Wednesday
November 26, 2014

Posts by steve


Total # Posts: 27,016

math
original price for x radios is 1200/x So, (x-6)(1200/x + 10) = 1200
November 6, 2014

math
look at the multiples of 4 0 4 8 12 16 20 ... You can also consider that since the second number is 1 times the row number, then the row is 4.
November 5, 2014

algebra help please
well, just plug in the value for t: t=5: 2200 + (-480*5) = 2200-2400 = -200 and do the others the same way
November 5, 2014

please help! algebra
clearly there is no constant difference. Check for constant ratio (-12)(-5) = 60 (60)(-5) = -300 ... we have a winner. SO, what is 1500 * -5 ?
November 5, 2014

Trig
well, if you insist on using tan, then note that the base of the slide is √(250^2 - 107^2) = 225.9 cm out from spot directly under the slide's top. So, now we have tan θ = 107/225.9 = 0.47 θ = 25.3°
November 5, 2014

Math, please help
subtract the area of the painting from the total area. If the matte has width w, then (10+2w)(15+2w) - 10*15 = 10*15 4w^2 + 50w - 150 = 0 2(2w-5)(w+15) = 0 w = 5/2 = 2.5
November 5, 2014

Math
no way to tell the perimeter from just the area. All we know is that the smaller dimension is greater than 1.7 m.
November 5, 2014

Help please Math
No, what you want is a(bc) = (ab)c multiplication is associative. It is also distributive over addition: a(b+c) = ab + ac Of course, if a=1, a(bc) = (ab)(ac) because 1(bc) = (1a)(1b) = bc
November 5, 2014

pre-algebra
Nope. It triples every 4 hours, so in 24 hours it has tripled 6 times: x * 3*3*3*3*3*3 = x * 3^6
November 5, 2014

chemistry
since PV=kT, PV/T is a constant. So, using the given numbers, (.14 atm)V/(271+48) = (756 torr)(.295)/(271+18) You will need to reconcile atm and torr, and then solve for the new V
November 5, 2014

Algebra
not much of a scenario. They want a situation in real life which would produce such a decline and then increase in typing speed.
November 5, 2014

geometry - incomplete
how is point G defined?
November 5, 2014

TRIG WORD PROBLEMS
not sure just what you did, but if the height is x, then x/25 = tan 38° Actually, x is the shorter leg. The 38° angle is from the ground to the top of the building.
November 4, 2014

Calculus- Please Help!
Since moles is constant, nR is constant. SO, V dP/dt + P dV/dt = nR dT/dt You now have n = 2*6.02*10^23 P = 5 V = 15 dP/dt = -3 dV/dt = 0.6 So, plug in the numbers and solve for dT/dt
November 4, 2014

English
Thank you
November 4, 2014

English
In the Call of the Wild, Buck did not fight back when Hal was beating, him because? My answer is that he did not have the strengh
November 4, 2014

English
Thsnk you very much.
November 4, 2014

English
The hairy man represents what in the call of the wild? My answer is fear
November 4, 2014

calculus
v = ds/dt = 2/√(1+4t) a = dv/dt = -4/(1+4t)3/2 now just plug in t=6
November 4, 2014

physics-distance
r dθdt = .5 * 6.9 = 3.45 m/s is the linear speed. so, 3.45 m/s * 35*60 s = 7245 m
November 4, 2014

Algebra 2
(5+2w)(12+2w) - 5*12 = 168 Now just solve for w.
November 4, 2014

Algebra
that would be the plan. Should be pretty straightforward. One you get back to (1,1) you're done.
November 4, 2014

math
If there are v,w,x,y bike, trikes, tandems and unicycles, respectively, then we know v = 32 x=y Assuming all riders wear helmets, v+w+2x+y = 57 2v+3w+2x+y = 115 32 bikes 13 trikes 4 tandems 4 unicycles
November 4, 2014

Math
(x-2)^2 can never be negative. It is its minimum value of 0 when x=2. So, the vertex is at x=2. y(2) = -3, so the vertex is at (2,-3)
November 4, 2014

algebra
the slope must be 3, so now you have a point and a slope: y-2 = 3(x-0) y = 3x+2
November 4, 2014

Math Gr 12
OK. Now what? Hint: sin x = 1/1.25 = 0.8
November 4, 2014

math
the numbers are x,x+2,x+4 x + x+2 = (x+4)^2 - 201 Now just expand, collect terms, and solve the quadratic.
November 4, 2014

calculus - unclear
Seems like we need to know something about the production of bandages. Is it continuous? Instant batches of some fixed number? Production over a period of days? Is the consumption to be considered a continuous function? I see no way to solve this with the information given.
November 4, 2014

Calculus please help me
recall your second derivative concave up if f" > 0 inflection when f" = 0 concave down if f" < 0 So, you have f"(x) = 50x(x^2+75)/(x^2-25)^3 f" < 0 on (-∞,-5) f" > 0 on (-5,0) f"(0) = 0 f" < 0 on (0,5) f" > 0...
November 4, 2014

Algebr
just the way you would evaluate any complicated expression. Start deep and work outward: f^-1(5) = 13 f^-1(13) = 2 f^-1(1) = 5 So, you have f^-1((13+2)/5) =f^-1(3) = 1
November 4, 2014

Math
f decreasing means f' < 0 f' = 18x^2 - 126x - 144 = 18(x^2-7x-8) = 18(x+1)(x-8) Since that is a parabola which open upward, f' is negative between the roots. f(x) is decreasing on the interval (-1,8) This can be verified by looking at the graph: http://www....
November 4, 2014

Algebra
f(x) = (x+5)/3 f^-1(x) = 3x-5 g(x) = 1/(f^-1(x)+1) = 1/(3x-4) g(3) = 1/5 Of course, you might also have meant just what you typed, in which case g(x) = 1/f^-1(x) + 1 = 1/(3x-5) + 1 = (3x-4)/(3x-5) and so g(3) would be 5/4
November 4, 2014

maths
I'd say it depends on what is in the bag.
November 4, 2014

Algebra 1 please help answer
you have two conversion factors: $3 = 2 lb 1 apl = 5 oz So, to convert $ to lb, do $9 * 2lb/$3 = 18/3 = 6 lb 6lb * 16oz/lb * 1apl/5oz = 96/5 = 19.2 apples
November 4, 2014

Algebra 1 please help
7 gal * 25mi/gal = 175 mi
November 4, 2014

algebra
If A has a girls and B has b girls, then we are told: a-7 = b a+4 = 2b So, a=18 b=11 That means that A had 17 boys and B had 24 boys
November 4, 2014

Algebra HELP!
x in * 1m/39.37 in = x/39.37 m y = x/39.37
November 4, 2014

Math
#1 solve for x in x(1+.18/4)^(4*5) = 30000 #2 again, x(1+.045/2)^(2*15) = 50000 #3 100*(1/2)^(15/25)
November 4, 2014

geometry
Not sure what you mean by "rows" of wires. If you just need to find the perimeter of the rectangle, that is 2(0.7+0.5) km
November 4, 2014

Calculus
if g(x) = 1/√f(2x) dg/dx = (-1/2)f(2x)^-3/2 * f'(2x) * 2 so, g'(1) = (-1/2)f(2)^-3/2 * f'(2) * 2 = (-1/2)(5^-3/2)(-1)(2) = 1 / 5√5
November 4, 2014

Calculus
#1 f' = 3x^2-8x+5 f" = 6x-8 f is concave up when f" > 0 #2 f' = 6x^2-6x-6 maybe it cannot be factored, but since the discriminant is positive, it has real solutions. Use the quadratic formula to find them. #3 you want the slope to be 3. y' = 2e^x - 3 ...
November 4, 2014

mathematics
(y,z) = (5/2, -13/4)
November 4, 2014

Calculus
f' = 6x^2+9 clearly, f' is always positive, so there are no extrema, and no intervals where f is decreasing. Just think of what you know of the curve y=x^3
November 4, 2014

Calculus
the distance z is found using z^2 = u^2 + v^2 - 2uv cos 2pi/3 what are u and v? The girl's and boy's distances, where u = -6t v = 10t z^2 = 136t^2 - 60t^2 z^2 = 76t^2 so, now you know you have to find z(1/2), and then use z dz/dt = 152 t
November 3, 2014

Math
6*36 + 4*15 = ?
November 3, 2014

Math
48+64 + 2(48+64) = 336
November 3, 2014

Algebra
just evaluate as you would anyu other expression. work your way out from the inside: f^-1(3) = 4 (because they told you that f(4) = 3) So, now you want f^-1(4) That is 7, because f(7) = 4 The final answer is 7.
November 3, 2014

math
you want to spend less than $15 to buy three books. On average, the books must cost less than how much, each?
November 3, 2014

Algebra
f^-1(x) = (x-5)/4 So, f^-1(9) = 1 f^-1(1) = -1 So, no, the answer would be -1.
November 3, 2014

Algebra
No, you can't have h^-1 with both x and y in it. In fact, there are no x's here at all. Just interchange h and y and solve for the new h: y = (1+h)/(2-h) y(2-h) = (1+h) 2y - yh = 1+h h(1+y) = 2y-1 h = (2y-1)/(y+1) So, h^-1(y) = (2y-1)/(y+1) h^-1(5) = 9/6 = 3/2 check: h...
November 3, 2014

Math
rewrite as 3/9, 4/9, 5/9, ... 1/10, 4/10, ... 3/7, 4/7, 5/7 ... the 1st and 3rd are easy, but I'd have to pick 1/5 for (b) just because it's the only one with a 5 in the denominator. No idea on the pattern.
November 3, 2014

Algebra
Lots of problems posted, with no sign of effort on your part. No ideas at all?
November 3, 2014

Algebra
x = (3y-7)/(y+1) x(y+1) = 3y-7 xy + x = 3y - 7 y(x-3) = -(x+7) y = (7+x)/(3-x)
November 3, 2014

Algebra
E(t) is just a parabola. I'm sure you know how to find the vertex, where E is a maximum.
November 3, 2014

Math
4/9 * 36 = (4*4*9)/9 = 4*4 = 16
November 3, 2014

Math
If exactly 20, then it would be 8:12 So, since we have to add 5 marbles at a time (2+3=5), the next possibility is 10:15 makes 25 marbles
November 3, 2014

math
That depends - do the minutes roll over, or not? If not, then she had to buy 400 the 1st month 400 the 2nd month 600 the 3rd month That's $50+$50+$75 = $175 If they roll over at the end of the month, then she'd have to buy less in some cases.
November 3, 2014

Algebra
the max height is achieved at the vertex of the parabola, when t = 1 for (c), just solve 16t^2 - 32t - 240 = 0 16(t+3)(t-5) = 0 ...
November 3, 2014

Pre-Calc
90 days is 90/8.1 = 11.111 half-lives, so there would be 25*(1/2)^11.111 left
November 3, 2014

Math
well, -8 < -15/2 -3 < -3/2
November 3, 2014

math
2(x+y) = 25 xy = 32 x(25-2x)/2 = 32 25x-2x^2 = 64 2x^2-25x+64 = 0 x = 3.59 y=8.91
November 3, 2014

Math
m is undefined
November 3, 2014

Math
There are several ways to write the equation, depending on the information given: slope-intercept point-slope two-point x- and y-intercepts standard form general form So, read up on these topics, and you will learn several answers to your question
November 3, 2014

Maths
since 27 = 3*9, 3a-27 = 3a-3*9 = 3(a-9)
November 3, 2014

mathematics Probability
Since 2 is the only prime that is even, P(prime & even) = P(2) = 1/5
November 3, 2014

Math
raise 16 to the power on both sides. That gives 8 = 16^(3/4) take log base 3 on both sides 4 = log_3(81) This is because blogbN = N logbbN = N
November 3, 2014

Math
there is no other way. The roots are the zeroes are the x-intercepts. The quadratic formula always works. Use it when in trouble. Or, try and factor the polynomial x^2+8x+15 = 0 (x+3)(x+5) = 0 the roots are -3 and -5 Surely your algebra book covers the topic in several places.
November 3, 2014

Math
You must have access to some graphing utility. Here is a good one: http://www.wolframalpha.com/input/?i=-2%2F3+d^2+%2B+4d&a=*MC.d^2-_*Variable-&a=UnitClash_*d.*Days.dflt--
November 3, 2014

Math
The whole setup is bogus I'd go with (c), since it correctly notes that the solutions are -4 and 9. But -4+4 is (0), not (-8) If this is a proposed way to solve for zeroes, it's really stupid. x cannot be both -4 and 9 at the same time. Run far, run fast from this ...
November 3, 2014

Algebra
f(x) = 1/(ax+b) f^-1(x) = (1-bx)/(ax) So, we want 1+bx = 0 x = 1/b Or, if f^-1(x) = 0, f(0) = 1/b
November 3, 2014

Math
since h is the height above the water, it hits the water when h=0: -5t^2+10t+35 = 0 t = 1+2√2
November 3, 2014

Calculus
f' = -sinx-1 f'=0 at sinx = -1, so x = 3π/2 f" = -cosx, so f"(3π/2) = 0 Looks like an inflection point, not max or min. So, no extrema anywhere.
November 3, 2014

algebra
6p^2-2p+3 = 3 6p^2 - 2p = 0 2p(3p-1) = 0 p=0 or p = 1/3
November 3, 2014

Trigonometry
no idea whatcha got? Convert each length traveled to an x & y displacement. Then use the law of cosines to find the third length.
November 3, 2014

Trigonometry
Hmmm. The 72 feet is measured on the slope, not out from the pole horizontally. I get top of pole is at 40 + 72 sin17° downhill point is 72 cos 17° from point beneath the pole cable^2 = (40+72 sin17°)^2 + (72 cos 17°)^2
November 3, 2014

Trigonometry
As usual, draw a diagram. It is clear that if the nearer student is x away from the spot under the balloon, then h/x = tan 28° h/(x+7) = tan 15° Eliminate x and you have h/tan28° = h/tan15° - 7 Now just solve for h
November 3, 2014

algebra
a#3 = a^2/3 = 9 a^2 = 27 ...
November 3, 2014

Algebra
f^-1(x) = (x+8)/3 So, we want (x+8)/3 = 3x-8 x+8 = 9x-24 8x = 32 x = 4 3*4-8 = 4 (4+8)/3 = 4 Note that the same results could have been achieved by setting f(x) = x 3x-8 = x 2x = 8 x = 4 Why? because f(f^-1) = x by definition. So, if f^-1(x) = f(x), then f^-1(f) = f^-1(x) x = ...
November 3, 2014

Math
elimination, or matrix inverse?
November 3, 2014

math
Well, as long as I'm clarifying :-) :-) :-) That would be 45 seconds, not .45 seconds Or, if you insist on decimals, try .75 minutes!
November 3, 2014

math
Not quite. After 12 minutes he has climbed 12 meters In the 13th minute, he climbs the final 3 meters and is done. Final time is thus 12:45
November 3, 2014

calculus
since x^2+y^2 = 36 x dx/dt + y dy/dt = 0 since we want dy/dt = -dx/dt, (x-y) dx/dt = 0 true when x=y, as might be expected. Or, when x = 6/√2 All that stuff about 4m and .5 m/s is just noise, unless there are other parts to the problem.
November 3, 2014

Pre calculus
r = 7/(5+4sinθ) r(5+4sinθ) = 7 5r + 4rsinθ = 7 5r = 7 - 4y 25r^2 = (7-4y)^2 25x^2 + 25y^2 = 49 - 56y + 16y^2 25x^2 + 9y^2 + 56y = 49 25x^2 + 9(y+28/9)^2 = 49 + 9(28/9)^2 25x^2 + 9(y+28/9)^2 = 1225/9 x^2/9 + (y+28/9)^2/25 = (7/9)^2 See http://www.wolframalpha.com...
November 3, 2014

Calculus
f(x) = 5x√(x+2) is continuous and differentiable on [0,2], so the MVT applies. f(2) = 20 f(0) = 0 So, the slope of the secant is 10 MVT says that f'(c) = 20 somewhere in [0,2] f'(x) = 5(3x+4) / 2√(x+2) f'(c) = 0 if 5(3c+4) / 2√(c+2) = 10 5(3c+4...
November 3, 2014

math
If the airport is at (0,0) first leg is to (-2.819,1.026) the second leg is on a course of S20°W for a distance of x where 1.026-xcos20° = 0 x = 1.092 So, the 2nd leg is to (-3.192,0)
November 3, 2014

Algebra
I'm sure that by now you have figured out that I made an error: (u^2+1 - u^2) / u(u-1) 1 / u(u-1) Now set that equal to 1/u 1 / u(u-1) = 1/u 1 = u-1 u = 2 check: 5/2 - 2/1 = 1/2
November 2, 2014

Algebra
I assume you mean (u^2+1)/(u^2-u) - u/(u-1) Clearly the LCD is u(u-1) (u^2+1 - u(u+1)) / u(u-1) (-u+1) / u(u-1) Now put both sides over the LCD, throw out u=0,1 and set the numerators equal. Then solve for u. What do you get?
November 2, 2014

Algebra
If the savings account pays x%, then (x+10)/x = 65/15 x = 3 check: .03m = 1500 m = 50000 So, $50K was invested .13(50000) = 6500
November 2, 2014

Algebra 2
there are 10 digits; only 8 allowed to start, so 8*10^6
November 2, 2014

Algebra check?
all correct good work. You can also check your answers by typing in the expression at wolframalpha.com
November 2, 2014

Algebra
If you're trying to find the expression for the area, you have for some reason combined the x^2 and x terms (a no-no). The area is 1/2(2x^2+4x+2)(x^2+3x-4) (x+1)^2 (x+4)(x-1) As you say, not sure which way to go. You have an expression for the area. Was there some other ...
November 2, 2014

algebra
huh. That's quite a question just to drop in. Have you not studied your algebra text? The basic idea is that if an equation is true, it remains true if you apply identical operations on both sides of the equal sign. The goal is to choose the operations in an order which ...
November 2, 2014

Math
You are correct to feel ill at ease. You have confused area and perimeter. You want (x+7)(6) = 120
November 2, 2014

algebra
After x miles, you want 8 - x/30 = 12 - x/18
November 2, 2014

Calculus I
If by optimal age, you mean producing the maximum offspring, then yes, you want to find where dr/dx = 0 r(x) = log(e^-.1x * 4x^1.5)/x That's kind of messy, and not tractable to algebraic solution. Netter use a graphical or numeric method. Looks like dr/dx=0 at x=1.07875 ...
November 2, 2014

Algebra
√7 (7-√7) + 9√7 7√7 - √7√7 + 9√7 16√7 - 7
November 2, 2014

Algebra 1B
You may be more familiar with the term "discriminant." The discriminant is b^2-4ac, the value inside the square root symbol. So, in this case, the surd being considered is the square root of the discriminant.
November 2, 2014

Math (I've been on this problem for 3 hours)
well, as I recall, the equilibrium price and quantity are where supply equals demand. So, we want 2p-q+10 = (p+q)(q+10)-3642 since q = 2p+10, that means (p+2p+10)(2p+10+10) = 3642 6p^2+80p-3442 = 0 p = 18.195 so, q = 46.390 Check: 2(18.195)-46.390 +10 = 0 (18.195+46.390)(56....
November 2, 2014

Math (I've been on this problem for 3 hours)
If the supply and demand functions for a commodity are given by 2p - q + 10 = 0 and (p + q)(q + 10) = 3642 respectively, find the equilibrium price and quantity that give market equilibrium. (Round your answers to two decimal places.) Equilibrium price =
November 2, 2014

physics
then it hits a brick wall, and bursts into flame. How much energy is released by the explosion of the fuel tank?
November 2, 2014

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