Tuesday
July 26, 2016

Posts by steve

Total # Posts: 42,098

math
a = (√3-√2)/(√3+√2) b = (√3+√2)/(√3-√2) Clearly ab=1 Doing the squares directly is a bit cumbersome, so let's rationalize the denominators: a = (√3-√2)^2 = 5-2√6 b = (√3+√2)^2 = 5+2√6 Now ...
June 24, 2016

Math
clearly, real-world distances cannot be negative. You have to use a little common sense along with the math. Even if you allowed for negative distance, that would mean the boat burrowed into the cliff!
June 24, 2016

science
Nope. p = mv 0.5 = 50v 0.01 = v v = 0.01 m/s Try redoing your calculation and you will see that the units do not wind up as m/s.
June 24, 2016

Math
w+y = 30 9.95w + 13.50y = 351.75 Now just solve for w and y
June 24, 2016

math
500 e^(7*.04)
June 24, 2016

math
Note that if x = 5-2√6 1/x = 5+2√6 Now just crank it out
June 24, 2016

math
just plug and chug: #(#3) = #(3^2-3) = #6 = 6^2-6 = 30
June 24, 2016

maths
multiply top and bottom by 5-√3: (5-√3)/(5+√3) = (5-√3)^2/22 now just expand that out to see a and b.
June 24, 2016

SIMULTANEOUS EQUATION
5x^2-5x-63 = 5(x^2-x) - 63 Recall that (x-a)^2 = a^2-2a+a^2 Here we have 2a = 1, so a = 1/2. So, add and subtract 1/4 * 5 = 5(x^2-x + 1/4) - 63 - 5/4 = 5(x - 1/2)^2 - 267/4 To get the roots, set that to zero: 5(x - 1/2)^2 - 257/4 = 0 5(x - 1/2)^2 = 257/4 (x - 1/2)^2 = 257/20 x...
June 24, 2016

Simultaneous equation
From the first equation, x = (3y+14)/5 Use that in the other equation to get 3(3y+14)/5 + 5y = 18 9y+42 + 25y = 90 34y = 48 y = 48/34 = 24/17 = 1 7/17 x = (3y+14/5) = (72/17 + 14)/5 = 310/85 = 3 55/85 = 3 11/17 You could also have used other substitutions for x, or using the ...
June 24, 2016

maths
The first digit cannot be zero, so it must be 1,2,3,4 Now just start listing them: 103 112 ... 310 400
June 24, 2016

math
you need to remember that you can always multiply by 1 without changing anything. The trick is to make sure that the units cancel correctly 1 ton = 2000lb that means that 1ton/2000lb = 2000lb/1ton = 1 8.9*10^5ton * 2000lb/ton * 1kg/2.204lb = 8076*10^5kg or, 8.076*10^8kg or,you...
June 24, 2016

math
1st two are ok 2.9x10^11 = 0.029x10^13 Now you can add them to get 3.729 x 10^13
June 24, 2016

Pre-Cal
each inverse trig function has a principal domain. Review those. tan 5π/6 = -tan π/6 = -1/√3 but, tan^-1(-1/√3) = -π/6 cos -π/4 = cos π/4 = 1/√2 but, cos^-1(1/√2) = π/4
June 24, 2016

Math
or, you are reducing the concentration by a factor of 4/10, so you must increase the volume by a factor of 10/4. 10/4 * 40 = 100 So, you must wind up with 100ml, by adding 60ml of water.
June 24, 2016

Math year 10
since s=k-5, the product is ks = k(k-5) or s(s+5)
June 24, 2016

Math
4/80 = 5% of the caught fish were tagged. So, the 70 tagged fish must be about 5% of the total population.
June 23, 2016

algebra
f(1.5) = -4.96 f(1.8) = +0.77 Since f is continuous on the interval, and 0 is between -4.96 and +0.77, f must be zero somewhere in that interval. It cannot change from negative to positive without going through zero.
June 23, 2016

Physics
find v, the speed of sound. If the depth of the well is y, then the time taken for the sound to come back is y/v Using the equation of motion, we have 4.9t^2 = y Thus, the time it takes to hit the water is √(y/4.9) Adding up the times, we have √(y/4.9) + y/v = 0.6 ...
June 23, 2016

Pre-Cal: Word Problem
can you see how unhelpful that response is? What did you enter, and why was it wrong?
June 23, 2016

Pre-Cal: Word Problem
on the interval [-90,90] sin^-1 is 1:1 For cos^-1, the domain is [0,180] But you probably want radians instead.
June 23, 2016

Math
(a) using shells, v = ∫[1,3] 2πrh dx where r = x+2 and h=y=ln(x) using discs, v = ∫[0,ln3] π(R^2-r^2) dy where R=5 and r=x+2=2+e^y (b) use the same ideas with a horizontal axis. Just keep in mind the volume of a disc (or a washer with a hole inside) and a...
June 23, 2016

maths
100u+10t+h = 100h+10t+u - 396 u-t = t-h solve that and you get t = h-2 u = h-4 h = t+2 = u+4 since no digit is zero, we can have 531 642 753 864 975
June 23, 2016

math
18f = 33g f/g = 33/18 = 11/6
June 23, 2016

Physics
Hmmm. your math looks good. Using the 5.8R and 19.6 I get (2)(3.14)(5.8)(6.4 * 10^6)(1.22) = 284,398,592 which agrees with their rounded answer for distance. Divide that by 86400 seconds and it gives a speed of 3291 m/s, which is pretty close. Is your answer anywhere near ...
June 23, 2016

Physics
figure the radius R of the orbit The distance traveled in one orbit is thus 2πR Now just figure how many orbits it makes in 24 hours. That will give the total distance traveled. Then just divide that by the time (86400 s) to get the speed.
June 23, 2016

Calculus
(a) The semicircles have a diameter equal to x, or y/5. So, each semicircle has an area of πd^2/2 = π/2 (y/5)^2 = πy^2/50 Now add up all the thin discs and you get a volume of ∫[0,10] π/50 y^2 dy = 20π/3 (b) Now the sections have diameter equal ...
June 23, 2016

Math(Please Help Assignment Due Tomorrow)
you can get a handle on this stuff at http://davidmlane.com/hyperstat/z_table.html
June 23, 2016

Math (pre-celc 12)
or, now that you know f, f+g-f = g so, g(x) = (10-3x)-(x-2) = 12-4x
June 23, 2016

Math (pre-celc 12)
come on; this is Algebra I (f+g)-(f-g) = 2g 2g = (10-3x)-(5x-14) = -8x+24 g(x) = -4x+12
June 23, 2016

Math (pre-celc 12)
(f+g)+(f-g) = 2f so, 2f(x) = (10-3x)+(5x-14) = 2x-4 f(x) = x-2 You can find g(x) in a similar way.
June 23, 2016

for all real numbers x and y,it x*y=x(x-y) then x*
Let z = x*y = x(x-y) x*(x*y) = x*z = x(x-z) = x(x-(x(x-y)))
June 23, 2016

Math
If the height is h miles, then h cot3.5° - h cot9° = 13
June 23, 2016

math
extra parentheses are often useful when entering expressions online, as formatting is often rudimentary The text formatting in printed material often makes the parentheses unnecessary In any case, if the expression is unambiguous without the parentheses, they are unnecessary.
June 23, 2016

Math
There is no such number. Now, if you mean integers, then that would be 6499 or 6500 depending on your rules for rounding with terminal 5's. And next time ask a question, instead of just dropping a misspelled sentence fragment with bad grammar.
June 23, 2016

Chemistry
so, you have 75 grams How many moles of bentoite is that? Note that each mole of bentoite contains 3 moles of Si.
June 23, 2016

Psychological Stats
you can play around with Z table stuff at http://davidmlane.com/hyperstat/z_table.html
June 23, 2016

MATH
10^-4 million = 10^-4 * 10^6 = 100
June 23, 2016

math
#1 because (x-y)^2 = (y-x)^2 why don't you try the others? Just remember that (z)^2 = (-z)^2
June 23, 2016

maths
xy = 5/6 x/y = 15/8 6xy = 5 8x/15 = y 6x(8x/15) = 5 48x^2 = 75 x^2 = 75/48 = 25/16 x = 5/4 y = 2/3
June 23, 2016

Algebra
If there are w,x,y,z pizzas of the sizes, then we have 100w+144x+196y+256z = 300*256 z >= 150 y > x 40 <= w <= 50 You have said nothing about how much they need to make from the sales, so the price information is just noise.
June 23, 2016

Calculus
for a cube of side s, v = s^3 dv/dt = 3s^2 ds/dt Thus, ds/dt = 2/15 mm/s a = 6s^2 so da/dt = 12s ds/dt da/dt = 16 mm^2/s
June 23, 2016

Algebra
assuming simple interest, 2500*7*r/12 = 19.76 r = .0135, or 1.35%
June 23, 2016

Algebra
Jack bought x/3 - 10
June 22, 2016

Algerbra
There are none. All accounted for by the equation.
June 22, 2016

Math
7, since there are 7 apples. I suspect you have omitted something.
June 22, 2016

Math (exam tomorrow)
In that case, just look at the graph. It is clear that cos(x) is steepest where it crosses the x-axis. Without calculus, I can't think of an analytical test to prove where the slope is steepest. Are there any similar problems in your text?
June 22, 2016

Math (exam tomorrow)
the slope is given by the derivative f(x) is increasing fastest where the slope is steepest. That is, the derivative has a maximum. Take a look at the graphs of f and f' and you will see that for this problem, f is increasing fastest when x = 3π/4 http://www....
June 22, 2016

math
No way to tell. All we know is that wxy is isosceles, and wx < 38
June 22, 2016

Math
What you have is 4 d^4 w^3 * 6 d w^4 ---------------------------- 3 d^3 w * 8 d w^2 collecting powers of each variable, that is 24 d^5 w^7 ----------------- 24 d^4 w^3 I think you can see what cancels out now, right?
June 22, 2016

math
If you mean 4(2^(x^2)) = 8^x 2^2 * 2^(x^2) = (2^3)^x 2^(2+x^2) = 2^(3x) 2+x^2 = 3x I'm sure you can do that. Next time you post one of these, try showing some of your work first, ok?
June 22, 2016

Maths
I can't parse your words. Try using math symbols instead. Something like x((3 * 1/5)+(3 * 1/10)) = 9/10 or something. You've mangled the values and operators.
June 22, 2016

math
If the base has side x, then x^2 + 4x(x+1) = 96
June 22, 2016

math
NO, YOU DO NOT When you divide 345 by 145 you get 2.3 You are doing it backwards! By hand, you need to start out with 345)125 345 is the divisor, not the dividend!
June 22, 2016

math
you are dividing backwards: 345/145 = 2.3
June 22, 2016

Math
To figure the height after 1 minute, h/150 = tan 28°29' Now, having h, you know that 3h is the altitude after 3 minutes. So, find the angle θ such that tanθ = 3h/150 Or, in one step, θ = arctan(3*150*tan28°29')
June 22, 2016

MATH ARITHMETIC SEQUENCES
I assume you meant 1,1.1,1.2,... Tn = 0.9 + 0.1n So, to find which term is 3, 0.9 + 0.1n = 3 0.1n = 2.1 n = 21 So, T21 = 3 Makes sense. Every 10 terms another 1.0 is added: T1 = 1 T11 = 2 T21 = 3 T31 = 4 ...
June 22, 2016

Science
google is your friend. Just type in the left side of the equation and you will get many hits showing the balanced result.
June 22, 2016

Math
If the 100 is in base 2 or 5, then 100*100*100 = 1000000 regardless of base
June 22, 2016

maths
just add 180°
June 22, 2016

math
If we're allowing decimals, then I'd say the smallest is 0.123456789 If not, then I'd have to go with 1,023,456,789
June 22, 2016

math
Since 13.5 = 3*4.5, 3 times as much zinc is also used.
June 22, 2016

math
since 8 = 2^3, you have 2^2 * 2^x = 2^(3x) 2^(2+x) = 2^(3x) 2+x = 3x x = 1 check: 4(2^1) = 8^1 4*2 = 8 yep
June 22, 2016

math
just type your rational function in at wolframalpha.com Be sure to use parentheses. It will show how it interprets your input.
June 22, 2016

maths
suppose that there is a number x such that 0/0 = x Now, clearing the denominator, we have 0 = 0*x but that is true for any x, so 0/0 is undefined.
June 21, 2016

Math
or, if you really do want grams, figure how many grams of dextrose are in 100ml of the solution
June 21, 2016

geometry
I think you left out some coordinates. However, E is clearly 1/4 of the way from C to D.
June 21, 2016

CALC
dy/dx=−4xe^(y−x^2) dy/dx = -4xe^y e^(-x^2) -e^-y dy = 4x e^(-x^2) e^-y = c-2e^(-x^2) y = -ln(c - 2e^(-x^2)) since y(1) = 11, -ln(c-2e^-1) = 11 c - 2e^-1 = e^-11 c = 2e^-1 + e^-11
June 21, 2016

math
add up all the fares and divide by how many days.
June 21, 2016

Math/Conversions
Your answer is how much was left, not how much she drank. Read the question carefully...
June 21, 2016

Algebra
x/5 - g = a x/5 = a+g x = 5(a+g)
June 21, 2016

PHYSICS
F=ma the tension in the string is the downward weight of the 2kg mass. The force on the 3kg mass is that weight.
June 21, 2016

math
Draw a diagram. If the chord has length 2x, then x/200 = sin 34°
June 21, 2016

maths
That would be 8(1+2+3+...+14+15) You can find the sum of the first n numbers, right?
June 21, 2016

maths
using the law of cosines, AC^2 = 96^2 + 80^2 - 2*96*80 cos56°
June 21, 2016

math
3/8
June 21, 2016

math
1/5 * 3/4
June 21, 2016

Maths
20m^2 * 1.5m * 1000L/m^3 ---------------------------- = 600 min        50 L/min
June 21, 2016

CALCULUS
The graph should make things clear: http://www.wolframalpha.com/input/?i=%7Cx%5E2%2F2-2%7C
June 21, 2016

Math
14
June 21, 2016

maths
ok now you do the same.
June 20, 2016

Math
Let z = x+yi Then we have x^2+y^2-2x+2yi+xi-y=2i That means we have x^2+y^2-2x-y = 0 2y+x-2 = 0 Thus, x = 2-2y and so 4-8y+4y^2+y^2-4+4y-y = 0 5y^2-5y = 0 5y(y-1) = 0 so, y=0 x=2 or y=1 x=0 Or, z=2 or z=i I'll let you verify that both of those z values satisfy the original...
June 20, 2016

CALCULUS
surely the initial mass is positive. Kind of makes things more real. Looking at the original equation, if y(0) < 0, we have exponential growth, not decay.
June 20, 2016

CALCULUS
this is just like the other one. You already know about radioactive decay, and how it is an exponential function, right?
June 20, 2016

CALC PLEASE HELP
dy/dt = ky dy/y = k dt ln y = kt + ln c y = c*e^(kt) Now plug in your values to determine c and k.
June 20, 2016

maths
triangles BDA and BDC are congruent.
June 20, 2016

Calculus
you can find the area B of the base (a triangle), and its height (the z-intercept) v = 1/3 Bh
June 20, 2016

Math (pre-celc 12)
the order does not matter. There are 21P3 ways to select an ordered group of 3 items from 21. Whoever is chosen first, there are 21 available people. 20 for the 2nd, and 19 for the 3rd.
June 20, 2016

Math
So far you have only mentioned 4 places. Any data on the other three? A lot of possibilities will fit what you have required so far.
June 20, 2016

physics
10+12 √(10^2+12^2)
June 20, 2016

algebra
2x+2x+2+2
June 20, 2016

Science chemistry
I only found TETRACHLOROMETHANE
June 20, 2016

Maths
(n+1)/d = 1/3 n/(d+1) = 1/4 If that's too hard to work through, then just consider that 5/15 = 1/3 4/16 = 1/4
June 20, 2016

Mathematics
14000(1+.12)^2 vs 14000(1+.12/2)^(2*2)
June 19, 2016

math
2(r^4-1)/(r-1) = 30 r=2 The last 4 terms don't matter, unless you are interested in how many there are.
June 19, 2016

Math
t+b+f = 7.56 f = 2t 1.1t + 1.25b + f = 8.68 Now just crank out the desired answers
June 19, 2016

Maths
w/250 = cot50°
June 19, 2016

Physics
How can you explain work, in regards to electricity? I understand it as the product of energy used, usually displacement. I cant understand or explain it as far as electricity is concerned. I'm not sure if I understand it at all.
June 19, 2016

Math
oops. 2sin^2(1/2 y) = 1 - cosy
June 19, 2016

Math
f(x+y)-f(x) = sinx cosy + cosx siny - sinx sin^2(1/2 y) = 1 - cosy That should get you on your way... The rest is just algebra.
June 19, 2016

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