Saturday
January 31, 2015

Posts by steve


Total # Posts: 28,516

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

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

mathematics
no idea what a heading (not bearing!) of "1a" is. I also don't see a question in there yet. Nor the distance to point B. In fact, the whole things is garbled. Better clean it up if you expect any meaningful help.
January 28, 2015

10th algebra
since (x+a)^2 = x2+2a+a^2, you want 2a = 22. So, plug in a=11 and you have c = a^2 = 121
January 28, 2015

MATH
after x hours, you have the distance d is d^2 = (38x)^2 + (46x)^2 - 2(38x)(46x)cos(135°) so, just solve for x in (38x)^2 + (46x)^2 - 2(38x)(46x)cos(135°) = 214^2 x = 2.75 So, in LA, it is then 12:00 + 2:45 - 2:00 = 12:45 pm
January 28, 2015

Algebra
all you have to do is sub in the values of f and g: f(x)-g(x) = (-2x+4)-(-6x-7) just add up all the terms and collect like values. What do you get?
January 28, 2015

math
19 > -n/5 + 9 n/5 > 9-19 n/5 > -10 n > -50
January 28, 2015

Math
just sub in the value: -a^-2 = -(a^-2) = -1/a^2 = -1/(-5)^2 = -1/25
January 28, 2015

Math
1/23
January 28, 2015

Math
well, the point-slope form is y-7 = -4(x+7) now rearrange things into y = mx+b form.
January 28, 2015

math
#1 subtract 5 from both sides, then multiply through by 9. #2 similarly.
January 28, 2015

maths
well, since -7 - 1 ≠ 6, that will be hard to do.
January 28, 2015

math
subtract 15 from both sides, then divide through by -2.
January 28, 2015

Math
I'll do one, just for grins. if you're taking calculus, you should surely be able to do r = 3+2/(1+0) to get the radius when t=0! Having mastered the arcane art of plugging in a value, and knowing that dr/dt = -2/(1+t)^2 you can probably figure what dr/dt is when t=3.
January 28, 2015

Math 6 grade
if the percent is greater than 100, that is more than the number. per cent means per 100. 100% is 100 per 100, or all of it.
January 28, 2015

math
(sinx+cosx)^2 = sin^2 x + 2 sinx cosx + cos^2 x now recall the most fundamental of your trig identities, and the double-angle formulas.
January 28, 2015

physics
a = F/m
January 28, 2015

physics
a = v^2/2s = 29.9^2/116.4 = 7.78 m = F/a = 14.5/7.78 = 1.88 to find t, s = 1/2 at^2 clearly the force must act directly opposite its direction of travel.
January 28, 2015

maths
so, draw your Venn diagram, and start filling in the numbers. Start with the 2 in the center, and then fill in the other numbers so they fit.
January 28, 2015

geometry
the side of a square with diagonal d is d/√2
January 28, 2015

math
3/2 x^2 + 10x + 16 = 1/2 (x+4)(3x+8) This is just an exercise in factoring. Now you can easily read off a,b,c
January 28, 2015

math
4cm is 4 times as big as 1 cm, so you want a distance 4 times as big as 4km.
January 28, 2015

math
v(x) = (20-2x)^2 * x Of course all real numbers is wrong. The material is only 20 inches square. You cannot include numbers like 500 in the domain. You have to cut two tabs out, so each must be less than 10 in width. 0 <= x <= 10 The base of the box is 20-2x, and must be...
January 28, 2015

Chemistry
$132/76lb * 13.534g/cm^3 * 16.387cm^3/in^3 * 1lb/453.592g = $0.85/in^3
January 28, 2015

Math. Just checking
correct
January 28, 2015

Algebra
it's not always easy. Thus, since you know that #1 adds 5 each time, you expect T(n) = 5n But, T(1) = 5*1=5, not 1, so adjust the starting term: T(1) = 5*1-4 T(n) = 5n-4 or, -4+5n
January 28, 2015

Algebra
#1 clearly you have to add 5 each time, so T(n+1) = T(n) + 5 explicitly, that means T(n) = -4 + 5n You can do the others similarly.
January 28, 2015

Calculus
use partial fractions: 1/((x-2)(x+3)(x-4)) = -1/10(x-2) + 1/35(x+3) + 1/14(x-4) Now it's just a bunch of simple logs.
January 28, 2015

Calculus
you know that d/du tan-1(u) = 1/(1+u^2) So, use the chain rule and you have u = 2x/(1-x^2) du/dx = 2(1+x^2)/(1-x^2)^2 so, the derivative is 1/(1+(2x/(1-x^2))^2) * 2(1+x^2)/(1-x^2)^2 = 2/(1+x^2) to see why this simplifies no neatly, consider that if x = tanθ 2x/(1-x^2) = ...
January 27, 2015

math123
shift the decimal point till you have a number between 1 and 10: 0.000089956 0.00089956 * 10^-1 0.0089956 * 10^-2 0.089956 * 10^-3 0.89956 * 10^-4 8.9956 * 10^-5 Or, just count the leading zeroes and add 1. Then make that a minus power.
January 27, 2015

Math
Two obtuse angles cannot both be on the bottom left of the transversal. Anyway, L and M are parallel if the alternate interior angles are equal. or if consecutive interior angles are supplementary. Corresponding angles are usually involved when comparing similar figures. ...
January 27, 2015

math
That would be 4 * 1 1/4
January 27, 2015

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