Monday
March 2, 2015

Posts by STEVE


Total # Posts: 29,297

Math
k^-3 = 1/k^3 So, you want 1/k^3 = 1/256 k^3 = 256 Now, 256 = 2^8, so k = 2^(8/3) = 2^2 * 2^(2/3) = 4∛4 Hmmm. we got trouble. (a) and (b) are out. 4^-3 = 1/4^3 = 1/64 64^-3 = 1/64^3 = 1/4096 I think that 1/256 is a mistake. Or, the -3 is a mistake. 16^-2 = 1/16^2 = 1/256 ...
January 7, 2015

Math
wow - use run-on sentences much? If the base is x by y and the height is z, just break the area into rectangles lateral area: 2(xz+yz) total area: 2(xz+yz+xy) Now just plug in your numbers. You didn't say which was which.
January 7, 2015

math
2/3 = 16/24 3/4 = 18/24 So, what do you think is in between them?
January 7, 2015

Math
5^13 = 5^6 * 5^7 The powers on the right can be any two numbers which add up to 13.
January 7, 2015

physics
how long does it take the dart to fall 0.32 m? 4.9t^2 = 0.32 with that t, find the distance is 13.5t
January 7, 2015

Algebra 1
2(x+y) = 100 But, y = 3x+2, so 2(x+3x+2) = 100 ...
January 7, 2015

math
20*2πr = 45*60 must be a wind turbine.
January 7, 2015

math
6C2 = (6*5)/(1*2) = 15
January 7, 2015

Algebra
remember that log x^n = n*log x So, log(4)(3x + 4)^5 = 15 5log(4)(3x + 4) = 15 log(4)(3x + 4) = 3 3x+4 = 4^3 = 64 3x = 60 x = 20 Expanding (3x+4)^5 would not help, because then you just have a polynomial, but the log of a sum cannot be simplified. log(x^2+3) is not log x^2 + ...
January 7, 2015

Math
Assuming you mean (1+2x)/(x+4) = 3/(x-1) (1+2x)(x-1) = 3(x+4) 2x^2 - x - 1 = 3x + 12 2x^2 - 4x - 13 = 0 Now it's just a regular old quadratic equation to solve. Note that right from the beginning you have to exclude -4 and 1 from the domain.
January 7, 2015

Math
2x^2-2 = 2(x-1)(x+1) 2x^2-8x+6 = 2(x-1)(x-3) Now rewrite your fractions with the factors, put all over a common denominator of 2(x-1)(x+1)(x-3) and simplify the numerator. Probably something will cancel out. Non-permissible values are those that make any denominator zero.
January 7, 2015

Math
#1 I haven't followed the argument through yet, but I think if you play around with 0 < a < 1 (x+1)^a <= (x+1)^1 x^a + ax^(a-1) + ... + ax + 1 <= x+1 things will work out.
January 7, 2015

MATHS
well, (42)^2 - (38)^2 - (17)^2 = 31 so that should get you started...
January 7, 2015

maths
well, you have a = π/2 r^2 θ So, plug in a and r to find θ, and then you know that the arc length s = rθ Or, do it at one fell swoop: s = r(2a/(πr^2)) = 2a/πr
January 7, 2015

Maths trigonometry
secAcotB-secA-2cotB+2=0 secA(cotB-1) + 2(cotB-1) = 0 (secA+2)(cotB-1) = 0 Now it should be clear what the angles are.
January 7, 2015

Math
yes, as long as x≠1 (1-x) = -(x-1), so you have -x^2(x-1) ------------- (2x-3)(x-1) and the x-1 factors cancel.
January 7, 2015

Algebra
well, does it work in both equations x-3y = -5-3*2 = -11 ≠ 1 So, I'd say a resounding NO.
January 7, 2015

Algebra
the 2nd equation says that y = 2x-4 So, substitute that into the 1st to get 2x + 4(2x-4) = -2 Surely you can solve that, and then find y ...
January 7, 2015

Math
p' = 1-p that should get you started.
January 6, 2015

algebra
11x + 11(x+1) > 100 11(x+1) + 11(x+2) < 200 22x > 89 22x < 167 4.04 < x < 7.59 So, the numbers can be 55 66 77 66 77 88 77 88 99
January 6, 2015

math
I can't find the integers until you clarify what the difference between five times the greater even integer is 14 means
January 6, 2015

Math
To find the x-intercept, set y=0 and you have 1.8x = 6.3 x = 3.50 Now do similarly to find the y-intercept. Set x=0.
January 6, 2015

math
The wall is 174 x 66 x 6 inches. That is 29 x 16.5 x 3 bricks. If we have to round up (no partial bricks reused), then that is 29 x 17 x 3 = 1479 bricks.
January 6, 2015

PHYSICS NEED HELP ASAP
157-75 = 82 km/hr = 22.78 m/s -22.78m/s ----------- = 3.25 s -7.00 m/s^2 so, now just use your motion formula. 157 km/hr = 43.61 m/s, so s = Vo t + 1/2 at^2 and plug in your numbers.
January 6, 2015

math
You know that the sets of numbers have to range from 2 to 8 to satisfy the max and range requirements. Half of them must be greater than 5 and half must be less than 5. 6 must occur most frequently. So, starting with a small set, we could start out with 2 5 6 6 8 Since there ...
January 6, 2015

hvac
Assuming a constant voltage, then since E = IR is constant, (1.2)(240) = I(540) Now it's easy to find the new current.
January 6, 2015

Finite Math
just solve for r in 24000(1+r)^5 = 34616
January 6, 2015

math-algebra
yes, (3a^5)^2 = 9a^10 6x^2 * 12x^3 = 72x^5 Why did you assume x=5?
January 6, 2015

Math
well, 10x^2+3x-1 = (5x-1)(2x+1) now the rest is a cinch.
January 6, 2015

math
If there are x quarts of 2% fat, then the rest (40-x) is 7%. So, just add up the fat content: .02x + .07(40-x) = .05(40) x = 16 Looks like (B) to me. You can actually get the right answer without even doing the math. C and D are clearly out, since the total is not 40 quarts. ...
January 6, 2015

Bosaso
You can do all kinds of fun Z table stuff at http://davidmlane.com/hyperstat/z_table.html
January 6, 2015

math
9.5 * 11.00 * 1.07 = ?
January 6, 2015

physics
Let the two forces be ax and by a^2+b^2 = 25 a^2 + b^2 - 2abcos120° = 37 or a^2+b^2+ab = 37 ab=12 So, it looks like the two forces are 3kN and 4kN
January 6, 2015

maths
I have a bit of trouble deciphering just what you mean, but my best guesses are 4x + 4x + 2-3y+8 = 8x-3y+10 or 12x or 3(2-3y+8) = 30-9y
January 6, 2015

physics
conserve momentum: 70*(+5) + 5(-20) = (70+5)v v = +10/3
January 6, 2015

math
If the bottles numbered w,x,y,z respectively, then we have w+x+y+z = 20840 w = 8120 y = 3960 x = y+2000 Now you can solve to find z.
January 6, 2015

math
GCF(30,48,72) = 6
January 6, 2015

math
clearly a painter can paint 1/180 of the job in one day. So, 20 painters can paint 20/180 = 1/9 of the job in a day, making the total 9 days. So, it takes 3 days less. Not also that you could reason that if the number of painters is increased by a factor of 5/4, the time taken...
January 5, 2015

Physics
since c=18, r = 18/2pi Now look at the fountain sideways. The height h can be found by noting that h/r = tan 55.0° Now just figure h.
January 5, 2015

math
n = 5*35
January 5, 2015

geometry
The height is 24tan63° + 24tan38°
January 5, 2015

math
hey - let's learn the distributive property! 6x6 = (5+1)x6 = 5x6 + 1x6 = 30+6 = 36
January 5, 2015

math
1+2 = 4-1
January 5, 2015

Math
well, we have aq = 2(pq), so 7x+6 = 2(3x+5) x = 4 ab = 3(pq) = 3(17) = 51
January 5, 2015

Math
((x + 2)/5) + ((3x - 4)/10) 2(x + 2)/10 + (3x - 4)/10 (2x+4 + 3x-4)/10 5x/10 x/2 I think you forgot to divide by 10 at the end.
January 5, 2015

Math problem solving
Clearly the maximum area is when four of the sides of the octagon are along the sides of the square. Thus, that leaves us with four unused triangles, each of side s where s/√2 + s + s/√2 = 750 s = 750/(1+√2) The area of each such triangle is thus (750/(1+&#...
January 5, 2015

Math
Looks like 12 and 15 to me
January 5, 2015

exponents ,factor,fraction
is there supposed to be a "c" in the expression? Whatever, just plug in the numbers for the letters and evaluate. Show your work in case of trouble.
January 5, 2015

distance
I get |2+9/4|/√(1/16 + 1) = (17/4)/√(17/4) = √17/2 To see how, take a look at http://en.wikipedia.org/wiki/Distance_between_two_straight_lines
January 5, 2015

Math
20+8y-9y-21 = -y-1 Now check the others: 2(10+4y-7y-19) = 2(-3y-9) = -6y-18 Nope and so on Hint: try grouping for #D
January 5, 2015

algebra 1
well, did you try actually checking the possibilities? 21 > 16+2 yes 21 < 16+5 no and so on for the others
January 5, 2015

Mathematics
ln u^n = n * ln u ln u*v = ln u + ln v ln u/v = ln u - ln v Better review the basic properties of logs.
January 5, 2015

algebra
I assume you mean +17/22 though "opposite" is a vague term with no precise mathematical meaning.
January 5, 2015

Solid mensuration
since a = 1/2 r^2 θ, just plug in π/3 and 6, and calculate a = (1/2)(36)(π/3) = 6π
January 5, 2015

math, solving Oblique Δ
A+B+C=180°, so C=115° Now use law of sines: b/sin49° = c/sin115° = 10/sin16° #2: sin88°/8 = sinB/7, so B = 61° or 109° But, since A=88°, B cannot be 109°, so there's no ambiguous case here. Now you know A and B, so you can find C and...
January 5, 2015

algebra
You just want to find x/y. I'll do #3, as the first two are trivial. xa+xb = yc+yd x(a+b) = y(c+d) x/y = (c+d)/(a+b)
January 5, 2015

algebra
the amount of gold in each alloy is the %age times the total mass: .10x + .30y
January 5, 2015

math
You have the answer. Did you guess it, or calculate it? You know that even numbers are multiples of 2 (2k), so odd numbers are of the form 2k+1. So, you want 2k+1 + 2k+3 + 2k+5 - (2k+3) = 50 4k+6 = 50 4k = 44 k = 11 So, the numbers are 23,25,27
January 5, 2015

Mathematics
just figure the difference between the outside and inside volumes: V = πr^2 h, so you want π(10.4+0.8)^2(25) - π(10.4^2)(25) = 25π(11.2^2-10.4^2) = 432π
January 4, 2015

Calculus
If the balloon is at height h, then the distance z from the child to the balloon is z^2 = h^2 + 40^2 When h=30, z=50 So, now we want dz/dt when h=30 2z dz/dt = 2h dh/dt Just plug in z=50 and h=30 and dh/dt=5 and solve for dz/dt
January 4, 2015

Algebra I
as with all word problems, translate the words to symbols. Then you have equations which can be solved. If there are a adult and c child tickets, you have two sets of facts: the number of tickets and their cost. c + a = 64 1.00c + 2.50a = 109.00 Now you can use your math ...
January 4, 2015

computer science check
The above comment refers to the actual syntax of the program. During the design, however, it is quite common to write the calls first, as that sets up the program flow of logic. Then the function definitions fill in the details.
January 4, 2015

computer science check
The languages vary, but in the strictest case, functions must be defined before they can be called, so A is my choice.
January 4, 2015

physics
they absorb most light except in the orange wavelengths, which they reflect back to our eyes. Now, as to the physical/chemical properties of the "carrot" molecules which cause that behavior, I have no clue.
January 4, 2015

Pre-Calc
well, geez. when t=8, y=33+30cos(0) = 63 Isn't that what you wanted, the max height at t=8?
January 4, 2015

Pre-Calc
since cos(kt) has its max at t=0, and you want your max at t=8, then using your correct amplitude and period, we have y = 33 + 30cos((pi/8)(t-8)) So, now just plug in t=5 to answer the question. You can see the graph at http://www.wolframalpha.com/input/?i=33%2B30cos%28%28pi%...
January 4, 2015

Algebra 1
visit calc101.com and click on the "long division" button. It will show all the details.
January 4, 2015

Pre-calc/Trig
well, recall that a parabola with vertex at (h,k) is y-k = a(x-h)^2 and for the focus, take a peek at http://www.purplemath.com/modules/parabola.htm
January 4, 2015

Trig/Precalc
(a) Try using the product-to-sum formula cos(a)cos(b) = 1/2 (cos(a-b)+cos(a+b)) (b) We have tan x/2 = (1-cosx)/sinx tan 15 = (1-cos30)/sin30 = (1-√3/2)/(1/2) = 2-√3 sin15 = √((1-cos30)/2) = √((1-√3/2)/2) = √(2-√3)/2 sin15 = √((1+...
January 4, 2015

Pre-calc/Trig
(a) as y increases, x increases, so it opens to the right
January 4, 2015

math
Since P(x) = R(x)-C(x) P'(x) = R'(x)-C'(x) max profit occurs where R'(x) = C'(x) Since you have R' and C', you can see that C(x) = x^3-59x^2+1315x + 5000 R(x) = 1000x-2x^2 + k no idea what k is, since you don't specify what R is for any ...
January 4, 2015

Errrr.
billy: "no" to which question? If you mean "no, he does not have to follow the grid (that is, travel only horizontally or vertically)," then Reiny's comments (Thanks for stepping up, Reiny) solve the problem If you mean "no, he cannot travel ...
January 4, 2015

Math
did he have to follow the grid, or could he take diagonal shortcuts?
January 4, 2015

Math
t = s+8 (s-3) = 2 + (t-3)/3 Now just solve for t. s = t-8, so (t-8-3) = 2 + (t-3)/3 t-11 = 2 + (t-3)/3 t-13 = (t-3)/3 3t-39 = t-3 2t = 36 t = 18
January 4, 2015

Maths
10y+x = 9(y+x)
January 4, 2015

Algebra 1
x+y = 10 x = 2/3 y Surely you know that 4 is 2/3 of 6 3 is clearly not 2/3 of 7 What do you care about 2/3 of 10? That was not part of the problem. The key to word problems is taking the given facts and expressing them in math symbols. It appears that you did not do that, but ...
January 4, 2015

Derivative
∫(4x^2+3)/x^2 dx = ∫4 + 3x^-2 dx And you know that ∫x^n = 1/(n+1) x^(n+1) (b) is the same thing. Just expand into a polynomial, then integrate the powers term by term. If you have no foundation in derivatives, it's curious that you've been assigned ...
January 4, 2015

maths
Just recall the power rule. y = x^n y' = n x^(n-1) (a) y' = 3(2x)-3(1) = 6x-3 For (b) and (c), just expand the polynomials, do the division as required, and then apply the power rule for each term
January 4, 2015

Derivative
g(x) = 5x^6 - 3x^-2 Just apply the power rule 3 times to get g(3)(x) = 5(6*5*4x^3) - 3(-2)(-3)(-4)x^-5 = 600x^3 - 72x^-5 Now take that two more steps for g(5)(x)
January 4, 2015

Maths
just use your facts about such sequences: a+5d = 48 6/2(a + a+5d) = 300 Now just solve for a and d.
January 4, 2015

math
<2 = 180-115 = 65 co(<2) = 90-65 = 25 or, make a general rule for the complement of any angle's supplement: 90-(180-x) = x-90 115-90=25
January 4, 2015

Math
Since 65 = 5x13, try that to see whether it fits the required perimeter. Only A and D could even possibly be a choice.
January 3, 2015

algebra word problem
just solve the equation when y=0. Just a normal quadratic solution.
January 3, 2015

Geometry
since AC=BD, 8x-10 = 2x+20 Now solve for x and evaluate BD=2x+20
January 3, 2015

Geometry
No, because 2/3 (x-6) = 2/3 x - 4
January 3, 2015

Geometry
2y+3x=6 has slope -3/2 So, the line you want has slope 2/3 ow you have a point and a slope, so the new line is y-5 = 2/3 (x-6)
January 3, 2015

algebra
well, just plug in 7a for all the x's: f(7a) = 3(7a)^2 + 8(7a) + 6 Now just evaluate the coefficients of powers of a.
January 3, 2015

constitution
Hmmm. How about <PRE> in upper case? </PRE>
January 3, 2015

constitution
let's see what <pre> text can look like </pre>
January 3, 2015

math
so ...
January 3, 2015

math
32x^2+9y^2=324 3y^2-x^2=3 Since 3y^2 = x^2+3, we have 32x^2 + 3(x^2+3) = 324 I think you can solve that fairly easily, right? The intersections are at x=±3, y=±2. See the graphs at http://www.wolframalpha.com/input/?i=plot+32x^2%2B9y^2%3D324%2C+3y^2-x^2%3D3
January 3, 2015

physics
A = (3.5,3.5) B = (6.1,-3.5) C = (-2.0,-3.5) Now just add up the (x,y) components and convert back to magnitude and direction form.
January 3, 2015

Calculus
∫csc x cot^2 x dx = ∫csc x (csc^2 x -1) dx = ∫csc^3 x dx - ∫csc x dx You probably have handy the form for ∫csc x dx, and you can use the power reduction formulas for ∫csc^3 x dx, or note that d/dx (cscx cotx) = -csc^3 x - csc x cot^2 x
January 3, 2015

CALC AB
profit is revenue minus cost, or x*p(x) - c(x) = x(18-x/400)-(820+5x+0.01x^2) = -0.0125x^2 + 13x - 820 That's just a parabola, with its vertex at x = -b/2a = 520 work #2 the same way. Figure a quantity and a price in terms of x, the number of $10 rebates. Then, revenue is ...
January 3, 2015

Math Linear Equations
c'mon. The lines intersect where the functions are equal: -2 = 3x+1 Now find x, and you know darn well that y = -2, since one of the lines is y = -2 for any x. y = -2 is a function of x, like any other linear function. It just so happens that no matter what x is, y = -2! y...
January 2, 2015

AP CaLC. AB
Assuming you know that max/min problems involve finding when f'(x)=0, #1 If the base of the ladder is x feet from the fence, and the height up the wall is y, then the length z of the ladder is z^2 = (x+7)^2 + y^2 and using similar triangles, y/(x+8) = 8/x Now you can ...
January 2, 2015

equation and inequalities
In n games, he will chew 17n sticks of gum
January 2, 2015

math
well the price 2p for the 2 CDs produces 1.49 sales tax, so .05(2p) = 1.49 Now you can find p.
January 2, 2015

math-algebra HELP!!!!
do you not have a linear regression tool for finding a line of best fit? Use it, then the answers should be clearer. Just eyeballing the data, we can first sort it: 32 72 34 76 35 75 37 77 37 78 42 81 46 88 Looks to me like I'd expect about 44 chirps at 85°
January 2, 2015

Calculus
well, you know that critical points occur when h'(x)=0. So, we want 3x^2+b = 0 at x=2. So, b = -12 That means that h(x) = x^3-12x+d h(2) = 8-24+d = -4 So, d = 12, giving us h(x) = x^3-12x+12 The graph is at http://www.wolframalpha.com/input/?i=x^3-12x%2B12+for+x%3D0..3 ...
January 2, 2015

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