Monday
March 30, 2015

Posts by Steve


Total # Posts: 30,192

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

math
h = p-13 p = 29 so, h = 29-13 = 16 Alan is correct.
February 26, 2015

math
f = 2*5
February 25, 2015

Calc
#1 still does not contain the point (1,1) #2 I don't think there is such an A and B. There is a solution involving sin(√2 x), but that's not gonna fit the requirements. #3 y = e^x - e^2x y' = e^x - 2e^2x = e^x(1-2e^x) so, y'=0 when e^x=0 (never) 1-2e^x = ...
February 25, 2015

Algebra 2
(15^3-7^3)(15^3+7^3) (15-7)(225+105+49)(15+7)(225-105+49) (8)(379)(22)(169) (2^3)(379)(2 11)(13^2) 2^4 11 13^2 379
February 25, 2015

science
draw the batteries on the left, one above the other next over, draw two resistors, in line on the same wire. Connect the ends of the wire to the top and bottom of the batteries. Next over, draw two light bulbs beside each other. Connect the two top ends together, and the two ...
February 25, 2015

math
sure. You can label the axes any way you want. This is often useful when y varies by large amounts.
February 25, 2015

Calculus Chain rule
several ways expand and divide: 6/x * (x^2-1)^4 = 6/x (x^8 - 6x^6 + 4x^4 - 6x^2 + 1) 6(x^7 - 6x^5 + 4x^3 - 6x + 1/x) now take derivative: 6(7x^6 - 30x^4 + 12x^2 - 6 - 1/x^2) quotient rule: 6(4)(x^2-1)^3(2x)(x) - 6(x^2-1)^4(1) ----------------------------------- x^2 product ...
February 25, 2015

maths
no way. To plot a point, you have to know the coordinates, or have a way to calculate them.
February 25, 2015

intermeidatealgebra
you sure this isn't a trick question? Look at it carefully.
February 25, 2015

intermeidatealgebra
x+11/15
February 25, 2015

Math
it is C. Sorry, Tracy, not A.
February 25, 2015

Math
two complementary angles add up to 90 degrees. two supplementary angles add up to 180 degrees. So, what do you have to add to 47 to get those values?
February 25, 2015

Geometry
I like E, since you don't provide any clues as to the constraints on x and y.
February 25, 2015

Math Alg. 2
Well, let's see. #1: 1*1 2*1 4*3 8*7 16*17 Hmmm 2^1-1 2^2-2 2^4-4 2^6-8 2^8+16 Hmmm #2: 2 2*2+1 2*5+1 2*11+5 2*26+7 Hmmm 2^2-2 2^3-3 2^4-5 2^5-6 2^6-5 Hmmm. #3: clearly -3,-2,5 repeats as a sequence Sorry. I can't seem to get #1 and #2 right off. They almost follow a ...
February 25, 2015

Math Algebra
f(x0) = 2 f(x1) = f(2) = 2 f(x2) = f(2) must stay 2.
February 25, 2015

Math
look at the units 48 oz = 3 dollars 16 oz = 1 dollar 1 oz = 1/16 dollar so, 6.25 cents/oz you have 16oz/dollar, not 16cents/oz
February 25, 2015

Math- Calc 1
(1,1) is not on that curve. the other questions also have typos.
February 24, 2015

Calculus
d/du(tan u) = sec^2 u so, use that and apply the chain rule: sec^2(sec x) * secx tanx I'm sure you can do #2 y = sec^-1 x sec y = x secy tany y' = 1 y' = 1/(secy tany) y' = 1/(x √(x^2-1)) y = 2^(e^(sinx)) y' = ln2 2^(e^(sinx)) * e^(sinx) * cosx
February 24, 2015

Homework Help (Math)
Write your answer in <x,y> for the following question: If x=<6,-21>, then 1/3x.
February 24, 2015

Pre-Calculus(Trigonometry)
looks good to me
February 24, 2015

math
10x + 25x = 280
February 24, 2015

math
d/c = 2/7 c+15 = 2(d+15) now solve for c and d.
February 24, 2015

Math
6+9r-4(3r-7) 6+9r-12r+28 . . .
February 24, 2015

math
1/8 * 360 = ?
February 24, 2015

honors chemistry
the short answer is that the heavier molecules will require fewer to make up the 10 grams of mass.
February 24, 2015

math
lots of z table stuff here: http://davidmlane.com/hyperstat/z_table.html
February 24, 2015

Motion in 2d
well, y(t) = 39.11t - 4.9t^2 find t when y=0. Then multiply that by Vx. That's how far it went horizontally while going up and back down.
February 24, 2015

algebraic connections
if yu mean 12% per hour, then there will be 100*1.12^10
February 24, 2015

Algebra 2
just plug and chug. 4/(1-r) = 10 2/5 = 1-r r = 3/5 So, now you know the G.P.
February 24, 2015

Math/ Compouded semiannually ?'s
just refer to your compound interest formula. #1: solve for P where P(1+.10/2)^(2*1) = 30000 P = 27210.88 #2: same thing P(1+.12/2)^(2*2) = .25*175000
February 24, 2015

math
convert the two vectors p and w (fir plane and wind) to rectangular coordinates, and add them up. p+w is the resultant velocity on the ground. A vector w in the direction N63W, with magnitude w is <-0.454w,0.891w>.
February 24, 2015

math
Draw a diagram. Let the barge be in the canal, with Kim on the south shore, and Kent on the north shore, both pulling eastward. Then we have Kim: u = <50cos20,-50sin20> u = <46.98,-17.10> Kent: v = <kcos15,ksin15> = <0.966k,0.259k> You want the ...
February 24, 2015

Calculus
I suspect you meant p(x) = 10e^(-.1x) So, the mass will be ∫[0,a] 10e^(-0.1x) dx = -100e^(-.1x) [0,a] = 100 - 100e^(-a/10) = 100(1-e^(-a/10)) If that is 30, then a = 10 ln(10/7) So, the density decreases with increasing distance, meaning more of the mass is closer to x=0...
February 24, 2015

math
using the two-point form for line 1, it is y = 1/6 (x-1) + 1 Now do that for Line 2, and solve the two equations.
February 24, 2015

ALGEBRA
Still wrong.
February 24, 2015

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