# Posts by steve

Total # Posts: 52,274

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.

math
the opposite direction: 120+180 = 300

Math
20% = 1/5 3/8 * 4/5 = 3/10 1/5 + 3/10 = 1/2 so, x/2 = 40 ...

Maths
the jeans cost \$30 less 30/280 = 0.107 or about 11% cheaper

Math
He sold 9 eggs at 4/egg = 36 His cost was 40 I don't see any profit there. Looks more like a 10% loss.

Math
98/7 = 14 lbs/day average 7/2 (2a+6*2) = 98 so, a = 8 The median is the 4th day, so he cooked 8+3*2 = 14 lbs on that day. So, the mean and median are the same. In fact, that is true for all arithmetic sequences. Sn = n/2 (a1 + an) the mean is thus Sn/n = (a1+an)/2 The median ...

Maths
1 1/2 hours = 90 minutes, or 15 doubling periods. So, there will be 3*2^15 bacteria

Math
If \$x is at 8%, then the rest (3500-x) is at 5%. So, .08x + .05(3500-x) = 238 Now just solve for x. Extra credit: How much did Moon Unit get to invest?

Math- Slope
of course not. You have to have two points.

Math- Slope
The line through (2,4) and (-2,1) has slope 3/4 The line through (2,4) and (4,0) has slope -2 Remember that the slope is y2-y1 ------ x2-x1

Math_ Geometry
actually, you divide by 180. A n-sided polygon's interior angles sum to (n-2)*180. So, here we have (n-2)*180 = 1260 n-2 = 1260/180 n-2 = 7 n = 9

Math_ Geometry
1260 = 180*7 So, a 9-gon fits the bill

Trigonometry
just convert everything to x-y values, add them up, and change back to headings. If his heading is ?, then we need 160sin? - 20sin310° = v*sin80° 160cos? - 20cos310° = v*cos80° solve that and you get ? = 74.5° v = 172.1 makes sense, since the wind is ...

Math
just put together what you know: horse: 5 round, 10 square cat: 24 round, 6 square dog: 0 round, 19 square rabbit: 11 round, 0 square so, now you can easily figure what fraction are round.

Physics
final location: 30 E, 20 S total travel: 110 now you can find the displacement, using the Pythagorean theorem. no idea what distance in FPS is. All distance quoted were in meters.

math
tan x/2 = (1-cosx)/sinx so, tan(1/2 cos^-1(a/b)) = (1-a/b)/(?(b^2-a^2)/b) = ?((b-a)/(b+a)) so, if we let z = 1/2 cos^-1(a/b) tan(?/4+z)+tan(?/4+z) = (1+?((b-a)/(b+a)))/(1-?((b-a)/(b+a))) + (1-?((b-a)/(b+a)))/(1+?((b-a)/(b+a))) putting all over a common denominator, things ...

math
(3/4 - 3/5)x = 9 3/20 x = 9 x = 60 check: 3/4 * 60 = 45 3/5 * 60 =36 45-36 = 9

math
you can play around with Z-table stuff here: http://davidmlane.com/hyperstat/z_table.html

Math
For x ft^2 of flooring, T = V1 + V2*x x = (T-V1)/V2

Physics
that's "estimate" not stamate. 3700km/5.1days = 725.5 km/day So, for 6200 km, it will take (6200/3700) * 5.1 days

math
to get what? If you want a perfect square, (x+5)^2 = x^2+10x+25

math
(a) as with all these, divide the fence so that the lengths (1) equal the widths(2). Thus the pen is 600x300 (b) same problem, but now there are 4 widths, so the same principal applies. To minimize the fence, each pen has dimensions x and 25/x, where 4x = 5(25/x). That is, x^2...

geometry
Drop altitudes of length a from the ends of the shorter base. This gives you two right triangles at the ends, with altitude a and base x. Since the figure is isosceles, the two base angles are equal. Now you have Each base angle is 70° a/7 = cos70° x^2 + a^2 = 7^2 Now ...

geometry
as you recall a = ?r^2 c = 2?r so, the pool with cover has a diameter of 21 ft. The radius is thus 10.5 Now just plug and chug.

physics
If you mean that the balls pass as they have both fallen 400m, then you have 4.9t^2 = 400 v(t-2)+4.9(t-2)^2 = 400 v(20/?4.9-2)+4.9(20/?4.9-2)^2 = 400 v = 22.39 m/s

MATH
1/x = 1/10 + 1/12 - 1/20 x = 15/2

Math
5/3 * 1/3 = 5/9

math
the areas are in the ratio 4:9, so 4/9 * 63pi = ? Note that's pi, not pie!

maths
how about 18 * 7 1/4 ?

Maths ( arthmetic )
find a and d using what they have told you: a+3d = 10 a+10d = 3(a+3d)+1 Then just evaluate S20 = 20/2 (2a+19d)

physics
y = h + 100t - 4.9t^2 and you know that y=0 at t=6, so h + 100*6 - 4.9*36 = 0 I suspect a typo...

math
well, what is 1/8 of 64? 64/8 = ? now just take 7 times that.

maths
well, you know that 1.05 p = 262.50 so, ...

Math
I assume you mean (9a^4)^2 = 9^2 (a^4)^2 = 81a^8

Math-college
Actually, it is correct for some values of x. Now, if you want to solve (x + 3)(x -4) = 7 you cannot just set one factor equal to 7, because that means that the other factor must be 1. That is why we always set the left side equal to zero, because then if the product is zero, ...

statistics
just multiply all the quantities together.

Calculus
Since I cannot see the graphs, I have no idea what the numeric values are...

Calculus
concave up means f" > 0 That means f' is increasing. inflection points are where f"=0 and f'?0

Math
well, (3b^4)^2 = 9b^8

Math
well, 48 = 16*3 see where that takes you.

Math
getting rid of the expressions inside the parentheses, you have 7x = 2(-3)^2 + 3(8) 7x = 2*9 + 3*8 ...

Math
3x = # dogs 2x = # cats 3x+2x = 30 ...

Chemistry
the valence of Na is always +1

Science
2kW = 2000 J/s = 2000 Nm/s Now just convert that to kg

math
the yard is 5750x2200 GCD(5750,2200) = 50 so, using 50x50 cm stones will use the fewest Now just figure how many that will be.