Thursday

October 2, 2014

October 2, 2014

Total # Posts: 25,454

**math**

the other side, x, satisfies 4.2^2 + x^2 = (x+14)^2 Hmmm. You sure there's no typo?
*August 14, 2014*

**math**

a convex polygon with five equal sides. if you google that, you will see many images and descriptions.
*August 14, 2014*

**math**

since p = 2(x+y) = 8y, x+y = 4x x = 3y y:x = 1:3
*August 14, 2014*

**Math**

see the many related questions below
*August 14, 2014*

**Math**

OK. First, it's lookout, not lockout. The man is 25-1.7 = 23.3m up. If the building is at distance x from the tower, and has height h, we have 23.3/x = tan 70°20' (h-23.3)/x = tan 12°40' Now, you can eliminate x, and then solve for h: 23.3/tan70°20'...
*August 14, 2014*

**trigo**

As I interpret the data, it appears that the law of cosines will provide our answer. We want the supplement to θ, where 15^2 = 6^2+9^2 - 2(6)(9)cosθ cosθ = -1 Nope, that doesn't work. Maybe you can just describe the figure, giving labels to the points of ...
*August 14, 2014*

**math**

If x at 9%, .09x + .10(26000+3x) = 27650 x = 64231
*August 14, 2014*

**Trigonometry**

consider the pentagon as 5 isosceles triangles, each with vertex angle of 72°, and sides of 1.5 (the radius). Now you can easily calculate the base of each triangle. The perimeter is 5 times that.
*August 13, 2014*

**Algebra 2**

(x-3) / 2x * 6x^2 / 5 (x-3)(6x^2) / (2x)(5) (x-3)(3x)/5 and you can massage that as you will
*August 13, 2014*

**Complex Numbers**

if z = x+yi, you have two equations: (x-2)^2 + (y-2)^2 = 23 (x-8)^2 + (y-5)^2 = 38 They intersect at (1/5(20±3√10), 3/5(5∓2√10)) check: (1/5(20+3√10)-2)^2 + (3/5(5-2√10)-2)^2 = 23 You can verify the other.
*August 13, 2014*

**Precalculus**

If z = a+bi, we have (1+i)(a+bi) - 2(a-bi) = -11+25i Expand all that out and you get (-a-b)+(a+3b)i = -11+25i So, that means that -a-b = -11 a+3b = 25 a=4 b=7 So, z = 4+7i
*August 13, 2014*

**Precalculus**

I'd just multiply: (4-5i)^2 + (a+8i)(4-5i) + (-39+bi) = 0+0i Expand all that out and you have two equations in a and b. I get a = 2 b = 18 So, that leaves us with z^2 + (2 + 8i) z + (-39 + 18i) = 0 and the other root is thus -6 -3i
*August 13, 2014*

**math test review**

You know that 5^2 = 25 6^2 = 36 34 is less than 36. Now what do you think?
*August 13, 2014*

**Math**

no such number exists. Such terminology is bogus. If you mean 41 ten-thousandths, that would be 0.0041 You can have 41 thousand, but not 41 ten thousand.
*August 13, 2014*

**Math**

150% none (should be 70%) recall that 1.0 = 100%
*August 13, 2014*

**Calculus (need help with only d and e)**

The 2nd pill is shifted by 60 minutes. So, if the 1st pill is modeled by f(x), the 2nd pill will be modeled by f(x-t). Now just work with the new f(x).
*August 13, 2014*

**maths**

If you mean 9^(2x+1) = 81^x / 3^x expressing all as powers of 3, we have 3^(4x+2) = 3^3x so, 4x+2 = 3x x = -2 check: 9^-3 = 81^-2 / 3^-2 = 9^-4/9^-1 = 9^-3
*August 13, 2014*

**algebra**

your writing is so full of typos it's incomprehensible. When you get an answer, test it to see whether it works in the original equation.
*August 13, 2014*

**Algebra**

you could easily have verified it on your handy dandy calculator. Can't believe you went to the trouble of posting such an easy thing to check.
*August 13, 2014*

**math**

(25+12*15)*.12
*August 13, 2014*

**Algebra**

Your work so far is correct.
*August 13, 2014*

**statistic**

.20 * .30
*August 13, 2014*

**statistics**

Oops. I misread (b). My answer is ~rain & windy
*August 13, 2014*

**statistics**

(a) .20 * .30 = .06 (b) (1-.20) * .30 = .24 (c) .20 + .30 - .20*.30 = .44 (d) (1-.20) + (1-.30) - (1-.20)(1-.30) = .94 Note that (d) = 1-(a)
*August 13, 2014*

**math**

2pi = 6.28 so, you have 2pi r = C 6.28r = 27 now just divide by the 6.28 as usual to get r.
*August 13, 2014*

**Math**

You know that for the parabola y^2 = 4px It opens to the right The LR is 4p (So, if the shifted parabola is (y-k)^2 = 4p(x-h), our points and LR say (1-k)^2 = (3-h) (5-k)^2 = (-5-h) so, the parabola is (y-4)^2 = (x+6) So, now you have a 3rd point: the vertex at (-6,4) Now it&#...
*August 13, 2014*

**Algebra**

#1. x(2400-2x) #2. x(1800-6x)/2 Both of these are just parabolas, where the maximum area occurs at the vertex of the parabola. Recall that for y = ax^2+bx+c, the vertex is at x = -b/2a
*August 13, 2014*

**maths**

clearly, d = 3/2. So, if the first term is a, a(a+3d) = 34 a(a+9/2) = 34 . . .
*August 13, 2014*

**math**

Surely your text has sections on these topics. I expect that the accompanying graphs and sample problems there will be at least as good as any impromptu explanations here. Do a google on any of the above topics for many discussions. After that, if there's some kind of ...
*August 13, 2014*

**math**

http://www.wolframalpha.com/input/?i=x%2B2y-z%3D6
*August 13, 2014*

**maths**

total distance: 240 miles total time: 120/60 + 120/40 = 2+3 = 5 hours avg speed: 240/5 = 48 mph
*August 13, 2014*

**geometry**

why bother with a? Just prove x=7. 3(2x+4)+18 = 72 6x+12+18 = 72 6x = 42 x = 7
*August 13, 2014*

**maths**

3@5 = 3(5-3) = 6, so 4@(3@5) = 4@6 = 4(6-4) = 8
*August 13, 2014*

**algebra**

almost. If 2n=78, n=29 If 1/2 n = 78, n = 156 We customarily use a caret, as in 3^4, to indicate powers.
*August 13, 2014*

**math - typo**

10% of 4 is 0.4 None of the choices works. I suspect a typo in your presentation.
*August 13, 2014*

**Math**

If there were x 2-pointers and y free throws, then we know x+y = 18 (add the shots) 2x+y = 35 (add the points) Now just solve for x and y.
*August 12, 2014*

**math**

just as 5-3 = 2, 5/6 - 3/6 = 2/6 However, the instructions say to write the simplest form, so 1/3 would be my choice.
*August 12, 2014*

**Math**

Does 7 divide 3? Nope, so that cannot be a factor of 3u^3... List all the factors of each term: 3 u^3 x^5 y^8 3 7 u^6 x^5 Now pick the highest power of each prime or variable that appears in both terms: 3 u^3 x^5 That is the GCF.
*August 12, 2014*

**math**

you already have one pair: (1,1.50) Now just pick any positive integer, and multiply it by 1.50. That will give you other pairs: (2,3.00) (102,153.00) (9231,13846.50) For convenience of graphing, I'd stick with small numbers, though! :-)
*August 12, 2014*

**math trigonometry**

Draw a diagram, as usual. If the post is x meters from the house, which has height h, h/x = tan 45° = 1 So, h = x (h-20)/x = tan 30° = 1/√3 But, h=x, so (h-20)/h = 1/√3 h-20 = h/√3 (1-1/√3)h = 20 h = 20/(1-1/√3) = 47.32 m
*August 12, 2014*

**Math**

Oops. g◦f and f◦g are not onto, since (g◦f)(0) = 0 (g◦f)(1) = 2 And there is no x such that (g◦f)(x) = 1 (f◦g)(0) = 1 (f◦g)(1) = 1 (f◦g)(2) = 4 and there is no (f◦g)(x) = 2
*August 12, 2014*

**Math**

clearly g is not 1-1. For example, g(3) = g(2) Also, it is clear that both f and g are onto. Some good discussion can be found here: http://www.csee.umbc.edu/~stephens/203/PDF/7-3.pdf f◦g = 3g+1 = 3⌊x/2⌋+1 g◦f = ⌊f/2⌋ = ⌊(3x+1)/2⌋...
*August 12, 2014*

**arithematic**

the middle value is (51+64)/2 = 57.5 That is 6.5 away from each end, so |x-57.5| <= 6.5 See the graph at http://www.wolframalpha.com/input/?i=|x-57.5|+%3C%3D+6.5
*August 12, 2014*

**arithematic**

If the dimensions of the garden are x and y, with the building along side x, then x+2y = 81 So, the area (xy) is (81-2y)y = 81y - 2y^2 This is a parabola, with vertex at y=20.25 Now you can figure the other dimension. I suspect you meant to say 80 ft of fencing, but only you ...
*August 12, 2014*

**Math**

If the strip has width w, the pool is 60-2w by 80-2w So, (60-2w)(80-2w) = 1/6 (60)(80) Now just solve for w.
*August 12, 2014*

**Math**

If the dimensions of the whole garden are x and 2y (because there are two adjacent gardens, each x by y), 2x+4y = 100 2xy = 400 or, x+2y = 50 xy = 200 since x = 50-2y, (50-2y)y = 200 50y - 2y^2 = 200 y^2-25y+100 = 0 y = 5 or 20 So, x = 40 or 10 The garden is 10 by 40.
*August 12, 2014*

**6th grade math**

count the coins: n = d+13 count the value: 5n+10d = 440 5(d+13)+10d = 440 5d+65+10d = 440 15d = 375 d = 25 So, there are 25 dimes and 38 nickels
*August 12, 2014*

**Analytic Geometry**

(a) x^2+y^2 = 4 (b) surely you know how to figure the area and circumference of a circle of radius 2. (c) subtract that area from the area of the triangle. This is because the entire circle is within the triangle.
*August 11, 2014*

**Analytic Geometry**

Solving the equations in pairs, you find the vertices to be (2,5),(5,-1),(-3,-5) Now you can figure the incenter and inradius of the triangle. The equation of the circle is then easy.
*August 11, 2014*

**Algebra - eh?**

It appears you have something to do with the Pythagorean Theorem, but it's not immediately clear just what.
*August 11, 2014*

**coor. algebra**

work with units, just as with numbers. When doing conversions, just recall that you can always multiply by 1 and nothing is changed. You want to convert meters into miles, and seconds into hours. 3600 seconds = 1 hour So, 3600sec/hr = 1 Similarly, 1km = 1000m = 0.62 miles, so...
*August 11, 2014*

**Analytic Geometry**

Or, you can take the slopes of the sides. AB has slope 1/3 AC has slope 3/2 So, measuring as usual, angle A is arctan(3/2)-arctan(1/3) = 236.31°-198.43° = 37.88°
*August 11, 2014*

**Algebra**

all correct. Though I'd have written #2 as (9+5z)(9-5z) to associate it more readily with the difference of two squares.
*August 11, 2014*

**math**

.19a + .22b = 36.12 175a + 80b = 30080 a = 160 b = 26
*August 11, 2014*

**math**

5*5*5 = 125 she has 5 choices for each part.
*August 11, 2014*

**Algebra**

30w^4v^8 = 2*3*5 w^4 v^8 24y^3w^6v^2 = 2^3*3 y^3 w^6 v^2 The GCF is the highest powers of the factors that appear in both terms: 2*3 w^4 v^2 = 6w^4v^2 No other combination of factors and higher powers divides both terms
*August 11, 2014*

**math corrections**

if x=8, 8x = 64 so, now you have (4y)^2 = 64 Since 64=8^2, 4y can be 8 or -8
*August 11, 2014*

**math corrections**

If P(win) = p, P(lose) = 1-p p = 2/7 (1-p) so, p=2/9, 1-p = 7/9
*August 11, 2014*

**Algebra**

What is an algebraic expression for 5 more than z? My answer is z5
*August 11, 2014*

**polynomials and polynomial functions**

If you factor it, things should become clear: 3z(z^2-100) = 0 3z(z-10)(z+10) = 0
*August 11, 2014*

**math**

If you meant (1+sec20° cot20°)(1-csc20° tan20°) Then you have sec20° cot20° = csc20° csc20° tan20° = sec20° and the product becomes (1+csc20°)(1-sec20°) I don't see anything much else to do.
*August 11, 2014*

**Algebra**

Is 3 A an example of an algebraic expression? My answer is yes
*August 11, 2014*

**Algebra**

What is the word phrase for the Algebraic expression 4 (21 n)? My answer is 4 times the product of 21 and a number N
*August 11, 2014*

**Algebra**

well, 8 less than N is N-8, the product of 12 and x is 12x, so 12x-8
*August 11, 2014*

**Algebra**

What is the algebraic expression for the word phrase 8 less than the product of 12 and a number x.
*August 11, 2014*

**Maths**

check the definition of cosine. cos 65° = 15.5/length
*August 11, 2014*

**mathematics**

huh. what is 3 more than 2? Now just write down the digits in the right order.
*August 11, 2014*

**maths**

what is the smallest number divisible by both 6 and 8? 6 = 3*2 8 = 4*2 Every factor has to appear, so, you need 3*4*2 = 24
*August 11, 2014*

**math**

just plug in your numbers, using the amortization formula.
*August 11, 2014*

**Math**

D = |3 2| |2 3| = 5 Dx = |-3 2| |8 3| = -25 Dy = |3 -3| |2 8| = 30 x = Dx/D = -26/5 = -5 y = Dy/D = 30/5 = 6
*August 11, 2014*

**math**

plug in your data at http://www.gregthatcher.com/Mathematics/GaussJordan.aspx and see all the details unless you meant to use matrix inverses.
*August 11, 2014*

**Math**

(-4)(8) - (6)(-6) = -32 + 36 = 2
*August 11, 2014*

**Algebra**

your typos make it unclear whether you want y = 35x or y = x/35
*August 10, 2014*

**Accelerated Algebra**

so far, so good. The area of such a rectangle is x(40-x) = 40x - x^2 You want 40x - x^2 >= 350 -x^2 + 40x - 350 >= 0 Now, the roots of this function are 12.9 and 27.1 Since it is a parabola opening down, y is positive for x between the roots. So, for any value of x ...
*August 10, 2014*

**math**

I chose wolframalpha.com, which you can always use to verify your solutions. http://www.wolframalpha.com/input/?i=solve+10x%2By%3D278%2C+10y%2Bx%3D107+
*August 10, 2014*

**math**

v-w = -3 -x+y = 3 adding them up gives 0
*August 10, 2014*

**java**

in perl, $sum = 1; $sum += $n/$x**$n foreach $n (2..$r); print $sum; I leave it to you to provide values for x and r.
*August 10, 2014*

**Math**

g/b = 2/7 b = g+250 now just solve.
*August 10, 2014*

**maths**

looks ok to me.
*August 10, 2014*

**math**

if the triangle has side s, it has area = √3/4 s^2 perimeter = 3s if the circle has radius r, it has area = πr^2 perimeter = 2πr so, 3s+2πr = 12 s = 4 - 2π/3 r and we want to minimize the area a = √3/4 s^2 + πr^2 = √3/4 (4 - 2π/3...
*August 10, 2014*

**calculus**

df/dt = 1.2 - 0.24t now just plug in t=8
*August 10, 2014*

**calculus**

PI, not pie! It's a Greek letter, not a dessert. iv v = 2πr^2, dv/dr = 4πr now just plug in r=4 However, for a cone of height 8, v = 8/3 πr^2 If that's what you want, make the necessary change to the above logic.
*August 10, 2014*

**math**

List the factors of 81: 1,3,9,27,81 Pair them up and you have the available dimensions.
*August 10, 2014*

**Analytic Geometry**

(-1,5) and (-1,-3) are the ends of a vertical line. Since (3,1) is not at the same y-coordinate as either of those, the vertical line must be a diagonal. It has length=8. Since the diagonal has length 8, its sides have length 4√2, giving an area of 32. Knowing that the ...
*August 10, 2014*

**Math**

outside: (36)(25)(16.5) = 14850.00 inside: (34.5)(23.5)(15) = 12161.25 volume of material if a closed box: 2688.75 cm^3 Next, subtract the volume of the missing top. Finally, just multiply that by the density to find the mass
*August 10, 2014*

**Analytic Geometry**

This would have been a little tougher had the two points not lain on a horizontal line. As it is, (1,-2) lies 3 units to the left of (4,4) So, just pick the point (x,4) such that 1 is 3 units to the right of x. x = -2
*August 10, 2014*

**Precalculus**

r = a cosθ + b This is certainly not an ellipse. Play around some at wolframalpha.com For example, enter r = 2cosθ+2 and see the graph. Then mess around with a and b, positive and negative, with various ratios. The graph can have several distinct qualities. Read up ...
*August 9, 2014*

**Calculus-Math**

you just want dS/dt, which is just dS/dt = 2CR dR/dt - 2Cr dr/dt Now just plug in your values. Note that if r is constant, dr/dt = 0
*August 9, 2014*

**Calculus-Math**

x^2y^2 - 2x = 3 2xy^2 + 2x^2yy' - 2 = 0 y' = (2-2xy^2)/2x^2y = (1-xy^2)/x^2y Now use the quotient rule to get y" = ((-y^2 - 2xyy')(x^2y) - (1-xy^2)(2xy + x^2y')) / x^4y^2 = (2x^4-2xy^2-1) / x^4y^3 Now, if you wanted partial derivatives, go with Damon.
*August 9, 2014*

**Precal**

For (r,θ), x = r cosθ = 7 y = r sinθ = 5 For the new point, we have x = 2r cos(θ+π/2) = -2r sinθ y = 2r sin(θ+π/2) = 2r cosθ so, rectangular coordinates for (2r,θ+π/2) are (-10,14)
*August 9, 2014*

**Precalculus**

5pi/6 - pi/3 = pi/2 so you have 1/4 of a ring. The area of a ring is just the smaller circle subtracted from the larger circle. So, the area is 1/4 (pi (6^2-2^2))
*August 9, 2014*

**Precalculus**

Hmm. when θ=0, r = 4 when θ=pi, r = 4/3 so, the major axis is 16/3, and the semi-major axis is 8/3, with center at x=4/3, so it will be (x-4/3)^2/(8/3)^2 + y^2/b^2 = 1 and you can figure out b. As for the area, for an ellipse with semi-major axes a and b, area = pi*a*b
*August 9, 2014*

**Trigonometry**

draw an altitude. That will give you two right triangles that are 30-60-90 degrees. Since the sides of those triangles are in the ratio of 1:√3:2, and you have the long leg as half the base, or 10cm, the hypotenuse (the side of the isosceles triangle) has length 20/&#...
*August 9, 2014*

**Math**

Assume the ice packs closely enough that it fills the space involved. Since the volume of the chest is 2.5*1.5*2 = 7.5 ft^3, we will need at least 1/3 of that, or 2.5 ft^3 of ice.
*August 9, 2014*

**math**

surely your text has a discussion of scientific notation and the methods of its use. If not, a google search will provide copious information. Any explanation here would be less detailed, to be sure. For this problem, you have 3.2*10^-3 * 4.5*10^5 / 9.0*10^4 = 3.2*4.5/9.0 * 10...
*August 8, 2014*

**Algebra**

rewrite as 8y = -4x+6 y = -1/2 x + 3/4 so, y and all parallel lines have slope m = -1/2 all perpendicular lines have slope -1/m = -1/(-1/2) = +2
*August 8, 2014*

**Calculus-Math**

Not sure why the bother with saying u=g. Might as well just stay with u. Anyway, u = x+18 y = f(u) = 1/√u = 1/√(x+18)
*August 8, 2014*

**Calculus-Math**

clearly u(x) = 2x-4 f(u) = u^7 y = f(u) = u^7 = (2x-4)^7
*August 8, 2014*

**algebra**

Sure. Pick an easy multiple of 7: 7*40 = 280 Now, going down and up as far as you need, count by 7's: 280,273,266,259,252 280,287,...,497
*August 8, 2014*

**Duh - Algebra, not Calculus**

Could have saved myself some work if I'd kept that in mind!
*August 8, 2014*

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