Saturday

February 28, 2015

February 28, 2015

Total # Posts: 29,284

**math**

if there is $x at 4%, then the rest (15000-x) is at 5%. Now just add up the interest and solve for x: .04x + .05(15000-x) = 690
*February 24, 2015*

**probability**

for both red, we need 2/(n-2) * 1/(n-1) = 1/28 n = 8 Now you can do the other part.
*February 24, 2015*

**math**

1.12j = 8400 j = 7500 j/a = 5/3 a = 3/5 j = 4500 (14100-8400)/4500 = 1.267 so, Akinyi's money grew by 26.7%
*February 24, 2015*

**math**

2θ = 60,330,420,690,... θ = 30,115,210,345,...
*February 24, 2015*

**math**

r = 23.4/1.8 = 13 a = 1/2 * 13^2 * 1.8
*February 24, 2015*

**math**

∛(4/3 π) * 4.2 = 6.77
*February 24, 2015*

**Vectors Math**

so, have you picked out three vectors?
*February 23, 2015*

**MATH**

x y 1 4 5 1 8 6 10 5 not linear, since y changes direction not quadratic, since y changes direction twice. So, guessing cubic, I find -109/1260 x^3 + 1961/1260 x^2 - 2333x + 3130 I doubt that is what you had in mind, but anything else would be even more complicated.
*February 23, 2015*

**Math**

age now is x. x = 3(x+3)-3(x-3)
*February 23, 2015*

**pre-cal**

sounds like a plan.
*February 23, 2015*

**Physics**

the height in meters is h(t) = (Vo sinθ)t - 4.9t^2 Now just find t when h=0. You sure overload the symbol 0.
*February 23, 2015*

**Geometry**

where is R?
*February 23, 2015*

**algebra**

4/(x+4) + 4/5 = 5/2 4/(x+4) = 5/2 - 4/5 4/(x+4) = 17/10 4 = (17/10)(x+4) 4(10/17) = x+4 40/17 - 68/17 = x -28/17 = x
*February 23, 2015*

**Math**

looks like it. Are any of the numbers used more than once?
*February 23, 2015*

**Math**

no. 2*0^2 = 0 2*1^2 = 2*1 = 2 2*2^2 = 2*4 = 8 2*3^2 = 2*9 = 18 what you have is (2x)^2, not 2x^2
*February 23, 2015*

**geometry**

or, equivalently, if the angle with the ground is greater than the angle with the wall. Because then the side opposite the greater angle is longer.
*February 23, 2015*

**geometry**

if the angle the ladder makes with the ground is greater than 45 degrees.
*February 23, 2015*

**Math**

There are 9 values, so the median is the 5th value, or 4. No idea when you say that there is no data in 5. If these numbers are like bins containing data, then you have to count the values in each bin, and then find the middle value.
*February 23, 2015*

**Vectors**

a+(b•c) is undefined. You cannot add a vector and a scalar.
*February 23, 2015*

**[Calculus] U-substitution for Integrals**

u = 3x-5, so du = 3 dx, not just 3 ∫[1,5] (3x-5)^5 dx = 55552 Now, subbing in for u, the limits of integration are not 0-12. Rather, we have 1/3 ∫[-2,10] u^5 du = 55552 Where did you get 165888?
*February 23, 2015*

**Math**

count the vehicles: b+s = 21 count the wheels: 2b+4s = 54 assuming scooters have 4 wheels. If they also have 2 wheels, then the problem is bogus.
*February 23, 2015*

**Calculus 2**

at height y from the bottom, the area of the surface of the water is (5/4)y*10 ft^2 So, the weight of a thin layer of water at that height is (5/4)y*10*dy *62.4 = 780y dy lbs So, the work to lift all the sheets of water at height y is ∫[1,3] 780y(4-y) dy = 5720 ft-lbs
*February 23, 2015*

**Math**

nope C is a right angle obtuse means greater than 90. So, (b) D is a straight angle.
*February 23, 2015*

**Algebra**

Take a look here: http://www.wolframalpha.com/input/?i=solve+2x-3y%3C6%2C+4x%2B4y%3C8+
*February 23, 2015*

**Algebra**

g(f) = 1/4 f - 3 = (3x+4)/4 - 3 = 3/4 x - 2 f(g(-2)) = f(-7/2) = -13/2 f(g) = 3g+4 = 3(x/4-3)+4 = 3/4 x - 5 f(g)=5 means 3/4 x - 5 = 5 3/4 x = 10 x = 40/3
*February 23, 2015*

**Math**

since the new prism has dimensions 1/2 the old one, its volume is 1/8 the old volume.
*February 23, 2015*

**Math**

the slope is (-2-5)/(9-5) = -7/4 y-5 = -7/4 (x-5) so, f(x) = -7/4 (x-5) + 5
*February 23, 2015*

**Math**

Not quite sure what's what here, but I'll take a stab at it. h(-6) = -1 so, if 3-x = -6: x = 9 j(9) = h(-6)+4 = 3 A' = (9,3)
*February 23, 2015*

**Math**

see related questions below
*February 23, 2015*

**algebra**

you want to solve for h where π/3 * 25^2 * 7.2 = π * 15^2 * h
*February 23, 2015*

**algebra**

just add the exponents and multiply the numbers. What do you get?
*February 23, 2015*

**alleged math**

I looked it up in the answer key!!
*February 23, 2015*

**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**

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*

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