Wednesday

April 1, 2015

April 1, 2015

Total # Posts: 30,251

**Calculus**

If the fenced side is y and the wall sides are x, then we have xy = 480 and the cost is c = 12*2x + 8y = 24x + 8(480/x) = 24x + 3840/x dc/dx = 24(x^2-160)/x^2 dc/dx = 0 when x = 4√10 So, the garden is 4√10 by 120/√10
*March 5, 2015*

**Calculus**

As with most such problems, I expect you will find that the maximum area occurs on a square page. But, let's check it out. If the dimensions are x and y, we have (x-4)(y-4) = 16 a = xy = x*(16/(x-4) + 4) da/dx = 4x(x-8)/(x-4)^2 da/dx = 0 when x=8 So, the page is 8x8, with ...
*March 5, 2015*

**delgado community college**

The seawater's mass is 1.025 g/ml * 1000ml = 1025g the bromine's mass is .000065 * 1025 = 0.066625 g
*March 5, 2015*

**math**

the new area is (7*2)(4*2) Note that the area grows by the square of the magnification ratio
*March 5, 2015*

**algebra**

each ball has volume 4/3 pi * (2.54/2)^3 = 8.58 cm^3 There are 15 of them, so add 15 times that to the volume of water, which is pi * 3^2 * 9 = 254.47 Note how they coyly avoided saying the balls were 1" in diameter. Saved you the step of doing the conversion to cm.
*March 5, 2015*

**Math**

B is the complement of A, so B/A = 69/21 =23/7 Surprise, surprise!
*March 4, 2015*

**MATH**

no, there are 2 halves in 1. There are 4/5 halves in 2/5.
*March 4, 2015*

**Calculus (Partial Derivatives)**

dH/dt = ∂H/∂x dx/dt + ∂H/∂y dy/dt ∂H/∂x = -13/(2√x) ∂H/∂y = 0.3√(0.1y+20) dx/dt = 300 dy/dt = 10/√y So, plug and chug, with t=2
*March 4, 2015*

**math**

divide the change in the dependent by the change in the independent. For #2, that is 2/1,2/1,2/1,... xo it's linear For #2, that's 9/2, 9/3, 9/3, 9/3, 9/3 They are all the same except for the first, so unless there's a typo, it's not linear.
*March 4, 2015*

**trig - eh?**

tan(40/90) ? That's an odd notation. Is there some reason why you did not say 4/9? Evan that seems unusual for such a problem.
*March 4, 2015*

**Algebra difference quotient**

f(x+h)-f(x) = 2(x+h)-3/4 - (2x-3/4) = 2h So, the quotient is 2h/h = 2 Next, f(x+h)-f(x) = 3(x+h-1)^2 - 3(x-1)^2 = 3(x^2 + 2(h-1)x + (h-1)^2) - 3(x^2-2x+1) = 3h(2x+h-2) Divide that by h, and you have 3(2x+h-2) = 6x+3h-6
*March 4, 2015*

**Geometry**

since the triangle are congruent, we know that EI=UA, so 3x-4 = 2x+3; x=7 Now you can find all the sides, and so on. For the other, you have FA = GR = 24 So, GR:RC:GC = 2:1:3 = 24:12:36 and now you can go on.
*March 4, 2015*

**math**

8sin2x + 2cosx - 5 = 0 16 sinx cosx + 2cosx - 5 = 0 16sinx cosx = 5 - 2cosx 256 sin^2x cos^2x = 25 - 20cosx + 4cos^2x 256cos^2x - 256cos^4x = 25 - 20cosx + 4cos^2x 256cos^4x - 252cos^2x - 20cosx + 25 = 0 I don't see any easy roots there, so a graphical approach may be your...
*March 4, 2015*

**trig equations**

cos^2x-5sinx+5=0 1-sin^2x - 5sinx + 5 = 0 sin^2x + 5sinx - 6 = 0 (sinx+6)(sinx-1) = 0 so, sinx = -1/6 or 1 Now you can find x. Watch for signs in quadrants.
*March 4, 2015*

**algebra**

did you check your earlier post? http://www.jiskha.com/display.cgi?id=1425519642 Was there something unclear there?
*March 4, 2015*

**algebra**

revenue = price * quantity, so if there are x price decreases, we have revenue is y = (6-.25x)(330+15x) = -3.75x^2 + 7.5x + 1980 Now, just find the vertex of that parabola to get the maximum revenue and its price. Recall that for ax^2+bx+c the vertex is at x = -b/2a
*March 4, 2015*

**Math (advice)**

A good rule of thumb is, that if you have a question, there are others who do also. Evidently they were also too shy to ask it, so you should. the teacher knows this, too, so he'd be much happier if someone (you!) asks the question, since it's easier to explain it to a...
*March 4, 2015*

**Algebra**

false: only for b>0 true
*March 4, 2015*

**ITT**

f(x) = -3(x^2+4x) - 5 = -3(x^2+4x+4) - 5 +3(4) = -3(x+2)^2 + 7 so, the vertex is at (-2,7) clearly, (0,-5) is the y-intercept solve for x to get the two x-intercepts see http://www.wolframalpha.com/input/?i=-3x^2-12x-5
*March 4, 2015*

**math**

sure. Sometimes you have to clear away the words and just ask what have I been told? What do I already know about the subject? What do they want to know?
*March 4, 2015*

**math**

a gallon is 16 cups so, the concentrate is 2/18 = 1/9 of the total volume. so, what is 1/9 of 16 fl oz?
*March 4, 2015*

**statistics/normal distribution**

you can play around a lot with Z table stuff here: http://davidmlane.com/hyperstat/z_table.html
*March 4, 2015*

**math**

(30*15*20 - 30*15*15)/5^3 = 18
*March 4, 2015*

**Geometry**

if x is line-of-sight, 8000/x = sin 40° if x is along the ground, 8000/x = tan 40°
*March 4, 2015*

**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*

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