Sunday
March 29, 2015

Posts by Steve


Total # Posts: 30,148

Math
If 30 spoke E&F and 10 spoke E&F but not S, then that means 20 spoke E,F,S. So, in your Venn diagram, the small triple intersection in the center has a 20 in it. But, since only 20 spoke French and Spanish, and all of them also spoke English, there are 0 who spoke no English.
February 2, 2015

Calculus
y^2 = (x^2−1)^2 y = ±(x^2-1) That is, y = (x^2-1) or y = (1-x^2) The area between two functions f(x) and g(x) is ∫ f(x)-g(x) dx. hat is, it is the sum of all the thin strips whose height is the difference between the curves.
February 2, 2015

Calculus
I get for the area ∫[-1,1] (1-x^2)-(x^2-1) dx = ∫[-1,1] 2-2x^2 dx = 2(x - x^3/3)[-1,1] = 8/3
February 2, 2015

Precal
The names monomial, binomial, etc, are usually reserved for polynomial functions, where all the terms are just powers of x (or other variables). The above function, with its 5^x factor is not a polynomial, as generally used. The terms of a polynomial are separated by + and - ...
February 1, 2015

Math
h(t) is just a parabola. The max height is reached at the vertex. For the parabola ax^2 + bx + c the vertex is at x = -b/2a. So, for h(t), the vertex is at t = 3. h(3) = 152 It hits the ground when h=0. To find that, just use the quadratic formula.
February 1, 2015

Math
c(x) = 25 for 0 < x <= 6 25 + 4⌊x-6⌋ for x>6
February 1, 2015

Algebra 2
√(79-5x) = 6x+4 79-5x = (6x+4)^2 = 36x^2+48x+16 36x^2+53x-63 = 0 (4x+9)(9x-7) = 0 x = -9/4 or 7/9 but, you have to check for spurious roots: √(79-5(-9/4)) = √(79+45/4) = 9.5 but, 6(-9/4)+4 = -9.5 This is the spurious root. If you square both sides, it becomes...
February 1, 2015

Math
GCF(32,40) = 8 so there are 4 rows of irises and 5 rows of tulips, all rows with 8 bulbs.
February 1, 2015

Physics
The horizontal and vertical speed are both 19.8/√2 = 14 m/s At that speed, it takes 35/14 = 2.5 seconds to get to the goal. The height of the ball is y = 14t-4.9t^2 y(2.5) = 4.375 m Looks like it will clear the bar by 1.325 m I'll let you decide the vertical velocity...
February 1, 2015

Physics
the height of the ball as a function of time is y = 31.1*sin37.0°*t - 4.9t^2 = 18.7t - 4.9t^2 So, you want to find t when y = 5.5 (and is on its way down). t=3.5 s Since the horizontal speed is constant, just multiply it by 3.5 to find the distance. v = 18.7 - 9.8t and ...
February 1, 2015

Geometry
Look. You had x^2+6x If you consider that as x^2+2ax, a=3. to complete the square, you have to add a^2, which is 9. Just follow the steps I took in my solution. I assume you can take the square root of 25 when you get that far...
February 1, 2015

Geometry - ahem
(x+a)^2 = x^2+2ax+a^2
February 1, 2015

Geometry
you were supposed to complete the square. x^2 + 6x = 16 x^2 + 6x + 9 = 16+9 (x+3)^2 = 25 x+3 = ±5 x = -3±5 and you get your solution. To complete the square, you divide the coefficient of x by 2, since (x+a)^2 = a^2+2ax+a^2.
February 1, 2015

Math
apparently you didn't bother to follow the hint, so I'll give you a push... dx/dt = -600 mi/hr h = 2 tanθ = 2/x sec^2θ dθ/dt = -2/x^2 dx/dt Now plug in your numbers and find dθ/dt. watch the units.
February 1, 2015

physics
Assuming constant acceleration, s = 1/2 at^2, so 1/2 * a * 3^2 = 41 a = 9.111 And, we all know that F = ma
February 1, 2015

precalculus
sinC/c = sinA/a, so sinC/52.8 = sin27°30'/28.1 sinC = 0.8676 C = 60°11' or 119°49' Since A+C < 180 in either case, there are two possible triangles. Knowing A and C, you now know what B can be, and then use the law of sines again to find b.
February 1, 2015

Math 20-1
(0,0) is 0 < 0.6? Of course, you haven't said what the region is. Maybe it doesn't include (0,0) . . .
February 1, 2015

Math 20-1
you can start by noting that 7*12 = 84
February 1, 2015

Algebra
the slope of the line joining the points is 1, so . . .
February 1, 2015

math
x + 4x = 90, so x = 18 ...
February 1, 2015

geometry
7' = 84", so the ratio is 84:16 Now reduce that to see which choice it matches.
February 1, 2015

math
split the terms into two pairs, and you can see that you have b(r+v) + y(r+v) (b+y)(r+v)
February 1, 2015

math
sorry. My bad. I was thinking we wanted the series to converge, not the sequence.
February 1, 2015

math
the sequence is 3/2, 6/5, 15/14, ... I don't see how it can converge, since each term is greater than 1.
February 1, 2015

math
10/2 (2a+9d) = 145 a+3d + a+8d = 5(a+2d) a=1 d=3
February 1, 2015

math
The vector from the sun to the object is <5,4,22> <5,3,-2>+<5,4,22>/11 = <60/11,37/11,0>
January 31, 2015

advanced functions
and then gets hit by a train.
January 31, 2015

geometry
sorry - no triangle has sides of 2,5,7. That is just a straight line of length 7. Whoever devised this problem was sadly unaware of properties of a triangle. Anyway, supposing you have a real triangle, if the sides are doubled, so is the perimeter.
January 31, 2015

Calculus
starting at time 0, when the first dose is taken, the amount after t hours is 80*(1/2)^(t/22) the 2nd dose: 80*(1/2)^((t-24)/22) the nth dose: 80*(1/2)^((t-24n)/22) Play around with that as t gets large.
January 31, 2015

Pre Calculus
oops. Since 0-length numbers are not allowed, we really have only 340 possibilities.
January 31, 2015

Pre Calculus
since there are 4 choices for each digit, and the numbers may be 1,2,3 or 4 digits long, you have 4^1 + 4^2 + 4^3 + 4^4 = (4^5-1)/(4-1) = 1023/3 = 341
January 31, 2015

Calculus
if y = u^n, dy/dx = n u^(n-1) du/dx, so y' = 3(x^2 + 8x +3)^2 * (2x+8)
January 31, 2015

math
looks good to me
January 31, 2015

elementary differential geometry
if you google the question, you will be directed to several discussions on the matter, in varying degrees of complexity.
January 31, 2015

Calculus
make that sec^2 x and not 1/sec^2 x
January 31, 2015

math help
since a^2-b^2 = (a-b)(a+b) (x+5)^2 - (x-5)^2 = (x+5-(x-5))(x+5+x-5) = (10)(2x) = 20x So, A=20
January 31, 2015

Calculus
-x^2+x+6 = -(x-3)(x+2) As you know, this is a parabola, opening downward. So, it is positive between the roots: -2 and 3. So, f(x) is concave up in that interval. So, (a)
January 30, 2015

pre calculus
P(-2) is the remainder when P(x) is divided by (x+2) P(-2) = -5, so P(x) = (x+2)(x^2-1) - 5
January 30, 2015

Calculus
h(t) = 2 + 0.2t so, plug that in to express v(t) Then find dv/dt Or, since dv/dt = pi/4 h^2 dh/dt, plug in h(t) and dh/dt=0.2 to express dv/dt
January 30, 2015

math
pi*(4x)^2 - pi(4y)^2 = 16pi x^2 - 16pi y^2 = 16pi (x+y)(x-y) Your mistake was in saying that pi(4x)^2 = pi*4x^2 Bzzzzt Parentheses are yur friends.
January 30, 2015

Math
u(t) = √(g(t)) So, if f(t) = √t, u(t) = f(g(t)) = (fog)(t)
January 30, 2015

absolute value
|x+1| - |x-1| If x>1, |x+1| = x+1 and |x-1| = x-1, so |x+1| - |x-1| = (x+1)-(x-1) = 2 Similarly, if x < -1, |x+1| - |x-1| = -(x+1) - -(x-1) = -2 If -1 < x < 1, |x+1| > 0 |x-1| < 0, so |x+1| - |x-1| = (x+1)- -(x-1) = 2x
January 30, 2015

HELP ME PLEASE
Just work your way out from the inside -1(-a)^2 + (-(-a))^2 = -1(-a)^2 + (a)^2 = -1*a^2 + a^2 = -a^2+a^2 = 0 recall that (-a)^2 = (-a)(-a) = +a^2
January 30, 2015

Algebra 1
the surface area is the two circular bases, plus the curved sides. a = πr^2 + πr^2 + 2πrh = 2πr(r+h) = 2π(3x-2)(3x-2+x+3) = 2π(3x-2)(4x+1)
January 30, 2015

Algebra 1
The radius of a cylinder is 3x-2cm. The height of the cylinder is x+3cm. What is the surface area of the cylinder?
January 30, 2015

algebra
just divide each term, then add them up: 6s^7p^8/3s^3p = 6/3 s^7/s^3 p^8/p = 2s^4p^7 6s^5p^6/3s^3p = 2s^2p^5 27s^3p^4/2s^3p = 9p^3 So, the final sum is 2s^4p^7 - 2s^2p^5 + 9p^3
January 30, 2015

Math
What is the GCF of the terms 8c^3+12c^2+10c? my answer is 2c
January 30, 2015

Algebra 1
How can the polynomial 6d^4+9d^3-12d^2 be factored?
January 30, 2015

Algebra 1
There is a circular garden in the middle of a square yard. The radius is 4x. The side length of the yard is 20x. What is the area of the part of the yard that is not covered by the circle?
January 30, 2015

algebra
well, 36x^3-73x^2-45x-6 = (9x+2)(4x^2-9x-3) Or, if you want to do the division manually, enter the polynomials at http://calc101.com/webMathematica/long-divide.jsp
January 30, 2015

algebra 2
(f◦g)(4) = f(g(4)) = f(-14) = -49 since g(4) = -2(4)-6 = -14 and f(-14) = 3(-14)-7 = -49 or, you can just define (f◦g)(x) = f(g) = 3g-7 = 3(-2x-6)-7 = -6x+25 so, (f◦g)(4) = -24-25 = -49
January 30, 2015

math
1 3/4 + 1 1/3 + 1 3/4 = ?
January 30, 2015

algebra
-4 2/3
January 29, 2015

calculus
42?
January 29, 2015

math
23x = 127
January 29, 2015

calculus
the weight of a thin sheet of water of thickness dy and area 9x is 9x*62 dy At depth y, the width across the water surface is 2∜y, so the weight of the sheet of water is 1116∜y dy Now, since work = force * distance, we have to add up all the work lifting thin ...
January 29, 2015

algebra
visit here to see the graph. To do it yourself, get a sheet of graph paper. Plot two points on the line and connect them. Extend the connecting line segment on both ends, and that is the graph of the equation. If you cannot plot a point, you have some studying to do. http://...
January 29, 2015

Albebra
(10-2y)(10-2y)
January 29, 2015

Algebra 2
not clear just what is happening. A hiatus is a rest period. I don't expect much traveling is done during the stops. Anyway, I'd say that if the distance traveled is x, then since time = distance/speed, x/40 = 2 + x/50 Now just solve for x.
January 29, 2015

College Algebra
If the distance is x miles, the time Allison drove is x/65. So, since distance = speed * time, x = (x/65)(41) + 144
January 29, 2015

Math
use your sum/difference formulas: cos(x+y) = cosx cosy - sinx siny now use the difference formula, and then add them up and see what drops out.
January 29, 2015

Math 20-1
2x^2 - 7x + 3 > 0 (2x-1)(x-3) > 0 the roots of the equation are 1/2 and 3 Since the parabola opens up, 2x^2-7x > -3 when x is outside the interval between the roots: x < 1/2 or x > 3 See http://www.wolframalpha.com/input/?i=2x^2-7x%3E-3
January 29, 2015

Math 20-1
< or >
January 29, 2015

college algebra
x/6 + 8
January 29, 2015

Calculus
when the balloon is at height h, tanθ = h/300 so, sec^2θ dθ/dt = 1/300 dh/dt you know that when h=300, θ=π/4. You know dh/dt = 80, so just solve for dθ/dt
January 29, 2015

Math Help!!
you have a line containing the points (2,20) and (5,14) where y is 1000's of gallons of gas at price x. So, just use your two-point form for the line, and then find y(2.50).
January 29, 2015

Algebra 2
switch x and y, then solve again for y: x = 3y+12 x-12 = 3y (x-12)/3 = y or, y = x/3 - 4
January 29, 2015

physics
at 1329 m/s^2 it will take 43/1329 = 0.032 seconds to achieve takeoff speed. Now that is some acceleration!! You sure there's not a typo somewhere in there? Anyway, once you have the correct takeoff time, just plug in the distance formula s = 1/2 at^2 to find the required ...
January 29, 2015

Math 20-1
Since 7*12 = 84, you can start with a 7x12 rectangle. After that, just start increasing the width and using the appropriate length. There's no end of possible sizes with area greater than 84.
January 29, 2015

Math
1D ok 2A You count leading zeros for the exponent, but you cannot ignore any zeroes after the first nonzero digit. They are part of the value. 3A ok 4B 1/8000 = 0.000125 your answer is for 8000, not 1/8000 5C doubling n doubles then exponent, roughly equivalent to squaring the...
January 29, 2015

maths contant
the slope is -9/2 tan 77° = 9/2 tanθ is negative in QII, so our desired angle is 180-77 = 103°
January 29, 2015

calculus
The left term can be seen as (sin3x/x)^3 - 3 = 27(sin3x/3x)^3 - 3 now, we all know that lim sinu/u = 1 as u->0, so the limit of all that is just 27-3 = 24 multiply that by x^4 and you just wind up with 0 as x->0 Still not sure what that x^4 is doing in there. It just ...
January 29, 2015

Calc II
since the slope anywere is just y'=2x, you want to find where 2x = 5/2 x = 5/4 So, the desired point is (5/4,25/16) For the other one, figure the slope of the tangent line, and then follow the same steps.
January 29, 2015

Calculus
#1 I only see one point and a number. #2 at the given point, the slope is -1.2 So, the line there is y-0.36 = -1.2(x+0.6)
January 28, 2015

math
19g/(5cm)^3 = 19/125 g/cm^3 water has density 1g/cm^3, so the wood will float. (duh!)
January 28, 2015

Math
since cot t appears several places, let g(t) = cot(t) Now we have u(t) = g/(9+g) So, let f(t) = t/(9+t) and you have what you want. f◦g = f(g) = g/(9+g) = cot t/(9+cot t)
January 28, 2015

Math
If you mean A = 2600e^(0.08t) that is 8% compounded continuously
January 28, 2015

Math
g(x) = x/(9+x) f(x) = ∛x
January 28, 2015

Math
f°g°h = f(g(h)) = f(h^2) = √(h^2-5) = √((x^3+6)^2-5) = √(x^6+12x^3+31)
January 28, 2015

Algebra
get all the T stuff together: 5.5*10^2(1/T) = 17.8 Now you can start working the numbers: 1/T = 17.8/550 T = 550/17.8
January 28, 2015

Math
If their scores are x and y, we have x/y = 1/5 (x+48)/y = 5/9 Now just solve for y (x+48)/y = x/y + 48/y, so 1/5 + 48/y = 5/9 48/y = 16/45 y = 135 check: x = 27 (27+48)/135 = 75/135 = 5/9
January 28, 2015

Math
since we have our minimum at t=0, the function will look like y = -cos(kt) The brightness varies by ±0.30, so that is the amplitude. y = -0.30 cos(kt) Since the low is 5.5, the axis of the curve is at 5.5+0.30, so y = 5.80 - 0.30cos(kt) The period of cos(kt) is 2π/...
January 28, 2015

Algebra
you are correct
January 28, 2015

math
when x=0, y can be anything, so the points lie on the y axis. It just happens that (0,0) lies on both axes. Now show a counterexample.
January 28, 2015

algebra
w-9 = m+9 (m-9)/(w+9) = 1/2 Now, solve for w: m=w-18, so (w-18-9)/(w+9) = 1/2 2w-54 = w+9 w = 63 check: m=63-18 = 45 (45-9)/(63+9) = 36/72 = 1/2
January 28, 2015

Trigonometry
If the point in question is D, then we have AD+DC = 5 BD/AD = tan 60° BD/DC = tan 45° so, we have BD/√3 + BD/1 = 5 Now just solve for BD, the desired distance.
January 28, 2015

Math
1/5 1/20
January 28, 2015

Math
1/2 + (2/3)(1/2) = 1/2 + 1/3 = 5/6 That's how much he painted on Mon and Tue. So, that left how much for Wed?
January 28, 2015

Math
A $1,600.00 principle earns 7% interest, compounded semiannually twice per year. After 33 years, what is the balance in the account. My answer is $112,992.00
January 28, 2015

Algebra 1
does the rule y=-3x^5 represent an exponential function
January 28, 2015

Calculus
what does "x^3 x^4" mean?
January 28, 2015

Algebra 1
Is the following written in scientific notation? 4.8 X 100^7 My answer is no
January 28, 2015

algebra
just use your formula: 1500(1+0.035)^18
January 28, 2015

Pre-Calc
using the difference formula, you have sin(x)cos(π/6)+cos(x)sin(π/6) - sin(x)sin(π/6)+cos(x)sin(π/6) = 1/2 2cos(x)sin(π/6) = 1/2 2cos(x)(1/2) = 1/2 cos(x) = 1/2 x = π/3 or 5π/3 http://www.wolframalpha.com/input/?i=sin%28x%2B%28pi%2F6%29%29-...
January 28, 2015

mathematics - eh?
3/4 - 32 ?? I suspect that your problem is poorly stated.
January 28, 2015

statistics
1/17259390 times the value of the prize. So, if the prize it at least that much, a $1 ticket expects to make more than a buck.
January 28, 2015

math
Can't do it. If you draw A,B,C then D can be anywhere on a circle of radius 2.82 with center at C. There are two places on that circle where AD = 7.
January 28, 2015

grammar
people are there is no preposition here four quarters fell... past tense makes no distinction in number. (except for "to be") it is confusing sometime, all right. A good example is "the number" is singular "a number" is plural
January 28, 2015

mathematics
since the ratio is constant, 3/4 = x/120
January 28, 2015

Chemistry
A nice discussion is here: http://www.quora.com/Why-can-chlorine-atoms-not-form-hydrogen-bonds-even-though-they-have-very-similar-electronegativity-to-nitrogen-which-can
January 28, 2015

Pages: <<Prev | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | Next>>

Members