Tuesday
September 23, 2014

Posts by STEVE


Total # Posts: 25,187

math
I'll do #1. You can try the others. 625 = 5^4, so f(x) = 1/5^x or 5^-x
September 3, 2014

calculus
As usual, draw a diagram. If x is the distance of the beam from the perpendicular line to the wall, then x/8 = tanθ x = 8tanθ So, dx/dt = 8sec^2θ dθ/dt When θ = π/6 (and that's pi, not pie!!) dx/dt = 8(4/3)(20*2π) = 1280π/3 m/s
September 3, 2014

calculus
Draw a diagram. d^2 = x^2+6^2 2d dd/dt = 2x dx/dt When d=10, x=8 Now plug in your values.
September 3, 2014

calculus
this is exactly analogous to your other problem with the revolving spotlight. See what you can do for it. Here, you are solving for dθ/dt instead of dx/dt.
September 3, 2014

Root Words
well, ambi- means two, so I guess that is more than one. I'd give my right arm to be ambidextrous!
September 3, 2014

Algebra
2√18 - 5√32 + 7√162 2√9√2 - 5√16√2 + 7√81√2 I think you can take it from here, no?
September 3, 2014

Math
I'd say any 5-digit number is greater than any 4-digit number.
September 3, 2014

Math
3% = 0.03 1/4 % = 0.0025 The proposed answer is incorrect, and so is yours. I think, however, that yours is a typo.
September 3, 2014

math
all polynomials have domain of all reals No polynomial has any kind of asymptote x^2-6x+5 = (x-3)^2 - 4 So you can find the vertex, which is a minimum. Since the vertex is farther away from x=-1 than it is from x=6, f(-1) > f(6) Since f(3-x) = f(3+x), it is evidently not 1:1.
September 3, 2014

algebra
If the dimensions are x and y, 2x+y=120 xy = 1350 Solve that to get x and y. There are two possible solutions. Note that the area is xy = x(120-2x) = 120x-2x^2 That's just a parabola. The vertex represents the maximum area.
September 2, 2014

math
for any color, just divide its number by the total to get the fraction desired.
September 2, 2014

math
have you no calculator? or, just type that into google for any calculations. You might want to use / for division.
September 2, 2014

math
of course it is. It's just a different proportion.
September 2, 2014

math
c = .026*60000 + .034*(89400-60000) = 2559.60
September 2, 2014

Numerical Analysis
consider the table for the two functions shown x f(x) g(x) -5 -350 0 -4 -176 1 -3 -72 2 -2 -20 3 -1 -2 4 0 0 5 1 4 6 2 28 7 3 90 8 4 208 9 5 400 10 It is clear that f(x)=g(x) somewhere in [1,2], since f(x)<g(x) when x<1 and f(x)>g(x) when x>2. Or, if you rearrange ...
September 2, 2014

Math
1.2^0 / 1.8^2 = 1/1.8^2 I suspect a typo, as we haven't really gone anywhere.
September 2, 2014

Calculus
If we call A's position at noon (0,0) then we have the positions of A and B after t hours A: (12t,0) B: (0,60-9t) The distance is thus d^2 = (60-9t)^2 + (12t)^2 = 225t^2-1080t+3600 At t=2, d=√(42^2+24^2)=√2340=48.37 So, at any time t, 2d dd/dt = 450t-1080 Now ...
September 2, 2014

Math
Perimeters are in the same ratios as the sides. You are unclear which rectangle is which, but I am assuming the larger one has perimeter 65, so the smaller one has perimeter 65 * 2/5 = 26 You are correct.
September 2, 2014

Math
Doesn't matter how many squares there are. The board is square, so each side is √11 = 3.3 cm must be a travel set. I suspect a typo.
September 2, 2014

Calculus
any line through (8,4) in the first quadrant is y-4 = m(x-8) So, if the line in question has slope m, the x-intercept is 8-(4/m) and the y-intercept is 4-8m So, L = √x^2+y^2 = √((8-(4/m))^2 + (4-8m)^2) = -4/m √((m^2+1)(2m-1)^2) Of course, there are other ways...
September 2, 2014

algebra
assuming any partial tiles are thrown away, the floor is 16 x 6 tiles So, 96 tiles are needed So, 5 boxes of 20 must be purchased, for $270
September 2, 2014

Algebra 2
If you will enter your expressions at wolframalpha, you can check your answers. Be sure to use enough parentheses so things are right. The web site will show you how it interprets your input.
September 2, 2014

MATH
start out with x x x x x minimum=5: 5 x x x x range=7: 5 x x x 12 median=9: 5 x 9 x 12 Now you can fill in any other values fitting in those intervals.
September 2, 2014

math
do you not have a calculator? Just add the numbers. Heck, you can even just enter 21456+9087 into google and it will calculate the sum.
September 2, 2014

Algebra 2
a - 2a/5 = 3 you have to multiply everything by 5: 5a - 2a = 15 You only multiplied the -2a/5 and the 3.
September 2, 2014

Algebra1
I assume you want the value for C. When you have an equation, as long as you do the same thing to each side, it remains true. So, C+4 = -24 You want C by itself, so if you subtract 4 from both sides, you have C+4-4 = -24-4 4-4=0, and of course, C+0 is just C, yo now you have C...
September 2, 2014

math
what's to explain? Write the facts in symbols: p^2 + (p+5)^2 = 625 Now just solve for p and find p+5
September 2, 2014

Algebra
$/ml is what we want. So, of course, that means that x $ / y ml = x/y $/ml = z $/ml z = x/y
September 2, 2014

Algebra 1
you are correct. Keeping the units around can help with this kind of problem. 15 gal * y mi/gal = x mi Note that the gal units cancel, leaving mi on both sides of the equation. If the units agree at the end, chances are good that your calculations are correct.
September 2, 2014

Algebra 1
just convert everything to decimal, and then the listing is easy, right? -√9 = -3 is a rational number. As such, it is, of course, also real.
September 2, 2014

Algebra 2
1: correct 2: (∞,3]U(5,11] all values less than or equal to 11, except those greater than 3 and less than or equal to 5.
September 2, 2014

college algebra
(x^2+x-6)/(x^2-4) = (x-2)(x+3) / (x-2)(x+2) Now divide that by (x+3) / 2(x+2) or, equivalently, multiply by 2(x+2)/(x+3) Lots of factors cancel.
September 2, 2014

college algebra
since x^2-x-12 = (x-4)(x+3), just multiply top and bottom by (x-4) x/(x+2) + (4x-3) / (x+2)(x-2) requires a common denominator of (x+2)(x-2). So, just multiply the first term top and bottom by (x-2) and then just add the numerators.
September 2, 2014

math
width: w length: w+4 2(w + w+4) = 84 Now just solve for w and calculate w+4.
September 2, 2014

math
c(1+.60) = 2000 Now just solve for c.
September 2, 2014

math
The side shortened least is longest, so (x-14)^2 + (x-13)^2 = (x-12)^2 Now, we all know that the 3-4-5 triangle is the only one with sides which are consecutive integers. So, x-14=3, making x=17. Solving the equation gives the same result.
September 2, 2014

math
what's to explain? Write the facts in symbols: p^2 + (p+5)^2 = 625 Now just solve for p and find p+5
September 2, 2014

math
(x+y)y = 70 (y-x)x = 12 now proceed
September 2, 2014

algebra
good work. Just for the future, recall that the domain of all polynomials is all real numbers.
September 2, 2014

math
221 = 13*17 you can use that to answer your question, rather murkily stated.
September 2, 2014

Physics
try C(x) = 4.00 + 0.40⌈10x⌉
September 1, 2014

Geometry
clearly, HJ+JK=HK, so x/4 + 3x-4 = 22 now just solve for x and evaluate the distances
September 1, 2014

KIPP Believe
divide the 740 into 20 equal parts of x each. There are thus 17x students and 3x faculty. So, 17x+3x=740 20x=740 x=37 So, there are 17*37 = 629 students 3*37 = 111 faculty
September 1, 2014

Math Proof
we want to show that |x1 + x2 + ... + xn| <= |x1| + |x2| + ... + |xn| Let's take n=3 We know that the inequality holds for n=2, so now we have |(x1+x2)+x3| <= |(x1+x2)| + |x3| But, we already know that |x1+x2| <= |x1|+|x2|, so we now have |x1+x2+x3| <= |x1|+|x2...
September 1, 2014

Math
Only the student can tell what was intended. We've provided two solutions, so our work is done here.
September 1, 2014

Math
Not quite 9^(1/2) = 3 but (n^4)^(1/2) = n^2 so the answer is 3n^2
September 1, 2014

Math
looks good to me.
September 1, 2014

MA 112
for a proportion, the two ratios must be equal So, a = a+b which can only happen if b=0. But, we cannot divide by zero, so a/b and (a+b)/b would both be undefined.
September 1, 2014

math
the numerator is a whole number, and it is multiplied by the other whole number.
September 1, 2014

Math
I get x^2+x-6 in the numerator, so better double-check your math.
September 1, 2014

Math
If there were x liters to start, then we have the following table: month water at end of month 0 x 1 x/2 + 1 2 (x/2 + 1)/2 + 1 = x/4 + 3/2 3 (x/4 + 3/2)/2 + 1 = x/8 + 7/4 ... n x/2^n + (2*2^n-2)/2^n = (x + 2*2^n-2)/2^n So, at the end of the 5th month there were (x+62)/32 = 4 x...
September 1, 2014

math
A. You can factor out 3/√x to get 3/√x (x^2-3x+2) 3/√x (x-1)(x-2) Or, if you don't want that extra 1/√x, now you can divide by it to get 3(√x - 1/√x)(x - 2) or 3(x-1)(√x - 2/√x) B. xy(x^2-4) xy(x-2)(x+2)
September 1, 2014

math
what is #x ?
September 1, 2014

algerbra
okay - your turn. Check the solutions to your other problems, and take a stab at it.
September 1, 2014

algerbra
Hint: graph the two lines. Note where they intersect.
September 1, 2014

algerbra
Using elimination, double the first equation and rearrange things a bit to get 6x+4y = 8 5x-4y = 3 Now add them up and it's clear that 11x = 11 and the rest is easy
September 1, 2014

math
If x at 10%, the rest (8900-x) at 9%, then calculate the interest: .10x + .09(8900-x) = 831 x = 3000
September 1, 2014

math
You need the Binomial Theorem: (a+b)^n = a^n + n a^(n-1) b + ... So, you have (3x-2)^3 = (3x)^3 - 3(3x)^2(2) + 3(3x)(2^2) - 2^3 = 27x^3 - 54x^2 + 36x - 8 (4x+5)^2 = (4x)^2 + 2(4x)(5) + 5^2 = 16x^2 + 40x + 25 Subtract them to get 27x^3 - 70x^2 - 4x - 33
September 1, 2014

MA112
Look at the common factors on both sides d(a-b) = b(c-d) What you want to do now is unclear, but go for it.
September 1, 2014

math
as with the other, just plug in the value for x: -2(4^2) + 5(4) - 10
September 1, 2014

math
That would be 3(-2)^2 - 2(-2) + 5 = 3(4)+4+4 = 20
September 1, 2014

algerbra
If there are no typos, then 8 = 6x-4 means x=2 So, that means that -3(2)-4y=2 y = -2
September 1, 2014

algebra
the equation for the height is h = 80 + 960t - 16t^2 As you recall, the vertex (maximum height) is at t = 960/32 = 30 Now just figure h(30)
September 1, 2014

math packet
(4)(-3/5)(10/-9) = -120/-45 = 8/3
September 1, 2014

math
one of my favorite sequences. Thanks for sharing.
September 1, 2014

math
just solve for p in -2000p² + 2000p + 1700 = 5000 The problem is that D has a maximum of 2200 when p = 0.5 I suspect a typo somewhere. Is D the monthly demand, or the weekly demand?
September 1, 2014

math
x^2 + (x+4)^2 = 20^2 Think of a scaled-up 3-4-5 triangle.
September 1, 2014

Algebra 2
Rearrange things a bit and you have 2m^2-8m + 6n^2-5n^2 2m(m-4) + n^2 It's kind of a strange problem; is there a typo in there somewhere?
September 1, 2014

PRE CALC
Just list the facts as given: u+f+t = 39 t = u-16 u+5f+20t = 208 Now just solve as usual
August 31, 2014

math
length=2w 2(w+2w) = 60 ...
August 31, 2014

math
If q quarts are to be drained, then .40(12-q) + 1.00q = .60(12) ...
August 31, 2014

algebra
S = P(1 - 0.25)
August 31, 2014

stats
since 2500 is exactly the mean (0 std away), look up P(Z < 0) in your standard table. Or, just consider the data and pick what seems reasonable in that case.
August 31, 2014

math
If x L are added, then .01(40) + .04x = .02(40+x) ...
August 31, 2014

Math
see related problems below
August 31, 2014

physics
(E).893J
August 31, 2014

Math
When you solve for a variable, you want it all by itself: P = I/rt r = C/2π
August 31, 2014

Algebra
#1 correct #2 If y=1, 4y-2=2 and 3*2 is not 18 You should have done 3(4y-2) = 18 4y-2 = 6 4y = 8 y = 2
August 31, 2014

AP Calc. AB
well, since -0 = 0 and -8 = -(8), it should not be hard to make the required change to the function I provided. I mean, you do remember your basic algebra, right?
August 31, 2014

AP Calc. AB
as x-> 0, 1/x -> ∞ 2^(-1/x) -> 2^-∞ = 0 when x>0 2^(-1/x) -> 2^∞ = ∞ when x<0 So, in those two cases, we have lim x->0+ = 8/(1-2^-∞) = 8/(1-0) = 8 lim x->0- = 8/(1-2^∞) = 8/-∞ = 0 http://www.wolframalpha.com/...
August 31, 2014

AP Calc. AB
a different problem was recently posted here where the left limit is 2 and the right limit is zero. Tweaking it a bit, we have (8)/(1-2^(-1/x)) which fits your criteria. If you can come up with any function where the left and right limits for some value of x are different, you...
August 31, 2014

Math Compounded daily
1450(1+.12/365)^(365*1) = 1634.84 Some problems specify that we use 360 days per year. In that case, change the expression as needed.
August 31, 2014

trigonometry
a circle of radius r has circumference 2pi r, so one lap = 6pi feet So, 20 laps = 120pi feet
August 31, 2014

Algebra 2
since distance = speed * time, (x+3.5)(5) = (x-3.5)(12) x = 8.5 Now you can easily show how far it went.
August 31, 2014

Algebra 2
distance = speed * time, so if the plane's speed is x and the wind speed is y, we have 4(x+y) = 5040 5(x-y) = 5040 x = 1134 y = 126
August 31, 2014

Math
to get the x-intercept, set y=0 and you have -5x = 10 to get the y-intercept, set x=0 and you have 2y = 10 Look at your graph.
August 31, 2014

Algebra
If the only possible value for x is 3, then the function must factor into (x+3)(x+3) = x^2+6x+9 When they say the only possible value, they mean the only value which makes the equation true. Naturally, x can have many other values, but in those cases, the value on the left is ...
August 31, 2014

Calculus
at time t hours, the distance d is d^2 = (60t)^2 + (35t)^2 when t=3, then, d=208.39 Since 2d dd/dt = 7200t + 2450t = 9650t at t=3, dd/dt = 28950/(2*208.39) = 69.46 km/hr
August 31, 2014

math
as usual, you need to find the common denominator. Assuming you meant 2/(m+3) + 1/m the LCD = m(m+3). So, you have (2m + m+3) / m(m+3) = (3m+3) / m(m+3) On the other, I think you have 2/((x+1)(x+2)) + 3/((x+2)(x+3)) so the LCD is (x+1)(x+2)(x+3). That gives you (2(x+3) + 3(x+1...
August 31, 2014

Calculus 2
Using shells, you have thickness dy, so v = ∫[1,3] 2πrh dy where r = y and h = x = 1/y v = 2π∫[1,3] y*1/y dy = 2π∫[1,3] dy = 2πy [1,3] = 2π(3-1) = 4π That strikes me as odd. Let's try discs (washers) of thickness dx. The ...
August 30, 2014

algebra
x + x-3 = 21 x = 12
August 30, 2014

Algebra 1
width: w length: 2w-3 after the changes, we have (2w-3-2 + w-1) = 24 Now just solve for w, the original width.
August 30, 2014

math
L+M=250 3/5 L = M-40 Now we can substitute for M, and we get 3/5 L = 250-L-40 8/5 L = 210 L = 131.25
August 30, 2014

math
rotation does not change lengths.
August 30, 2014

Algebra
12x^2+8x = 4x(3x+2) 9x^2-4 = (3x-2)(3x+2) I think you can see which factor cancels.
August 30, 2014

Math
If they get shares of x,y,z, respectively, then x = 2/3 y y = 1/4 z x+y+z = 1360 We want to know what y is, so substitute in for x and z: 2/3 y + y + 4y = 1360 17/3 y = 1360 y = 240
August 30, 2014

physics
dropped stone hits water: 24.4-4.9t^2=0 t=2.23 stone has fallen 6.6m: 4.9t^2 = 6.6 t = 1.16 So, Jill's thrown stone only has 2.23-1.16=1.07 seconds to hit the water: 24+1.07v-4.9*1.07^2 = 0 v = -17.19 m/s
August 30, 2014

Physics Help!!!!
total distance covered: 20+30+40=90m total time: 30s avg speed: 90/30 = 3m/s final displacement: 20-30+40=30m north avg speed: 30/30 = 1 m/s north
August 30, 2014

Physics
total distance covered: 20+13+10=43m total time: 45s avg speed: 43/45 = 0.96 m/s final displacement: 20-13+10 = 17m avg velocity: 0.38 m/s away from entrance
August 30, 2014

maths - 2nd take
what a lot of bother I went to above. The distance from (2,3) to (5,4) is √10. Since the circles are orthogonal at the intersections, the two given points and the centers of the circles form a square, with diagonal √10. So, the side of the square, which is the ...
August 30, 2014

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