Wednesday

October 1, 2014

October 1, 2014

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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