algebra
well, x+y = 10000, so x=10000-y and you have .02(10000-y)+.015y = 193

Math- Tax
Just add up the terms. The tax is 20+60+120+.05(25000-1000-2000-3000) = 200 + .05*19000 = ...

geometry
the value of x does not matter, if it is just the ratio of ares you want. Just draw the figure, and it should be clear that (x/2)^2 + (x/2)^2 = y^2 simplify, and then your ratio is just x^2/y^2

Math_sales tax_ discount
100 * 0.80 * 1.07 = ?

math
It is (x-5)(x+4) just having the problem given the way it was, you ought to have looked for a factor in common with the numerator. Don't let the teacher be cleverer than you!

Coordinate geometry
set it up so that the three vertices are at (0,0), (a,0), (0,b) Then the median to the hypotenuse has endpoint (a/2,b/2) So, its length ?((a/2)^2 + (b/2)^2) = ?(a^2/4 + b^2/4) = 1/2 ?(a^2+b^2) which is half the hypotenuse.

Math
clearly, infinity! extra credit: what if x -> 0 ?

Math-intergration
e^-? = 0 sin? and cos? are undefined, but lie between -1 and 1 multiplying by 0 leaves the result = zero

coordinate geometry
google is your friend. one definition is the locus of a point whose distances from a fixed point and a fixed line is the equal.

rationalizing
(a-b)(a+b) = a^2-b^2, so (?18-?17) * (?18+?17)/(?18+?17) = (18-17)/?(18+?17) A calculator has roundoff error. ?18 is very close to ?17. Not too close in this case, but ?188888 - ?188887 are very close, and (floating-point) precision will be lost when trying to include the ...

math
"of" means "times," so [(2/5)(2/3)]/(3/10) = (4/15)*(10/3) = 40/45 = 8/9 also, "division sign is divided by" is gibberish.

Order with fractions
you are right; I misread the words. Here is what you wrote, using only math symbols: 2/(2/3) + 3/4/(4/5) Now start inserting parentheses until it means what you think it should. If you use wolframalpha.com, it will show what your entered text really means: http://www....

Order with fractions
why all the words? 2/3 + 3/4/5 = 2/3 + 3/20 = 49/60 2/3 + 3/(4/5) = 2/3 + 15/4 = 53/12 without parentheses, multiplication and division are done left to right, before any addition or subtraction.

Maths
the inside space is a 6x6x6 cube. So, just subtract it: 8^3-6^3 = ?

composite functions
Assuming the usual carelessness with parentheses, I guess you have f(x) = 2/(3x-1) g(x) = (x+4)/x g(f) = (f+4)/f = (2/(3x-1)+4)/(2/(3x-1)) = 6x-1

Algebra 2
(b) as always, max height (the vertex) is at t = -b/2a = 1 (a) figure h(1) (c) solve -16t^2+32t+28 = 0

math
p((1+r)^2-1) = 220 p(2r) = 200 now just solve for p and r.

maths
well, we know that a/c = b/d, so a^3c/b^3d = (a/b)^3 * c/d = (c/d)^4 ac^3/bd^3 = a/b * (c/d)^3 = (c/d)^4 see what you can do with that.