Sunday
March 29, 2015

Posts by steve


Total # Posts: 30,152

math
∛(250z^4x^7) = ∛(125z^3x^6 * 2zx) = 5zx^2 ∛(2zx)
February 23, 2015

math 107
A: 22π + 2*60 B: if by "end section" you mean a semi-circle, π*11^2 If the triangle is included, then π*11^2 + 60*22/2 C: the diagonal of the rectangle has length √(60^2+22^2) = 2√1021 That should enable you to figure the triangle ...
February 23, 2015

math
assuming the points lie sequentially on a line, then AD = AB+BC+CD
February 23, 2015

calculus
Q: What do you get when you cross a mosquito with a mountain climber? A: Nothing -- you cannot cross a vector and a scaler.
February 23, 2015

Pre-Algebra
that is correct. So, you will have to describe things in detail, or provide a url for the diagram. Note that the real url is disabled, so you will have to be crafty. inserting some spaces or using the word "dot" might help.
February 23, 2015

Pre-Algebra
Having no diagrams to consult, no help can be given.
February 23, 2015

NIST banepa
depends on how long it takes to travel the 50 meters. Given a sufficient speed, it could reach any desired height.
February 23, 2015

Algebra 2
Since the nth swing has length 100*0.99^(n-1), you want to find n when 100 * 0.99^(n-1) < 50 .99^(n-1) < .5 (n-1) log.99 < log.5 n > 69.9 So, on the 70th swing the arc is less than 50 cm. Now you know the parameters for the geometric sequence. Just use the sum ...
February 23, 2015

algebra
polynomials have a domain of all reals numbers. rational functions, being the quotient of two polynomials, do also, with the exception of values where the denominator is zero. So, 1/-x has a domain of all reals except x=0 rational functions with linear denominators always have...
February 23, 2015

Vectors
Homework dumps generally get little help, unless you show how you tried and failed to solve the problem. I'll do this one, but you can't expect us to do your work. We did it for ourselves already. the dot product is only defined for two vectors. (a•b) is a scalar...
February 23, 2015

math
the area of the floor is 3*4 = 12 m^2 So, how many of those tiles fit into each square meter? draw a little picture and the answer will be clear.
February 23, 2015

math
pick any amount of mango juice you want. add 0.5 to that for the orange juice.
February 23, 2015

physics(waves)
You multiplied by 0.28s, but the period is 0.28 ms.
February 23, 2015

Vectors
well, what are the vectors I and B? they have given you the magnitudes and directions. Turn that into i,j,k components.
February 22, 2015

Vectors Math
a x a = 0
February 22, 2015

Trigonometry (Logarithmic Function)
so, log 24 = (1/2) log9 + 3 log2
February 22, 2015

Algebra
Try using the symbols = < > and <= >=
February 22, 2015

Math vectors
clearly, AF = 1/2 AB AE = AF + FE = AB/2 + BC/2 BC = 2FE Now, since AF+FE=AE, FE=AE-AF BC = 2(AE-AF) = 2(EC-AF)
February 22, 2015

Math
the curves intersect at (5,2) and (5,-2) So, the volume can be done using shells or discs. Using shells, consider the volume as a bunch of nested shells, each of thickness dy, radius y+2 and height the distance between the curves: (9-y^2)-(y^2+1) v = ∫[0,2] 2πrh dy...
February 22, 2015

Algebra
since the remainders are equal, 2312-1417 = 895 2312-1059 = 1253 1417-1059 = 358 are all multiples of y. The GCF of those is 179. Divide any of the given numbers by 179 and the remainder is 164. So, y-x = 179-164 = 15
February 22, 2015

Algebra
T15-T5 = 10d = 40 so, d = 4 Now you can find T1 and T60 Then the sum is 30(T1+T60)
February 22, 2015

math vectors
well, you need a•b = 0, so (2)(4)+(2k)(-k) = 0 . . .
February 22, 2015

Math vectors
that would be a•b/|b| = (5)(1)+(-5)(2)+(3)(3) ----------------------------- √(1^2+2^2+3^2)
February 22, 2015

Math
For the consecutive number stuff, it is always best to recall that 1+2+3+...+n = n(n+1)/2 Then you can multiply that and shift it in various ways. Or, you can remember your arithmetic series stuff, and recall that the sum of the first n terms of an A.P. is n/2 (T1+Tn) = n/2 (...
February 22, 2015

Math
42000(1+.03)^5
February 22, 2015

math
could be zero. blue stripe: 110 oz red stripe: 110 oz white stripe: 110 oz pink stripe: 20 oz red and 40 oz white There are not enough constraints to find a unique solution.
February 22, 2015

Math
use what you know about arithmetic progressions. 10/2 (2a+9*2) = 200 2a+18 = 40 2a = 22 a = 11 So, the numbers are 11,13,...29 check: 5(11+29) = 200
February 22, 2015

Math check
#1 ok #2 ok #3 ok #4 ok #5 8(180) = 1440 each angle is 144, not the sum.
February 22, 2015

Math
#1 n(n+1)/2 >= 2000 n^2+n-4000 > 0 n > 62.7 So, 63 days #2 clearly the sum must be even. sum = n/2 (24+(n-1)(-2)) http://www.wolframalpha.com/input/?i=n%2F2+%2824%2B%28n-1%29%28-2%29%29+for+n%3D1+to+50 #3 1-digit #'s: 3 teens: 13 20's: 23 30's: 30-33
February 22, 2015

math
what do you mean by "solve"? As it stands, there's not much to be done except expand the polynomial. (a+b)^3 = a^3 + 3a^2b + 3ab^2 + b^3 so, you have (3x)^3 + 3(3x)^2(-2y) + 3(3x)(-2y)^2 + (-2y)^3 = 27x^3 - 54x^2y + 36xy^2 - 8y^3
February 22, 2015

math
25
February 22, 2015

math
if the small base has side 2x, then each face of the pyramid is a trapezoid with area a = (2x+10)/2 * √((5-x)^2 + 30^2) So, to find the minimum area, da/dx=0 Unfortunately, this never happens. Have I set it up wrong? Since the height of each face is constant, and the ...
February 22, 2015

math
In the real world, one would normally subtract a smaller volume from a larger one. So, the volume in question is v = πh(R^2-r^2) when h=30 and r=10, v = π(625-100)(30) = 15750π cm^3 since the volume of water does not change, dv/dt = 0. So, (R^2-r^2) dh/dt + h(-...
February 22, 2015

Geometery
beats me -- where is N?
February 22, 2015

Math
if the first odd integer is 2k+1, then the others are 2k+3,2k+5,2k+7 So, adding them up you get 8k+16=48 k=4. the numbers are 9,11,13,15 Your idea is also good, but to guarantee odd numbers, you need even numbers+1. In some situations you might get a solution for x but find ...
February 22, 2015

AP CALC
You have to take f(x/2), not f(x). Thus, the derivative is 1/2 e^(-(x/2)^2) = 1/2 e^(-x^2/4) So, at x=1, the slope is 1/2 e^(-1/4) = 0.3894 So, it looks like (b) is the choice. See the graphs here: http://www.wolframalpha.com/input/?i=plot+y%3D%E2%88%9A%CF%80%2F2+*+erf%28x%2F2...
February 22, 2015

fractions
the toppings overlapped.
February 22, 2015

AP CALC
Then you get 97/3
February 21, 2015

AP CALC
I also got (e). However, that is an algebraic area, which includes the sign. If you want the geometric area, you have to split into two parts, because it crosses the x-axis at x=0.
February 21, 2015

calculus
I assume you meant y(t) = 19(1+e^(-cos(t)) so, v(t) = 19sin(t) e^(-cos(t)) v(1) = 19 sin(1) e^-cos(1) = 9.31 v(4) = 19 sin(4) e^-cos(4) = -27.64
February 21, 2015

math
take a look here http://www.wolframalpha.com/input/?i=y%22%27+%2B+4y%22+%2B+4y%27+%3D+e^%28-2x%29
February 21, 2015

Math
ok up to the last line. x = -5/17
February 21, 2015

math
time to review proof by induction. Assume the sum is true for k=n. Show that if it is, then it is also true for k=n+1 1 = 1(2)/2 So, it is clear that the equation is true for k=1. Now, assume it is true for k=n. That is, 1+2+...+n = n(n+1)/2 Now, add n+1 to both sides: 1+2...
February 21, 2015

math
That is just 1+2+...+n I'm sure you have seen that before.
February 21, 2015

Calculus
or, minus all that.
February 21, 2015

Calculus
recall that the derivative of csc u = cscu cotu du
February 21, 2015

Math
find the slope of L2 The slope of L1 is -1/(slope of L2)
February 21, 2015

Calculus
x∛(x-2) dx let u^3 = x-2 x = u^3+2 3u^2 du = dx now the integrand is (u^3+2)(u)(3u^2 du) and that's just a b unch of powers.
February 21, 2015

Math
T15-T5 = 10d = 40 so, d = 4 Now you can find T1 and T60 Then the sum is 30(T1+T60)
February 21, 2015

Math
5x+3y+12=0 has slope -5/3 So, our desired line has slope 3/5 (-6-3r)/(2+r-4) = 3/5 Now find r.
February 21, 2015

Trig application
If the fire is labeled F, then in ΔABF, the angles are A = 14° B = 34° If the altitude from F to AB meets it at point P, then h/AP = sin 14° h/PB = sin 34° so, AP = h/sin14° PB = h/sin34° AP+PB=30 h/sin14° + h/sin34° = 30 h(1/sin14°+1/...
February 21, 2015

Math
you can see from #2 that x = 3y+6. Plug that into #1 and you have 2(3y+6)+5y=15 Now find y, then you can get x.
February 21, 2015

Trig application
(A) 428nm/20knot = 21.4 hr the direction does not matter. You have a distance and a speed. (B) E: 20*12 sin 1.4° S: 20*12 cos 1.4° (C) Surely the same heading (not bearing!) as the yacht, no? Ignoring water currents and winds aloft.
February 21, 2015

maths
2.63*10^11 0.978*10^11 1.789*10^11 -------------- 5.397*10^11
February 21, 2015

physics
since PE = mgh, ΔPE = mgΔh
February 21, 2015

Math
A^2/(√3/4 (A/2)^2) = 16/√3
February 21, 2015

algebra
5 tests at 82 pts each requires 410 points. So, remove the lowest score, add up the others, and see how much more he needs to get to 410.
February 21, 2015

maths
after n years, we have A: 4500*1.10^n B: 4500+525n so, plug in n=3 and see which is greater, and by how much.
February 21, 2015

Math
or, you can think of it as 5+10+...+50 = 5(1+2+...+10) = 5*55 = 275
February 21, 2015

Math
you know that y = -3x-2, so 2x+3(-3x-2) = 5 Now you can find x, and then y.
February 21, 2015

maths
whene revenue > cost, then there's a profit. So, for p pies, we need 8p > 200 + 3p
February 21, 2015

physics
each vector has two components, most commonly in the x and y directions. So, you have v = <31.8,0> + <0,-31.8> = <31.8,-31.8> |v| = 31.8√2 = 44.97 m/s in a southeast direction, since tanθ = -31.8/31.8 so, the momentum p = mv
February 21, 2015

physics
it takes 6.0/9.7 = 0.619 seconds to reach speed. so, s = 1/2 at^2 You have a, and now t.
February 21, 2015

Calc
I get 492.4 on a heading of 205°
February 21, 2015

Pre ALGEBRA
Looks like B to me. a cone and a pyramid have exactly one base. a sphere has 0 bases, which is also 1 or less. A cube has 6 faces, any of which could be called a base.
February 21, 2015

math
let the center of the earth be (0,0,0) find the coordinates of Sudbury. That will give you the tip of the vector pointing out. The negative of that is the vector pointing in. Take a look at spherical coordinates and their transformation to rectangular. You could start here: ...
February 21, 2015

math
when the water is y down from the top, the surface subtends an angle θ, so the cross-section has area 1/2 r^2(θ - sinθ) where cosθ = y/r So, plugging in our numbers, v = (400)(1/2)(20^2)(arccos(y/20)-√(20^2-y^2)) v = 800(arccos(y/20)-√(400-y^2...
February 21, 2015

math
if the square has side s and the triangle has side t (both in cm), then 4s+3t = 400 a = s^2 + √3/4 t^2 Now just express t or s in terms of the other, and you have a quadratic for the area. The vertex of the parabola will give the minimum area. The maximum will be ...
February 21, 2015

maths
since 9 = 3^2, 9^x = 3^2x So, you have 3^(x+1) = 3^(2x) x+1 = 2x x = 1 On the other one, I will guess you mean 3^2 * m^-1 = 243 m^-1 = 27 m = 1/27
February 21, 2015

Maths
2.500001 x 10^6
February 21, 2015

math
200000/2500 = 80 So, there were 120 to start with How far do you get on the rest?
February 21, 2015

Math
since the distance covered by constant acceleration a is s = 1/2 at^2, we have 1/2 a*10^2 = 500 a = 10 cm/s^2 50 m/s is the average speed during takeoff, not the acceleration.
February 21, 2015

trigonometry- college
I interpret your language to mean that BC is 20° south of west. I assume that the two-hour cruise from A actually arrived at port C, meaning AC is 100 mi. In problems like this, the first thing to do is always to draw a diagram. If you cannot do that, you have no hope of ...
February 21, 2015

physics
you have the numbers and the formula. What's the problem? All you need is the person's mass: 700/9.8 kg
February 20, 2015

math
s = (a+b+c)/2 If you found Heron's formula, why did you not read its explanation?
February 20, 2015

Math/algebra
If there are 52 bears, and one is left over after forming groups, then 51 must have divisors that are the # of groups and the # of bears in each group. 51 = 3*17, so there are either 17 groups of 3 or 3 groups of 17 After that, there is 1 bear left over, making 52 in all.
February 20, 2015

grammer
Reed is on the right track. I think it might have been better presented as Last night, my brother ________ me a secret. And you can prolly lose the comma.
February 20, 2015

Calculus
Take a look at this site. The very first problem is one just like yours, but with different numbers. http://tutorial.math.lamar.edu/Classes/CalcI/Work.aspx
February 20, 2015

math
that is just like the previous one. Just review your text section on linear DE's. There must be examples just like your problem.
February 20, 2015

math
y"' - 3y" + 2y' = e^(2x) D(D-1)(D-2)(y) = e^2x y = (1/4)(c1)e^x + (1/4)(c2)e^(2x) + (1/2)xe^(2x) + c3
February 20, 2015

algebra
v = 1/12 pi d^2 h now plug and chug...
February 20, 2015

Math
recall the dot product u•v = |u||v|cosθ 3*4 + 2*0 = √13 * 4 *cosθ cosθ = 12 / 4√13 θ = 33.7° Or, you could notice that v is just along the x-axis, so tanθ = 2/3 θ = 33.7
February 20, 2015

Physics
Just add/subtract the given acceleration to gravity. Then as usual, F=ma, where a is the net acceleration.
February 20, 2015

AP calc
Take a look here. The first problem is just like this. http://tutorial.math.lamar.edu/Classes/CalcI/Work.aspx
February 20, 2015

Math
(7+5+8)/(7+8+5+9+8+5)
February 20, 2015

Math
1/4
February 20, 2015

College Alegebra
√(23^2-18^2)
February 20, 2015

Trigonometry (Coterminal Angles)
just keep adding 2π till you get a positive value. 2π = 6π/3, so you get -10π/3 + 6π/3 = -4π/3 + 6π/3 = 2π/3 and we have a winner!
February 20, 2015

MATHS
The three pumps work 3*8*2=48 hrs in 2 days, so one pump can empty 1/48 of the tank in an hour. 4 pumps can empty 4/48 = 1/12 of the tank in one hour. so, . . .
February 20, 2015

College Algebra
1000(1+.08)^3
February 20, 2015

math
On L1, as x increases by 3, y increases by 5*3, so (4,17) is on L1 The perpendicular line has slope -1/5, so L2 is y-17 = -1/5 (x-4) Now you can convert that to slope-intercept form.
February 20, 2015

math
the area will be 2.5 * 2.5
February 20, 2015

Math
40+.25m = 142.75
February 20, 2015

ged
google is your friend. You have not provided much information here to work with, I must say...
February 20, 2015

trignometry
Oops. I see where. Reiny did it right.
February 20, 2015

trignometry
1/(1-csc) - 1/(1+csc) = ((1+csc)-(1-csc))/(1-csc^2) = 2csc/cot^2 = 2csc tan^2 = 2/sin sin^2/cos^2 = 2sin/cos^2 = 2tan sec I seem to have lost a - sign. Hard to tell just what the original equation was.
February 20, 2015

Math
7% of the sample is white. So, what's 7% of 4150?
February 20, 2015

Math
false.
February 20, 2015

maths
for any rectangle, the area is length * width. So, get out your calculator and punch in your numbers. watch out for the units. you can't mix m and cm. For the cardboard with the border, the whole thing with border on 4 sides has area (120+10+10)^2 = 19600 cm^2 The inside ...
February 19, 2015

Algebra 1
assuming x is a function of y, note that x drops by 1/2 each time. Looks exponential
February 19, 2015

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