Saturday
April 18, 2015

Posts by STEVE


Total # Posts: 30,628

math
nope. odd+odd+odd = odd
March 4, 2015

Math
If the I were a T, the word would be CONGRUENT Sure there's no typo?
March 4, 2015

Math
using the law of sines, if A is x miles away, and B is y miles away, x/sin10° = y/sin60° = 17/sin110° Now you can find x and y, and thus y-x.
March 4, 2015

Math
use the law of cosines x^2 = (13*40)^2 + (10*30)^2 - 2(13*40)(10*30) cos 135°
March 4, 2015

math
use the law of cosines. x^2 = 3^2 + 4^2 - 2(3)(4) cos 45°
March 4, 2015

math
cannot be done. three odd numbers will always add to an odd result.
March 4, 2015

math
If the circle is tangent to both axes, you know its center is on the line y=x. So, now you know that the center is at the intersection of the two lines: (2,2) So, the circle has radius 2, and is (x-2)^2 + (y-2)^2 = 4 See the graphs at http://www.wolframalpha.com/input/?i=plot...
March 4, 2015

math
f + (2f-5) + (2/3)f = 28
March 4, 2015

calculus
y = 2^(3x^2) y' = ln2 * 6x * 2^(3x^2) it helps to go at it like this y = 2^(3x^2) ln y = 3x^2 ln2 1/y y' = 6x ln2 y' = ln2 6x 2^(3x^2)
March 4, 2015

mathematics function
25-x^2 -x^3 e^-x cos(x/4) coth -1 x lots of possibilities
March 4, 2015

algebra
y-63 = (57-63)/(5-3) (x-3)
March 4, 2015

Algebra 1
must have done since 3x+y = -9, -3x = y+9 using that, we have (y+9)-2y = 12 -y = 3 y = -3 It would have helped had you shown your work.
March 4, 2015

Algebra 1
-3(3)+ 1= -9+1 = -8 you are correct
March 4, 2015

math
easy - just make sure the changes in y are not a multiple of the changes in x. x: 0 1 2 3 4 5 y: 1 3 -99 20 31 22 In fact, almost any six pairs you choose will likely not be a linear relationship.
March 4, 2015

math
y decreases by 5 as x increases by 1, so look for a rule like y = -5x Since y(0) = -1, y = -5x-1
March 4, 2015

Calculus 1
do this one just like the other one I worked out.
March 4, 2015

Calculus 1
see the post below for the way to get this done.
March 4, 2015

Calculus 1
y = 6/(1+e^-x) = 6e^x/(1+e^x) y' = 6e^x/(1+e^x)^2 so, at (0,3) the slope is 3/2 Now you have a point and a slope, so the line is y-3 = 3/2 (x-0) see the graphs at http://www.wolframalpha.com/input/?i=plot+y%3D+6%2F%281%2Be^-x%29%2C+y%3D3%2F2+x%2B3
March 4, 2015

general maths
since all the numbers are odd, there is no way adding three of them can give an even result.
March 4, 2015

math
take a look at a chessboard. There are at least two ways to figure it out.
March 4, 2015

Physics
Energy Budget for a Rocket in Free Space: Recall the analysis of the rocket engine in Project I, Flight of the Rocket. Although the momentum of the rocket and its exhaust is conserved (constant), their energy is not; energy must be supplied by the combustion of fuel. WARNING: ...
March 4, 2015

immaculate college
assuming you mean (2 sin(A/2))^2 = 2 4 sin^2(A/2) = 2 sin^2(A/2) = 1/2 sin(A/2) = ±1/√2 Now just find all the angles that fit that.
March 4, 2015

Math
volume is length * width * thickness
March 4, 2015

math
The smallest circle has a radius of 2. Each circle's radius is 3/2 that of the previous one. If there are n circles, then since the first and last circles are only traversed halfway, we have 2 + 4(3/2) + 4(3/2)^2 + ... + 2(3/2)^(n-1) = 665/8 Hmmm. I get a non-integer ...
March 4, 2015

math
looks good to me.
March 4, 2015

math
since all the digits are less than 5, just lop off the last 4 digits and replace them with zeros.
March 3, 2015

calculus
y = ln(x-√(x^2-1)) y' = 1/x-√(x^2-1) * (1-x/√(x^2-1)) = -1/√(x^2-1) so, the arc length is ∫[1,√2] √(1+y'^2) dx = ∫[1,√2] √(1+1/(x^2-1)) dx = ∫[1,√2] x/√(x^2-1) dx . . .
March 3, 2015

Physics
Energy Budget for a Rocket in Free Space: Recall the analysis of the rocket engine in Project I, Flight of the Rocket. Although the momentum of the rocket and its exhaust is conserved (constant), their energy is not; energy must be supplied by the combustion of fuel. WARNING: ...
March 3, 2015

math
10(6+2r) = 60+20r
March 3, 2015

calculus
a = pi d^2 da/dt = 2pi d dd/dt You have da/dt and d, so find dd/dt
March 3, 2015

math
2.60 + mg = 60.0 The weight is mg, so . . .
February 28, 2015

Math
If the terms were 2,4,6,8,10 could you do it?
February 28, 2015

Math
count the tablets and the ingredients: a + b + c = 225 12a + 17b + 22c = 4075 10a + 13b + 35c = 4975 Now just use your matrix tools.
February 28, 2015

Vectors
Just set up your determinants, and you will see how it works. If you multiply any row of a determinant by k, the value also is multiplied by k.
February 28, 2015

ap calc
Well, if you graph things, you have a curved triangular region with vertices at (-2,8),(-2,0),(0,0). So, using shells of thickness dx, you have the area as ∫[-2,0] 2πrh dx where r = 1-x h = y = -x^3 using washers of thickness dy, you have ∫[0,8] π(R^2-r^2...
February 28, 2015

ap calc
I think you have a typo. The given curve and lines do not enclose an area. Do you mean x=0. The parabola does not cross y=0 anywhere.
February 28, 2015

calculus
Those two curves do not enclose an area.
February 28, 2015

math
well, the only choices are 64 and 10 - nope 49 and 15 - nope 36 and 36 - yep 6+6=12 6^2+6^2 = 72
February 28, 2015

math
you can use the quadratic formula, and mess with all those fractions, or you can see that you really have 1/12 (12x^2-x-1) = 1/12 (4x+1)(3x-1) Now the roots become clear.
February 28, 2015

calculus
The curves intersect at (0,0) and (2,2) So, you can add up horizontal strips or vertical strips. In this case, vertical strips are easier (why?) a = ∫[0,2] (2x-x^2) dx = 4/3
February 28, 2015

Health
Does a diet will help you lose 10 pounds in 3 days debunk the nutrition myth? My answer is yes
February 28, 2015

calculus
the extrema occur where f' = 0 So, where do you have 9-4x^2 = 0? With those values, you can evaluate the integral to find the value of f(x) there
February 28, 2015

math
two complementary angles add up to 90. So, what do you have to add to 42 to get 90?
February 27, 2015

math vectors
come on. You can do a cross product, right? So, pick some vectors and do the math. For example, let u = <1,1,1> v = <1,-1,1> w = <2,1,3> (uxv)xw = <2,0,-2>x<2,1,3> = <2,-10,2> ux(vxw) = <1,1,1>x<2,-1,3> = <4,-1,-3>
February 27, 2015

Algebra
actually, as written, the equation is not true, but we'll let that go. When you divide by fractions, you invert and multiply: (a/b) / (c/d) = (a/b)(d/c) = ad/bc So, you have (x^2-1/x^2-9)(x^2+8x+15/x^2+3x-4) Now just factor everybody and start cancelling: (x-1)(x+1)(x+3)(x...
February 27, 2015

Geometry
If P = (x,y), then we have the two transformations (x,y) -> (x+2,y-2) -> (2-y,-(x+2)) so, 2-y = 2; y=0 -(x+2) = 6; x = -8 Hmmm. no luck. If we reflect first, then we have (x,y) -> (-y,-x) -> (-y+2,-x-2) so, -y+2 = 2; y=0 -x-2 = 6; x = -4 Looks like D to me. You ...
February 27, 2015

Math vectors
the point is, that any numbers will produce zero. You just have to remember that the cross product distributes: (a+b)x(a+b) = axa + bxa + axb + bxb since axa = bxb = 0 and axb = -bxa the sum is zero.
February 27, 2015

Science
This problem is poorly presented in so many ways. trains don't travel with a force, but rather a speed. If the speed is constant, then the net force is zero. When the conductor applies the brakes with a force of 500N, is that the force of his foot on the control, or the ...
February 27, 2015

math
3/5 * 1/12 = 1/20
February 27, 2015

math
he spent 7/9, so 2.50 is 2/9 of the original amount 2/9 x = 2.50
February 27, 2015

algebra
huh? how complicated can it be to plot four points and connect them?
February 27, 2015

trig
all reference angles are relative to the x-axis. So, add or subtract π until you get a value in the range [-π/2,π/2] 11π/6 = 2π - π/6 so, the reference angle is π/6
February 27, 2015

Pre-calculus (Trigonometry)
the ship is 500 sin 20° = 171 m from shore. A beam of 250m will illuminate 2√(250^2-171^2) = 365 m of shoreline.
February 27, 2015

3rd grade math
I know. Maybe one of the band members is not a musician, eh? Probably the drummer. :-)
February 26, 2015

3rd grade math
since 3 does not divide 16, how can 2/3 of the 16 players be girls? 12/16 are brass
February 26, 2015

algebra
1695/(x + x+65) = 3
February 26, 2015

Math
v = 1/3 πr^2h 3v = πr^2 h h = 3v/(πr^2)
February 26, 2015

math
61.4% is the amount paid. That is not the discount (which is the amount not paid)
February 26, 2015

Geometry
90° is 1/4 of a circle. So, what's 1/4 of the circumference or area? c = πd, so d = c/π c = 2πr, so r = c/2π a = πr^2 = π*(c/2π)^2 = c^2/4π Now just plug in c where you need it.
February 26, 2015

math
not quite If they start out with o and c dollars, then o-40 = c+40 4(c-80) = o+80 rearrange things a bit and you have o-c = 80 o-4c = -400 3c = 480 c = 160 now find o
February 26, 2015

Algebra II
a parabola with focus at (0,p) and directrix at y = -p is x^2 = 4py The vertex is midway between the focus and directrix, so your parabola has p = 1 x^2 = 4y Now shift things so the vertex is at (-2,5) and you have (x+2)^2 = 4(y-5)
February 26, 2015

math
since Mickey had only gone 5/6 of the way, Dylan's speed was 6/5 of his. The last 1/6 (40 mi) of the trip took Mickey 48 minutes. That should get you started.
February 26, 2015

Math
you want to find factors of 81. They are 1,81 3,27 9,9 Each choice gives a different perimeter.
February 26, 2015

math
210/35 + 54/18
February 26, 2015

Quick chemistry help
each molecule is Cl2.
February 26, 2015

math
(5000-600)/4 grams per book
February 26, 2015

math proportions
since the ratio of height:shadow is constant, 5'1"/3'4" = h/12'10" That's kind of messy, so convert all the values to just inches. Find h, then convert it back to feet&inches.
February 26, 2015

Math
(a) is clearly explained at http://tinypic.com/view.php?pic=15qynhv&s=4#.VO_LNywYFvA You can probably find the others as well. Usually the Binomial Theorem is involved. For instance, (b) f(x+h) - f(x) = (x+h)^4 - x^4 = x^4+4x^3h+6x^2h^2+4xh^3+h^4 - x^4 = 4x^3h+6x^2h^2+4xh^3+h^...
February 26, 2015

Math vectors
recall that one factor in the result is the sine of the angle between the vectors.
February 26, 2015

Math/Solve
correct
February 26, 2015

algebra
x+y = 70 y = 2x+10 Now go for it.
February 26, 2015

Math
If the costs are x,y,z, respectively, then we have 2x+2y+z = 10.20 x = 2y z = x+3 You want to find z.
February 26, 2015

linear algebra
(a) Nope if f(t) >= 0 but c < 0, cf(t) is not a nonnegative function Looks to me like (b) and (c) are both subspaces. Do we have to choose only one?
February 26, 2015

algebra
3x means he withdrew x dollars each week. You want x to be the starting amount, so x - 3*14 > 65
February 26, 2015

Calculus
d/dx e^u = e^u du/dx
February 26, 2015

Calculus
well, y' = 4x^3 + 8x - 1 So, at (1,4), the slope of the tangent is 11. That means the line there is y-4 = 11(x-1)
February 26, 2015

Calculus
when a is a constant, g'(au) = a g' You know that if y=2x, y'=2(1) y=3x^7, y' = 3(7x^6) The constant is just a multiplier, and carries through. So, what you have is g = √2 u + √7√u
February 26, 2015

math
you need more than just the scale.
February 26, 2015

Math
the time in the air is t when h=0 again. So, just solve for h(t) = 0. the max height is the vertex of the parabola, clearly when t=4.
February 26, 2015

math
y = x/3 + 7 now just plug in x=18 and evaluate for y.
February 26, 2015

Math
You found the union, not the intersection. 3.3: You found A-B, not the union. 4.4: Again, you found the union. The intersection is the elements in all three sets: {1,5}
February 26, 2015

math
one recall that the roots are -b/2a ±√(discriminant) so, if the discriminant is zero, both roots are -b/2a
February 26, 2015

math
the lateral surface area is just the circumference times the height. So, a = 4*15 = 60 if you have to include the ends, then that is additional 2πr^2, where r = 4/2π
February 26, 2015

MATH
graphing the other methods are exact.
February 26, 2015

Math
(2/5)(1/5) + (3/5)(1/3)
February 26, 2015

math
there are several similar problems in the related questions below.
February 26, 2015

Math!! Help ASAP
11.4 is correct.
February 26, 2015

maths
3 5/9 = 32/9 40 1/2 = 81/2 So, the common ratio, r^6 = (32/9)/(81/2) = 64/729 r = 2/3 T5 = 32/9 * (2/3)^4
February 26, 2015

maths
ar = a+4 ar^2 = ar+9 Now just solve for a and r
February 26, 2015

calculus
no ideas on any of the questions? They gave you the function, so things should just fall right out.
February 26, 2015

math
y = (x^4+4)^2 (x^3+4)^4 ln y = 2ln(x^4+4) + 4ln(x^3+4) 1/y y' = 8x^3/(x^4+4) + 12x^2/(x^3+4) y' = [8x^3/(x^4+4) + 12x^2/(x^3+4)]*[(x^4+4)^2 (x^3+4)^4] Now you can massage that as you will. Eventually you can arrive at y' = 4x^2 (x^3+4)^3 (x^4+4) (5x^2+8x+12)
February 26, 2015

Math
By "side" I assume you mean one of the bases. If the other base is x, then we have (6+x)/2 * 13 = 91 (6+x)/2 = 7 6+x = 14 x = 8
February 26, 2015

programming
as usual, the average is the sum of all the ages, divided by the number of pupils. Count the pupils as they come in: num_pupils = sum_of_ages = 0 loop { read in years, months num_pupils++ age_in_months = years*12 + months sum_of_ages += age_in_months } average_age = ...
February 26, 2015

math
see related questions below
February 26, 2015

maths
the values are 1/√3, 1, √3, ... I think you can see what the constant ratio is.
February 26, 2015

arithmetic
the sides of such a hexagon are the same as the radius of the circle.
February 26, 2015

Math
since 3x^2+11x-20 = (3x-4)(x+5) you have log(3x-4)+log(x+5)-log(3x-4) = log(x+5) log3(27) = 3 log(18) = log(9) + log(2) So, you have 1/6 (3) + 2 + log3(2) - log3(2) = 5/2 625 = 5^4, so you have log5(5^(4/3)) = 4/3 surely you meant loga w. If so, you have log_a(x^6 y^3 z^4 w^3)
February 26, 2015

Calculus
That's what I get. For shells, ∫[2e^-6,2] 2π(4-y)(6+log(y/2)) dy comes out the same. Amazing!
February 26, 2015

Calculus
2e^-x has a y-intercept of 2, so you have a sort of triangular region with vertices at (0,2),(6,2),(6,2e^-6) using washers, each washer has an area π(R^2-r^2) where r = 4-2 = 2 and R = 4-y = 4-2e^-x Now the integral is just π∫[0,6] (4-2e^-x)^2-2^2) dx You can ...
February 26, 2015

Math Help!
each face of the pyramid is an isosceles triangle with base 8 and height √(22^2+4^2) To see this, view the pyramid from the side. Drop an altitude to the center of the base, and you have a right triangle whose hypotenuse is the height of the triangular face.
February 26, 2015

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