Saturday
July 23, 2016

Posts by Steve

Total # Posts: 42,026

Calculus
The x values given are the right-left edges of the rectangles. You want right-side values, so figure f(x) at x = 9,11,14,15 Multiply each height by its interval's width, and the approximation is just 5*11+2*18+2*21+1*25 = 158 So, the average height is the area divided by ...
June 14, 2016

math
the radius i 7, so its circumference is 14π. Now just divide the length rolled by the circumference.
June 14, 2016

Calculus- PLEASE HELP
xy = 1334, so y = 1334/x 3(x-6)(y-6) = 2760 3(x-6)(1334/x - 6) = 2760 solve that and you get x = 29 or 46 so, the original sheet was 29 by 46 in. v(x) = (24012+4110x-18x^2)/x = 6(x-6)(667-3x)/x for v>0, we have 6 < x < 667/3 Makes sense, since we can't cut two 3&...
June 14, 2016

Math , new Oxford public school.
1/6 y = 3 - 1/7 x so, 1/3 y = 6 - 2/7 x Now use that in the other equation: 1/2 x - (6 - 2/7 x) = 5 11/14 x = 11 x = 14 or, you can use elimination. since 1/3 = 2/6, 2/7 x + 1/3 y = 6 1/2 x - 1/3 y = 5 Now add the two equations to get rid of the y: 11/14 x = 11 so, x = 14 Now ...
June 14, 2016

Maths
If there were p to start with, p(1-0.20-0.05)(1-0.45) = 33 p = 80 check: 20% of 80 is 16 gone 5% of 80 is 4 dead so, that leaves 60 45% of 60 is 27 sold That leaves 33
June 13, 2016

Math
depends on what the amount was at the start. But, 2^10 = 1024
June 13, 2016

Math
the rolling area of the cylinder is 84*120π cm^2 = 3.17 m^2 now just divide.
June 13, 2016

Math
7km/25min * 60min/hr = 420/25 km/hr = 16.8 km/hr If he says the speed is 28km/hr, he's working on some other problem. if there are various speeds, the average speed is the total distance divided by the total time.
June 13, 2016

math
just multiply 150 by the number of minutes in an hour or day.
June 13, 2016

Algebra
-11√112 = -11√(16*7) = -11√16√7 = -11*4√7 = -44√7
June 13, 2016

Algebra
if all you want to do is expand the factors, then recall that (x^m)^n = x^(mn) so, that gives you (4ah^2)^3(ah)^5 = 4^3 a^3 h^6 a^5 h^5 = 64 a^8 h^11
June 13, 2016

math - eh?
it would be nice if you asked a question, instead of just posting gibberish. At first I thought you wanted to solve two simultaneous equations: 1/2 (2x+3y )+12/7 (3x -2y )=1/2 7/(2x +3y )+4/(3x -2y )=2 but that became unwieldy fast. Are you trying to clear fractions? 1/2 (2x+...
June 13, 2016

algebra
recall that the line through (h,k) with slope m is y-k = m(x-h) Now just plug in your values.
June 13, 2016

Algebra
assuming direct variation, y = kx so, k = 2/3
June 13, 2016

Math
If C is the circumference of the earth, in inches, then that would be 6.7*10^9 * 12 / C So, look up C.
June 13, 2016

math
That would be correct.
June 13, 2016

math
ok, the next step is (x-6)(x+1) = 0 x = 6 or -1 Now just find y for each of those x values.
June 13, 2016

math
equate y and you have x^2-6x+7 = -x+13 x^2-5x-6 = 0 and I think you can take it from there, yeah?
June 13, 2016

Math
N = kA/P That mean that NP/A = k, a constant So, you want to find N such that 50N/65 = 50*12/50 where we have expressed A and N in thousands
June 13, 2016

math
p(1+18(r/12)) = 10450 p(1+2r) = 10600 (1 + 3r/2)/(1+2r) = 10450/10600 r = 0.03 now use that in either equation to find p.
June 13, 2016

Calc
using l'Hospital's Rule, the limit is the same as that of 2√x / √(1+2x) --> 0
June 13, 2016

rout
maybe they're separate problems. In that case, just use the normal formula v = π/4 d^2 h and use your numbers
June 13, 2016

Science
I assume you mean the number doubles every 20 minutes. In that case, after n periods of 20 minutes, there will be 100*2^n bacteria. So, how many times have they doubled in 2 hours?
June 13, 2016

Mathematics
just look at the information given: 7s+3h = 50 3s+2h = 24 now you take over...
June 13, 2016

math
sure looks like C to me did you try dividing dollars by months for some rows? They are all the same.
June 12, 2016

Math
recall your basic equation of motion: y = 300 + 500t - 4.9t^2
June 12, 2016

math
the values are correct. As the number of iterations grows, so does the f value, either positive or negative. And that's 2^x 2x means 2 times x: 2,4,6,8,...
June 12, 2016

math
irrational, real
June 12, 2016

math
it is integer, rational, real as to why, you'd better review the categories.
June 12, 2016

Calculus
since pi/x < pi/2 for this limit, tanθ will be positive so the limit is +∞
June 12, 2016

Math
well, where does sinx = cosx? Divide by cosx, and you have tanx = 1 Look familiar?
June 12, 2016

math
No way to tell. At most 36 runners, though.
June 12, 2016

math
not quite. You have to watch the units. 10 seconds is 1/360 hours.
June 12, 2016

math
well, how far does the hare go? distance = speed * time
June 12, 2016

math
probably the latter, as the previous post used half-angle formula. So, eku, I guess that gives a clue to this one, too, eh?
June 12, 2016

maths
x+y+z = 26 y = 3x You want minimal x^2+y^2+z^2, so check out a few possibilities: x y z ∑*^2 1 3 22 488 2 6 18 332 3 9 14 208 ... I think you can figure it out.
June 12, 2016

math
use your half-angle formula: tan(A/2) = (1-cosA)/sinA you can easily find cosA, and then just plug and chug.
June 12, 2016

Maths
Draw the unit circle. Draw a right triangle in standard position (right angle on the x-axis). Now label the sides. The hypotenuse is 1 The height is x Let angle A be at (0,0) So, sin(A) = x/1 = x That is, A = sin^-1(x) csc(A) = 1/sin(A) = 1/x So, A = csc^-1(1/x)
June 12, 2016

math
so, what's the problem? Get out your protractor and ruler.
June 12, 2016

math
upstream time is m/(r-s) downstream time is m/(r+s)
June 12, 2016

Math
something is messed up. I suspect a typo. In particular, I think 4.6 cakes will take a lot more than 3/5 lb of flour, unless they are very small cakes. Hmmm. 2/3 lb is about 3/5 cup. I know I can't make 4 cakes with that much flour!
June 12, 2016

Math
suppose you know how much you need to make 3 cakes. To make one cake, you just divide by 3, right? So here, just divide by 4 3/5. (2/3)/(4 3/5) = (2/3)/(23/5) = 2/3 * 5/23 = 10/69 All fractions work the same way.
June 12, 2016

Algebra
Usually people don't talk about "prime factors" of polynomials, but a complete factorization should do the job. Here are a few: a. 2a^2 - 2b^2 = 2(a^2-b^2) = 2(a-b)(a+b) b. 6x^2 - 6y^2 = 6(x^2-y^2) = 2*3(x-y)(x+y) c. 4x^2 - 4 = 4(x^2-1) = 2*2(x-1)(x+1) d. ax^2 - ...
June 12, 2016

Physics
so, did you draw the path? where did you end up? Hint: label the start (0,0) Distance covered is just the sum of all the line segments. Final displacement is found using the normal distance formula, which is just the Pythagorean Theorem.
June 12, 2016

Trigonometry
nothing to do but convert to x-y form, add them up, and then convert back. Luckily, they can be treated as complex numbers, making the job easier, using polar form. And, you can let wolframalpha.com do all the work (or any other handy calculator you know). You can check your ...
June 11, 2016

Mathematics
Nope. The A+B+C=180 Note that the sides AC = b AB = c Use the law of cosines to get a^2 = b^2+c^2-2bc cosA Now, having a, you can use the law of sines to get A: sinA/a = sinC/c
June 11, 2016

Math - Year 10 - Simult. equations
you know that 4y = -3x, so use that in 16x^2 + 16y^2 = 400 16x^2 + (4y)^2 = 400 16x^2 + 9x^2 = 400 and I think you can take it from there, right?
June 11, 2016

pre-algebra
Interesting. As a position relative to the surface, the value is -550. But, as you say, the depth is indeed 550 ft. "Depth" carries with it an implied negative value. I'd check to see just how they want you to interpret positive and negative quantities.
June 11, 2016

Math
best bet is to convert all to decimals. The it will be easy. SO, 2/3 = 0.6666 0.2 = 0.2000 and so on
June 11, 2016

Algebra
(a+b)(a+b) Now just expand that us usual
June 11, 2016

maths
if two polynomials have the same roots, one is a multiple of the other. So, x^2+px+q = 2(x^2-(5/2)x-(3/2)) so, p = -5/2 and q = -3/2
June 11, 2016

maths
If the roots are p and q, then we have pq = k Since p = 1/q, pq = 1 So, k=1 x^2-5x+1 has roots (5±√21)/2 I leave it to you to verify that the two values are reciprocals.
June 11, 2016

Logarithm
Your observation appears correct; the right side is 1/√(27^2) (3^x)^3 = 3^(3*x) = 3^(3x) 9 = 3^2, so 9*3^(3x) = 3^2 * 3^(3x) = 3^(3x+2) Now, on the right, for any value n, √(n^2) = n, so we have 1/27 = 3^-2 So, we want x such that 3^(3x+2) = 3^-2 3x+2 = -2 3x = -4 ...
June 11, 2016

Maths
Actually, the number is 58.
June 11, 2016

Algebra
reciprocals of equals are equal. Unless the equals are zero...
June 11, 2016

Calculus
as usual, for a given perimeter (sum), a square has maximum area (product).
June 10, 2016

math
(50*60 + 25*56 + 25x)/(50+25+25) = 58 now solve for x
June 10, 2016

math (significant digits)
you only have one s.d. .03 + 0.2 = .23 which becomes 0.2
June 10, 2016

math
that looks better.
June 10, 2016

math
since they are of equal weight, their average is just the arithmetic average of the two scores: 87 Why do I suspect that the problem was misstated?
June 10, 2016

Math
ar^2 = 4 So, you want to know a^5 r^10 = (ar^2)^5 = 4^5 = 1024
June 10, 2016

Math
a 1-cm thick layer of water has a volume of π*35^2 cm^3 = 3.848 L So, you want to know how long it takes to drain 20cm = 76.97L 76.97L ÷ 10L/hr ≈ 7.7 hr
June 10, 2016

maths
what does a circular pool is 300 mean?
June 10, 2016

maths
If 1/3 were bad, then 2/3 were good. So, he made (5 1/4)*(3/4)(712)(2/3) =
June 10, 2016

math
Just do the division. The remainder is (m-3)y + (n+3) To be divisible, the remainder must be zero, so that means m=3 and n = -3. Check: y^4 + 3y^3 + 2y^2 - 3y - 3 = (y^2-1)(y^2+3y+3)
June 10, 2016

Algebra
You must group terms with like exponents. For example, #20 3x^2 – [7x- (4x – x^2) + 3] = 3x^2 - [7x-4x+x^2+3] = 3x^2 - [x^2+3x+3] = 3x^2-x^2-3x-3 = 2x^2-3x-3 You can see this at this url: http://www.wolframalpha.com/input/?i=3x^2+%E2%80%93+[7x-+%284x+%E2%80%93+x^2%29...
June 10, 2016

Physical Science
That would depend on the applied force. F = ma You can take it from there.
June 10, 2016

O98 algebra
The sum of her first 5 scores is 382 6*77 = 462 6*85 = 510 So the last score must satisfy 462 < 382+x < 510 80 < x < 128 So, any score above 80 will get her a C grade.
June 10, 2016

Math: Inverse Function (Plz help)
f = 8+√(8+x) to find f^-1, swap variables and solve for f: x = 8+√(8+f) x-8 = √(8+f) x^2-16x+64 = 8+f f = x^2-16x+56
June 9, 2016

analytical math
no idea. How old is Mary now?
June 9, 2016

Math
42
June 9, 2016

Math
.20 * 20 = 4
June 9, 2016

Pre-Cal: Domain (cont.)
#8 the domain is all real numbers except 0 and -7 While the domain of [5(x+7)]/[7x] excludes only 0, (f/g)(x) requires evaluating both f and g, and since g(-7) is not defined, neither is (f/g)(-7)
June 9, 2016

Math
just keep adding 11
June 9, 2016

Algebra
or, since you are given a point and a slope, try using the point-slope form of the line: y-11 = (7/3)(x-3) That's good enough for me. What you want depends on what you mean by "the equation" of a line.
June 9, 2016

math
the surface consists of three pairs of rectangular faces. You have the length and width of each face, so find the three areas, add 'em up, and double that (since there are two of each size)
June 9, 2016

algebra 2B
I suspect a typo g(x) =− 2 −x 2+ 4 is the same as -2 - x^2 + 4 = 2-x^2 Clean it up and show how far you got.
June 9, 2016

algebra
y = (2x-3)/(7x+1) see http://www.wolframalpha.com/input/?i=%282x-3%29%2F%287x%2B1%29
June 9, 2016

Math
if you want the height, drop the altitude to the base. It divides the base into two parts, x and 12-x. Now, using the Pythagorean Theorem, you can find the height h using x^2 + h^2 = 8^2 (12-x)^2 + h^2 = 7^2 subtract and you get rid of h, leaving x^2 - (12-x)^2 = 64-49 24x - ...
June 9, 2016

Physics- Help!!
120 * (1200/100) = ?
June 9, 2016

math
do you see what a useless response that is? Restrict how? Anyway, I gave you the information you need. How about showing some effort of your own here?
June 9, 2016

math
infinitely many. Or did you want to restrict the available area? In the first quadrant, (4,4) is on the curve. There will be none to the left of (1,16) or to the right of (16,1). And don't count the lattice points on the curve...
June 9, 2016

Pre-Cal: Domain
the domains include all real numbers except where the denominator is zero. So, figure the resultant function, and then exclude any places where the denominator is zero. AND, exclude 0 and -7 because at those values f or g is undefined, so even though some mixture of them might...
June 9, 2016

Calculus
you are correct. 1/(x-1) -> ∞ I tried to pound a round peg into a square hole.
June 9, 2016

Calculus
note that if u = 1/(x-1) then what you have is sin(u)/u You have probably seen that this limit is 1, so follow the same argument. Or, try google. A good discussion is at math.ucsb.edu/~jcs/SqueezeTheorem.pdf
June 9, 2016

Math/Dosage Calculations
just add up the amounts (in fl oz): (1/3)(8) + (1/2)(16) + 3 = 41/3 fl oz. Now just convert that to mL. 1 oz = 29.57 mL Hmmm. I get 404 mL
June 9, 2016

Math
Just take each sentence and place the required digit in for one of the x's. Start with xxxx My hundreds digit is the last odd number. x9xx and move right along.
June 9, 2016

Math
w*2w = 1250 Now get w, then the length is 2w
June 9, 2016

Math
that would be the area of the inner cylinder, plus the area of the outer cylinder, plus the area of the two rings at the end. So, if R = outer radius r = inner radius h = length of pipe the total area is 2πrh + 2πRh + π(R^2-r^2) = 2πh(r+R) + π(R+r)(R-r...
June 9, 2016

Math - Year 10 - Simult. Equations
just plug in y=3x and you get x^2 + (3x)^2 = 10 Now x is easy, and then y=3x.
June 9, 2016

geography
how many time zones in between? That's the number of hours. Or, if you know the longitudes, since there are 24 hours in a 360° circle, each hour covers about 15°
June 9, 2016

geometry
since j is in the middle, mn = mj+jn = 6 3/4 + 6 3/4 = ?
June 9, 2016

trigonometry
If that fails, try cot (x-y)/2 and use your half-angle formula, and more parentheses next time.
June 8, 2016

math
sure, if so designated
June 8, 2016

Math
even without calculus, you can do these. Just think of what you know about lines and parabolas. Then you can verify your Algebra I with calculus. What do you think?
June 8, 2016

math(bearing)
There seems to be a lot of noise here If the bearing of Y from Z is 280, then the bearing of Z from Y is 280-180 = 100
June 8, 2016

Pre-Cal (Help Plz)
come on. x^2-4 is negative on the interval (-2,2) So, since |x^2-4| is always positive, that little arc below the x-axis is flipped up above it. Everywhere else, the two functions are identical. g(x) = -f(x) if |x| < 2 g(x) = f(x) if |x| >= 2
June 8, 2016

Pre-Cal (Help Plz)
take a look at the graphs and see what you can say. And why not use || for absolute value? It's not like you don't have the characters... http://www.wolframalpha.com/input/?i=plot+y%3Dx^2-4,+y%3D|x^2-4|
June 8, 2016

math
ok
June 8, 2016

Trigonometry
off course as measured how? Actual distance between target and position, or distance perpendicular to the intended course? In the first case, use the law of cosines. Both sides of the included angle are 152*2
June 8, 2016

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