Saturday
February 25, 2017

Posts by STEVE

Total # Posts: 48,786

algebra word problem
the nice wikipedia article on trajectory gives the equation, including the angle involved.
January 6, 2017

Algebra
how can y be negative? x+y+z = 54000 .08x + .06y + .09z = 4260 .08x = 6*.06y x,y,z = 36000, 8000, 10000 ----------------------------------- So, where did you go wrong? 8x+6(9y)=0 Why do you think the interest sums to zero?
January 6, 2017

algebra
G <= 2
January 6, 2017

Math
come on, man! It's still ?2u^(2/3) du = 2 (3/5) u^(5/3) + C = 6/5 (x^2+2x-3)^(5/3) + C
January 6, 2017

Math
I suspect a typo. You probably meant ?(4x-4)(x^2-2x-3)^(2/3) dx or ?(4x+4)(x^2+2x-3)^(2/3) dx Assuming the first, Let u = x^2-2x-3 du = 2x-2 dx Then you have ? 2u^(2/3) du which is easy. ... right? If there is no typo, you are in deep trouble.
January 6, 2017

Math
1+i = ?2 cis ?/4 (1+i)^101 = (?2)^101 cis (?/4 * 101) = 2^50 ?2 cis (25? + ?/4) = 2^50 ?2 cis 5?/4 = 2^50 (-1-i) or -2^50 (1+i) There appears to be a typo.
January 6, 2017

math
what do you mean 4y=6y-2x+1 ?? Why not just say 2y = 2x-1 If that is the case, then we have 2(2x-1) + x+2x-1 = 28 Use that to find x, and then y. If there's a typo in the problem, fix it and use the same logic.
January 6, 2017

Math
8000 * 0.095 * 120/365
January 6, 2017

math - eh?
by "cover the entire room" do you mean all the walls, floor, and ceiling? Strange use for border.
January 6, 2017

maths
Not sure what you mean. The angle of reflection on the surface is always equal to the angle of incidence. The critical angle for total internal reflection decreases with increasing index of refraction.
January 6, 2017

More calculus
the fence length f = 2r + r? since the area is constant, 1/2 r^2 ? = A ? = 2A/r^2 so, f(r) = 2r + 2A/r Now just find r where df/dr = 0 Use that to get ?
January 6, 2017

Calculus
You have the right idea. But a must be chosen so that lim (ax-10) = 1 as x->3+ f(x) is defined every where except at x=3, so define it to be 1 there, since the limit from both sides is 1. That is, f(3) = B a = 11/3 B = 1
January 6, 2017

Math
true for any number except zero.
January 6, 2017

calculus
the points are (4,1) and (4,-1). -2x + 4yy'+3 = 0 y' = (2x-3)/(4y) So, now you have a point and a slope, and the lines are y-1 = (x-4) y+1 = -(x-4) See http://www.wolframalpha.com/input/?i=plot+-x%5E2%2B2y%5E2%2B3x%3D-2,+y-1%3Dx-4,+y%2B1%3D-(x-4)
January 5, 2017

Algebra2
rearrange things to 3x^2+6x-5 = 0 Now use the quadratic formula.
January 5, 2017

Algebra2
Which expression gives the solution -5+2x^2=-6x?
January 5, 2017

calculus
5y + 5xy' + 2xy + x^2 y' = 0 Now collect terms and solve for y'
January 5, 2017

Calculus
f' = 3h^2 h'
January 5, 2017

Math
.450km / 10km/hr = .045 hr
January 5, 2017

pre calc
do this just like your previous exercise.
January 5, 2017

math
They are separating at a rate equal to the slower truck's speed. Since It took 6 hours to separate by 204 miles, that is 204mi/6hr = 34 mi/hr So, the slower truck is going 34 mi/hr You found the faster truck's speed, but then botched it again since 2*8 ? 146 !!
January 5, 2017

pre calc
If x is at 6%, then the rest y=(3000-x) is at 7%. So, x+y = 3000 .06x + .07y = 194.00
January 5, 2017

Calculus
look up the arc length. The particle must move along a curve. At each small interval, the curve can be considered a straight line, with "arc length" ds^2 = dx^2 + dy^2 Thus, adding up all the tiny hypotenuses gives. s = ?ds = ??(dx^2+dy^2) = ??(1+(y')^2) dx
January 5, 2017

Math Calc
I assume you mean y = 3x^(1/3) + 6x^(4/3) = 3(2x+1) x^(1/3) y' = x^(-2/3) + 8x^(1/3) = (8x+1) x^(-2/3) y" = -2/3 x^(-5/3) + 8/3 x^(-2/3) = 2/3 (4x-1) x^(-5/3) y'=0 at x = -1/8 y"(-1/8) < 0 so y(-1/8) is a maximum y"=0 at x = 1/4 so that is an ...
January 5, 2017

math
double the 1st equation and you have 6x-2y = -6 It is clear to see that since -6 ? -8 the two equations cannot have a single solution. The lines are parallel, and do not intersect.
January 5, 2017

Pre calc
adjust things a bit to get 6x+12y = 57 -12x+12y = 12 subtract and you get 18x = 45 x = 5/2 Now use that to find y. Or, note from the 2nd equation divided by 3 that -x+y=3 y=x+1 Use that in the 1st equation to get 2x+4(x+1) = 19 2x+4x+4 = 19 6x = 15 x = 5/2
January 5, 2017

pre calc
add the two equations to get 0 = x-1 x = 1 now use that to get y.
January 5, 2017

Algebra
f+s = 106 f+3 = 2(s-4) now crank it out.
January 5, 2017

math
PV=kT So, PV/T = k a constant. So, you want T such that 48*1/T = 1*16/305
January 5, 2017

Math
Any line not in the plane of GH is skew to GH. Skew lines necessarily cannot intersect. Not having any details of your diagram, it's hard to say much more. Maybe google can provide you with further relevant examples.
January 5, 2017

math
Try this. I just googled ABCD is aparallelogram in which BCis produced to E such thatCE = BC and got this hit, among others: http://www.meritnation.com/ask-answer/question/abcd-is-a-parallelogram-in-which-bc-is-produced-to-e-such-th/areas-of-parallelograms-and-triangles/...
January 5, 2017

math
F=ma v = at = Ft/m so, t = vm/F = 2.8*10^3*7.9 /6.7*10^5 = 0.033 seconds
January 5, 2017

math
a = v^2/(2s) = 0.614/0.744 = 0.8263 m/s^2 F = ma = 61.0*0.8263 = 50.34N
January 5, 2017

math check my answer ?
as written, f(x) has a range of all real numbers. Pick any value for f(x), and you can easily find an x to produce it. For example, suppose you want f(x) = 11 -3x-1 = 11 -3x = 12 x = -4 So, you must have a typo. Your range of f < -1 could be produced with f(x) = -3x^2 - 1 f...
January 5, 2017

geometry
a = 1/2 r^2 ? Use that once you supply the missing data.
January 5, 2017

Science
google is your friend. Try it.
January 5, 2017

math
g = 12.50 r = 0.75g y = 2.5r = 2.5 * 0.75 * 12.50 = 23.4375 or, using mixed numbers, y = 2 1/2 * 3/4 * 12 1/2 = 23 7/16
January 5, 2017

computer applications (commerce)
knowing that they differ by 2, start at 19 1: n=19 2: print n 3: n=n-2 4: n>0? 5a: yes: go to step 2 5b: no: stop Or, you could test every number against some criterion. In this case, divisibility by 2. 1: n=20 2: divide n by 2 3: remainder=0? 4: yes: print n 5: n=n-1 6: n&...
January 5, 2017

further maths
m•p = 0 n = h(i+j-2k) a+b-2c = 0 a+h = 2 b+h = -1 c-2h = 2 This gives the result m = 5/2 i - 1/2 j + k n = -1/2 i - 1/2 j + k I don't see a second solution, but maybe you can find one.
January 5, 2017

Maths
5/7 as many men, so 7/5 as much time.
January 5, 2017

MATH
well, p^2+pq-6q^2 = (p+3q)(p-2q) p^2-3pq+2q^2 = (p-q)(p-2q) So, what cancels?
January 5, 2017

maths
a = 2 pi r l
January 5, 2017

Math
look at the differences: 2,3,_,_,6
January 5, 2017

Math Calc
1. Think of f(x) = x^3 2. If f'=0, f does not change. 3. think of f(0). It clearly does not satisfy the MVT on [-1,1] The typos do not help...
January 5, 2017

Math Calc
clearly it is either 3 or 4. Since 4 is not a choice, 3 seems logical. Now, knowing what you do about cubic curves, and that this one comes down from the left, its first turnaround will be a minimum. So, it will be at x=3. Or, note that f" = -4x+14. f"(3) = 2 > 0...
January 5, 2017

Math Calc
This is a typical exercise using the chain rule. 2x^2 + y^3 =10 4x dx/dt + 3y^2 dy/dt = 0 Now, using your values, when x=1, y=2. So 4(1) dx/dt + 3(2^2)(3) = 0 4 dx/dt + 36 = 0 dx/dt = -9
January 5, 2017

Math!!!
recall that if z = x+iy zz* = (x+iy)(x-iy) = x^2+y^2
January 4, 2017

Math
well, 2mn-16m = 2m(n-8) so what can you do to get from -7n+? to ?(n-8) ?
January 4, 2017

algebra
p +4- 2 (p-10)> 0 p + 4 - 2p + 20 > 0 -p + 24 > 0 24 > p or p < 24
January 4, 2017

math
check out your sum-to-product formulas. sin(2A+C)+sin(A+2B) = 2sin((2A+C)/2)cos((A-2B)/2) C = ?-A-B 2A+C = 2A+?-A-B = A-B+? sin (2A+C)/2 = sin(?/2 + (A-B)/2) = cos(A-B)/2 and similarly for the others. Much stuff will cancel out.
January 4, 2017

Math
h(5)-h(2) -------------- = ? 5-2
January 4, 2017

Mathematical reasoning
p = rain does not come q = crops are ruined and the people will starve p -> q You have ~q, so ~p (contrapositive) since q = r and s, ~r or ~s = ~q
January 4, 2017

Math
recall that (x+a)^2 = a^2+2ax+a^2 You have 2a = 16
January 4, 2017

Math
C and D divide BE into three equal parts. 1.64-(-2.83) = 4.47 4.47/3 = 1.49 So, now you know how much goes in each blank space.
January 4, 2017

Calculus
x23-5
January 4, 2017

Calculus
x&sup4;-5
January 4, 2017

Calculus
x&sup0;¹²³-5
January 4, 2017

Calculus
x&sup5;-5
January 4, 2017

Calculus
x^²-5
January 4, 2017

Calculus - incomplete
Fill in the missing text that did not get pasted
January 4, 2017

Math
well, sums are not directly related products and quotients, so I think more information is needed. I will note, however, that a product is just a short way to write a sum. 4*3 = 4+4+4 or 3+3+3+3
January 4, 2017

Math
Note that the two points lie on the same horizontal line: y = -6 Graph that line segment, and it will be clear where the other two points lie, since width+height=13
January 4, 2017

pre Calc
come on. A vertical line has the same x-coordinate everywhere. Look at the point it passes through. Vertical lines are of the form x=h Horizontal lines are y=k
January 4, 2017

pre calc
Looks like you need to review your Algebra I... 8x ? 3y + 6 = 0 3y = 8x+6 y = 8/3 x + 2
January 4, 2017

pre Calc
clearly the slope is -3.5 Now think f=mt+b
January 4, 2017

Number Theory
4x+7 = 2(mod 15) 4x = -5(mod 15) 4x = 10(mod 15) so, what can x be so that 4x = 5k+10 for some k?
January 4, 2017

precalc
you know that cos(u) might either decrease or increase, depending on u. surely t/52 increases when t does. !!
January 4, 2017

Math
x = -2 is a vertical line. So, what is the horizontal line through the point? x = -5 is parallel to x = -2, not perpendicular.
January 4, 2017

Math
F = ma just add up the vectors, after dividing by the mass.
January 4, 2017

Math
surely you can graph the lines y = 2/3 x y = -2 y = -3x+1 then just take the pieces you need.
January 4, 2017

Pre Calc
the slopes must be the same, so (8-1)/(2-a) = (1-6)/(a+2-12) a = 30
January 4, 2017

profit&loss mathematics
come on. B paid 20% of A's cost: 1.20A C paid what A did: B/1.20 = 08.3333B So, B lost 16.666 % maybe my math looks as funny to you as your texting does to me...
January 4, 2017

profit&loss mathematics
B = 1.20A C = A = B/1.20 = (5/6)B so, that is ...
January 4, 2017

Maths
?x^2 h = 800 h = 800/(?x^2) The area is two circles plus a curved cylinder, so a = 2?x^2 + 2?xh the result follows, so just find x such that da/dx = 0
January 4, 2017

mathematics
sorry - a=20 ! :-(
January 4, 2017

mathematics
you must be studying geometric sequences, so just note that this is the sum of the sequence with a = 12 r = 3/5 Now just use your formula for the infinite sum: s = a/(1-r)
January 4, 2017

am I right ? or no?
you are correct that b^x is growth if b>1 and decay if b<1
January 4, 2017

Maths
convert the area to m^2 area = length*width, so divide by the width to get the length
January 4, 2017

Maths
0.5ha * (10000m^2/ha) / 12.5m = 400m
January 4, 2017

algebra - duh @Reiny
It usually helps to read the problem carefully. Nice work, Reiny
January 4, 2017

algebra
x+y <= 9x-5y 6y <= 8x 3y <= 4x You might also want to consider x+y <= |9x-5y|
January 4, 2017

Maths
n = d-7 (n+2)/(d+9) = n/d (d-7+2)/(d+9) = (d-7)/d d(d-5) = (d-7)(d+9) d^2-5d = d^2+2d-63 7d = 63 d=9 check: original fraction: 2/9 modified fraction: 4/18 = 2/9
January 4, 2017

Maths
if you have a unix system, you can use the bc calculator for arbitrary precision, as well.
January 4, 2017

Math
1/4 of 2 cups is ??
January 4, 2017

math
((3200/1.60)/4)^2 * 1.20/100 = 3000
January 4, 2017

Math
there are 4 choices for each digit, so 4^4 total ways. 3/4 of them start with a number less than 7, right?
January 4, 2017

Math;);)
the two points lie on the unit circle, clearly 54-19 degrees apart. The angle is 35°. or, use the distance formula to find the vector u-v. Then use the law of cosines to find the included angle.
January 4, 2017

math
Just plug in n=5: a5 = 6*5-4 = ?
January 3, 2017

Math
well, the equations is (x-(2-3i))(x-(2+3i)) = 0 ((x-2)+3i)((x-2)-3i) = 0 (x-2)^2 + 3^2 = 0 x^2-4x+4 + 9 = 0 x^2-4x+13 = 0 a+b = -4+13 = 9
January 3, 2017

Math
try using letters like a,b,c instead of the special characters that are getting mangled.
January 3, 2017

maths
if x<0>=0 then 4/(x<0>)^2 is undefined. I'll assume that x<n+1> = 4/(x<n>^2+5) If so, then x<0> = 0 x<1> = 4/(0^2+5) = 4/5 = 0.8 x<2> = 4/(0.8^2+5) = 4/5.64 = 0.7092 ... The actual root ? 0.72408 If I got the formula wrong, then ...
January 3, 2017

maths
areas grow as the square of the linear factor. So the areas are A:B = (8:10)^2 = 64/100 = 16/25 A/160 = 16/25 A = 16*160/25 = 102.4 cm^2
January 3, 2017

math
tan(x) = h/d = 4d/d = 4 x = arctan(4) = 76° for part b, h decreases, because x decreases.
January 3, 2017

math
3^-n = 0.2 3^n = 1/0.2 = 5 (3^4)^n = (3^n)^4 = 5^4 = 625
January 3, 2017

Maths
V = 4/3 ? r^3 A = 4? r^2 = 3V/r = ?(36?V^2) Now just plug in your numbers.
January 3, 2017

Algerbra
He will need (253.5/6)^(3/2) * 2 = 549.25 kg of clay So, he will need 55 10kg bags
January 3, 2017

Surfaces of cones
?r?(r^2+h^2) = 2160? (12x)?(144x^2+256x^2) = 2160 (12x)(20x) = 2160 x^2 = 9 x = 3 so, the volume is ?/3 r^2h = (?/3) (24*3)^2 (16*3) = 82944? V = 82944 cm^3
January 3, 2017

Maths
just expand the left side. It will be the same as the right side. One way to start would be (3x-1)(x+5)(4x-3) = 3x(x+5)(4x-3)-(x+5)(4x-3) Now, (x+5)(4x-3)=4x^2+17x-15 so you can proceed with = 3x(4x^2+17x-15)-(4x^2+17x-15) = ...
January 3, 2017

Math
sorry - only one equation.
January 3, 2017

Math
useless problem. 6 apples - 2 oranges =
January 3, 2017

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