Wednesday
October 1, 2014

Posts by STEVE


Total # Posts: 25,415

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

Algebra - wow - go with Damon
Nice one, Damon. My calculations get kind of complicated. Your is much, much simpler. At least we agree on the maximum y/x = 5.82
August 8, 2014

Algebra
The line y=kx is tangent to the circle in two places. This will occur in two places, one with maximum slope, and one with minimum slope (y/x). As a function of x, y = 3±√(6-(x-3)^2) Clearly the maximum slope is achieved on the upper half-circle. kx = -(x-3)/(y-3...
August 8, 2014

Math (fibonacci
y = 1985+x 200 = x+y Eliminate y and we have 1985+x = 200-x 2x = -1785 x = -892.5 and the numbers are 1985, -892.5, 1092.5, 200
August 8, 2014

math challenge
2 hours is 7200 seconds. one day is 1440 minutes. so, ...
August 8, 2014

Algebra
6.0 <= pH <= 6.5
August 8, 2014

Algebra
10 <= c <= 12 The middle time is (10+12)/2 = 11 Each extreme is only 1 away from 11, so |c-11| <= 1
August 8, 2014

maths
8 hours means $32 The rest must be in tips, or at least $118
August 8, 2014

Algebra
the total points are now 68+78+90+91 = 327 To average 85 on 5 tests, you need 5*85 = 425 So, how many points short is that?
August 8, 2014

math
since c = 2πr, r = c/2π since a circle has a = πr^2, a = π(c/2π)^2 = c^2/4π the square has perimeter 4*4π = 16π so, the circle has area a = (16π)^2/4π = 64π
August 8, 2014

Maths
10 = 2p-4 p = 7
August 8, 2014

Math 221
take a read here: https://people.richland.edu/james/misc/acmeth.html
August 8, 2014

Algebra 2
Read up on hexagonal numbers. You can get started here: http://en.wikipedia.org/wiki/Hexagonal_number
August 7, 2014

Algebra 2
is there a common difference? is there a common ratio? How about showing some effort here?
August 7, 2014

Algebra 2
If the 3rd entry were 116, it'd be arithmetic, with d=113.5 But as it is, it's neither
August 7, 2014

Algebra 2
what's the problem? Just write them out: a_1 = 0 a_2 = 5a_1 + 7 = 5*0+7 = 7 a_3 = 5a_2 + 7 = 5*7+7 = 42 and so on
August 7, 2014

Algebra 2
a_1 = -5 a_2 = 2(-5)+7 = 3 and so on
August 7, 2014

Algebra 2
a_1 = 9 a_2 = 3*9 = 27 and so on
August 7, 2014

Math 221
first note that each term has a w in it, so w(9-w^2) Now recall that a^2-b^2 = (a-b)(a+b), so since 9-w^2 is the difference of two squares (3^2-w^2), we have w(3-w)(3+w)
August 7, 2014

Algebra 2
Since you have figured r, and a = 0.48, Tn = 0.48*2.13^(n-1) T12 = 0.48*2.13^11 = 1965.25 S12 = 0.48(1-2.13^12)/(1-2.13) = 3703.98
August 7, 2014

Algebra 2
Clearly, a_n = 5*4^(n-1) So, S_16 = 5(1-4^16)/(1-4) =
August 7, 2014

Algebra 2
Sure. It's all clearly explained. For the first one, a_1 = 112 a_2 = -9.5*112(1-112) = 118104 and so on. Similarly for the other example.
August 7, 2014

trig
review your trig function definitions. I think that 41/x = tan 65 However, as your language is almost incomprehensible, it's hard to be sure.
August 7, 2014

Physics
In the absence of other factors, both will hit the ground at the same time, because the force of gravity is all that's acting on them, making them fall at the same speed. The horizontal speed of the bullet has no effect on the pull of gravity. However, in real life, the ...
August 7, 2014

math
b/g = 9/8 b = g/2 + 15 So, to start with there were 27 boys and 24 girls
August 7, 2014

computers
I'd say it's an IP address, as discussed here: http://technet.microsoft.com/en-us/library/cc958048.aspx and also, no doubt, in your study materials...
August 7, 2014

math
we have two points: (3,26) and (7,18) You are correct that y = -2x+b So, plug in either point. For example, 26 = -2(3)+b 26 = -6+b b = 32 y = -2x+32
August 7, 2014

math
no idea what "b" represents. And with only one data point, we cannot determine anything else. What was the starting pressure? Or, how much pressure did it lose each day? Please make sure your posting accurately reflects the problem as presented, maybe with some ...
August 7, 2014

math
a cubic foot is 12^3 = 1728 cubic inches. So, the quart weighs 60/1728 * 60 = 2.08 pounds But then we knew that, since "a pint's a pound, the world around."
August 7, 2014

physics
Just convert the data to rectangular coordinates: 11 @ 88° = 0.0349,10.9933 6.8 @ 115V = -2.8738,6.1629 so, now you want (x,y) such that 0.0349+x = -2.8738 10.9933+y = 6.1629 Then convert that (x,y) back to polar avlues.
August 7, 2014

Math
2^3 = 8 5^-2 = 1/5^2 = 1/25 so, (a) = 8/25 You cannot simply disregard the negative sign of the exponent, nor willy-nilly move items from bottom to top. You have directly replaced 2^-2 with 2^3 and 1/a^4 with a^4. 2^-3 = 1/2^3 = 1/8 So, (b) = 1/(8a^4)
August 7, 2014

MATH(HELP)
I believe your previous post said that there were then 30 more guppies than in the beginning. That means that there were 120 to begin with, since adding 1/4 of 120 means adding 30. However, that leaves us nothing to do with the goldfish or angelfish. I suspect you have still ...
August 7, 2014

MATH - eh?
list the facts: g/a = 2/3 a = 2/3 f The shop keeper decided to replace 1/4 of the guppies with some angelfish. The number of angelfish she added was equal to the number of the guppies she replaced. well, duh. Both sentences say the same thing. The last sentence leaves us ...
August 7, 2014

math
well, you have the equation. How many weeks from the time she started saving, until Christmas? $25/week, babe. I assume you know how many days per week . . .
August 7, 2014

math
looking at the data, it appears she saved #25 each week. So, after x weeks, her saving y would be y = 25x You can work into that by noting that if y = mx+b when x=7, 175 = 7m+b when x=15, 375 = 15m+b so, 8m = 200 m = 25 Now you have y = 25x+b plugging either point shows that b...
August 7, 2014

math
Sounds like a good plan. Was there a question in there somewhere?
August 7, 2014

Geometry
consider how many reds and the total cards there are for each draw. You multiply the chances for each event, giving 26/52 * 25/51 * 24/50
August 7, 2014

Math
Looks like 12 to me, since 144 = 12*12
August 7, 2014

spelling mistakes
theree guest lectures come from CMC hospital to give the trainee and her fellowmates a common introduction above community developement.
August 7, 2014

Statistics
well, 3000 is 1 std above the mean. So, check your Z table for the area of the tail above Z=1. Or, play around at http://davidmlane.com/hyperstat/z_table.html
August 7, 2014

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