Thursday
October 2, 2014

Posts by Steve


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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