Thursday
August 28, 2014

# Posts by Steve

Total # Posts: 24,457

Algebra
f(n) = 10(1.02)^n A: since f(0) = 10, we're looking for a growth of 11.04/10 = 1.104 1.104/.02 is about 50, so as a rough guess I'd go with a domain of [0,50]. B: y-intercept is the initial population (when n=0) C: (f(5)-f(1))/(5-1) = 0.21 Represents a constant growth ...
June 3, 2014

ly and solve for x.
try something simple, like 3 = x/2 You want x all alone, so get rid of that pesky fraction. Since 2/2 = 1, multiply both sides by 2 and you get 3*2 = x/2 * 2 6 = x Now, for your problem: 8/18 = x/225 You can clear the fraction on the left by multiplying by 18. 8/18 * 18 = x/...
June 3, 2014

Choose the term to complete this sentence?
hmmm. I don't see any mention of a proposed experiment, so ...
June 3, 2014

Geometry
area of sector is 60/360 * 81pi arc length subtended is 60/360 * 18pi For any other questions, you're on your own...
June 3, 2014

Pre-Algebra
Just use the distributive property: n(n-1)-4 n*n - n*1 - 4 n^2-n-4 Since f(x) = x^2-4x+3, and you want f(-3), just replace all the x's with -3 and you have f(-3) = (-3)^2 - 4(-3) + 3 = 9+12+3 = 24
June 3, 2014

Algebra 1 (Reiny)
#1 no solution #2 ok #3 ok but I had to try two different ways of inserting parentheses before I got your answer. Grrr. The spacing in "t + 2" was especially deceptive. #4 x = 0 or 2 This time, overkill. Use parens as needed, but only as many as it takes to avoid ...
June 3, 2014

Algebra 1
since the denominator is the same on both sides, just work with the numerators: d+2 = -6 d = -8 BZZZT! But thanks for playing. Since the denominator is d+8, d = -8 is not in the domain, because that would cause division by zero. Before clearing fractions, be sure to note which...
June 3, 2014

You can go overboard with the parentheses. In this case, there's no confusion if you just write 1/x = 2/x^2 so, x/x^2 = 2/x^2 x = 2 check: 1/2 = 2/4 yes
June 3, 2014

(4x-3)^2 = 16x^2 - 24x + 9 You have -9. A perfect square will never end in a negative number.
June 3, 2014

calculus
add the two vectors and you get <539,0> + <43,43> = <582,43> arctan(43/582) = 4.2° As a bearing, that's E 4.2° N, or 85.8°
June 3, 2014

Algebra 1
work with the amount of orange juice in each container. If x cups of 100% orange juice are added to 8 cups of 25% orange juice, she will wind up with x+8 cups of 40% orange juice. .25*8 + 1.00*x = .40(8+x) x = 2 check: There are 2 cups of oj in the 8 cups of 25% mix There are ...
June 2, 2014

Math
sure. Two intervals that overlap at a single point. x+y >= 3 2x-3y <= 1 y <= x/2 The single point which satisfies all three equations is (2,1)
June 2, 2014

geometry
If the smaller diameter is d, the other is d+8 d + d+8 = 28 Now just find d, and figure d+8.
June 2, 2014

Calculus
for polar coordinates, dA = 1/2 r^2 dθ since each tiny wedge of area can be considered a sector of a circle of radius r and angle dθ. So, since r = 8+4sinθ, a = ∫[0,2π] 1/2 (8+4sinθ)^2 dθ now just expand the quadratic and evaluate each term...
June 2, 2014

physics
If the positive direction is east, we have to add up the two velocities: 395 - 55 = 340 or, 340km/h east
June 2, 2014

Algebra 1
since time = distance/speed, 12/s - 1 = 12/(s+1) Hint: 3 is one less than 4.
June 2, 2014

algebra - incomplete
no idea - how long did it fly?
June 2, 2014

Algebra
#1 If the sides are x and y, then x^2+y^2 = 68^2 (not √68) xy = 16 so, y = 16/x x^2 + 256/x^2 = 68^2 x^4 - 68^2 x^2 + 256 = 0 since 256 = 4*64, we have (x^2-4)(x^2-64) x = 2 or 8 (discard the negative roots) #2 If the cardboard is of side x, then (x-8)(x-8)4 = 784 x^2 - ...
June 2, 2014

Algebra/very confused
If you mean square root, use √ and some parentheses. Do you mean 3 ln e = √(7x) - 3 ln 6 ?? If so, recall that ln e = 1 3 ln 6 = ln 6^3 I still doubt that's what you want. It still looks bogus.
June 2, 2014

Math
those double minuses make a +, so you really have -39+24+64 leading minus signs make some people uncomfortable, so bob moved it to the end.
June 2, 2014

Algebra - Math HW HELP!
just work with the clues. The number's digits are abcde palindrome means it is abcba tens digit must be 1 or 2, so b=1 or 2 a2c2a a1c1a c*a = 54, so c=9 and a=6 or vice-versa 92629 62926 91619 61916 c+a=15 well, we already knew that with the 9 and 6 divisible by 4 knocks ...
June 2, 2014

Math algebra
Assuming a \$26 budget per table, you have 8 favors and 8 flowers. The 8 flowers cost 8*2.50 That leaves for the favors, cost = (26-8*2.50)/8 Better be cheap favors! And if your total budget is \$26 for all the tables, forget it, since the flowers for a single table already cost...
June 2, 2014

math
10% = 1/10 So, it rises 1/10 as far as it runs horizontally: .2km or 200m
June 2, 2014

Calculus Help
It might be helpful to rescale things by letting u = (x-30)/30 so the u-values go from 0 to 5. Then, since we are expecting an exponential relationship, see whether you can find something that fits ∆y/∆u = ky + c See where that takes you
June 2, 2014

math
No reason to stop there. Factor out all those 3's: 81(x^2+1)(x-1)(x+1) If you must pick one of those choices, then use the last one, since it factors the 9x^2-9 as well. (factor completely!)
June 2, 2014

algebra 2
if the tortoise is last, then you just have to worry about the other 5 animals. So, in how many ways can you arrange 5 things?
June 2, 2014

algebra
If the vertex of the parabola is at (0,630), then the arch is modeled by y = (630/315^2)(315^2-x^2) = 630 - 2/315 x^2 If the work is being done at a position c ft to the right of the vertex, it will be at the point (c,y(c)), on a line with slope 1/5. Unfortunately, this makes ...
June 2, 2014

math [linear equations]
If you can plot points, remember that two points determine a line. So, pick two easy points and plot them. Then draw a line through them. So, what's easy? How about letting x=0 or y=0? That gives us 0-y=5 y = -5 x-0=5 x=5 So, our two points are (0,-5) and (5,0) Now it ...
June 2, 2014

College Algebra
Excuse me? You already know that the length is 20 more than the width. So, if the width is 80, the length is 100. Sure enough, 80*100 = 8000 Or, since you know the width is 80, and area = length*width 8000 = 80 * length length=100 Don't forget your algebra I now that you&#...
June 2, 2014

geometry
Trying to match the question with the choices sure stumps me. Using similar triangles, if we label the vertices of the triangle P,K,F, and the library L, then we have ∆LPF ~ ∆KLP we want the distance LP and FP, and we have LP/2 = FP/KP LP/8 = KP/FP so, LP/2 = 8/LP ...
June 2, 2014

Math Helppp
you can play around at http://davidmlane.com/hyperstat/z_table.html and do all kinds of neat Z-table stuff. Just enter your mean and std and you can see the areas (probabilities) for various kinds of calculations.
June 2, 2014

math
#1 ok, though I'd write it as 4.00t + 25.00 Lose all that "x" stuff, if for no other reason than because "x" is often used as a variable. "*" is better for explicit multiplication. #2 where did 350 come from? If t shirts are ordered, then t of...
June 2, 2014

math problem
the slope of the line is ∆y/∆x, so m = 6/7 Now you have a point and a slope, so the line is y-4 = 6/7 (x-0) or y-10 = 6/7(x-7) and you can massage them to whatever form you like, and convince yourself that they are really the same equation.
June 2, 2014

math
the fifth-root of x^20 is (x^20)^(1/5) = x^(20 * 1/5) = x^4 Because (x^4)^5 = x^20 Roots are just fractional powers.
June 2, 2014

math 1 question!!!!!!
I think I'd go with a line plot. Each column will indicate how many days have a particular number of calls. The mode will be the tallest column. Plotting with time intervals could produce the same information, but would require more analysis.
June 2, 2014

trig
you cannot draw it here. However, you can see them here: http://www.wolframalpha.com/input/?i=plot+y%3Dtan%28x%29%2C+y%3D2cos%28x%29+for+x+%3D+-pi..pi x is in radians, but the graphs look the same for degrees: http://www.wolframalpha.com/input/?i=plot+y%3Dtan%28x*pi%2F180%29%...
June 2, 2014

Math
Twenty tires are tested to see if they last as long as the manufacturer claims they do. Three tires fail the test. Two tires are selected at random without replacement for an inspection. Find the probability that both tires fail the test. Which is greater, the probability that...
June 2, 2014

Trigonometry, can someone check this please
money is no excuse. you evidently have the internet. A simple google search will provide oodles of explanations and examples. One key fact, which I found one of my students was having trouble with: For the purposes of the trig functions, the hypotenuse is not a side! When ...
June 2, 2014

Trigonometry, can someone check this please
you have posted quite a few of these, and I think you have missed them all. Better review the definitions of the basic trig function. For this one, you want arcsin(50/120)
June 2, 2014

Algebra/can you ck my work
variance of 4 means std of 2. 5 is below the mean by 2.5 std. P(Z < -2.5) = .0062 = 0.62% Think about it. Your answer indicates that virtually all of the pieces are defective. That would surely not ever be tolerated in a real-world situation. Take a visit to http://...
June 2, 2014

college algebra
If two numbers multiply to produce a product of zero, then one of them must be zero. So, if (w-80)(w+100)=0, then either w-80 = 0 w=80 or w+100 = 0 w = -100 Now pick the value that makes sense for this problem. Then check your conclusion by plugging in the value and seeing ...
June 2, 2014

college algebra
you have the right idea, but you should have said w(w+20) = 8000 w^2+20w = 8000 w^2+20w-8000 = 0 (w-80)(w+100) = 0 ...
June 2, 2014

College Algebra
x^2-9x-1 = 0 x^2-9x = 1 x^2 - 9x + 81/4 = 1 + 81/4 (x - 9/2)^2 = 85/4 x - 9/2 = ±√85/2 x = 9/2 ±√85/2 = 1/2 (9±√85) 2x^2+17x+2 = 0 2x^2+17x = -2 2(x^2+17/2 x) = -1 x^2 + 17/2 + 289/16 = -1 + 289/16 (x + 17/4)^2 = 273/16 x + 17/4 = ±...
June 2, 2014

Algebra 1
(x+a)(x+b) = x^2 + (a+b)x + ab If a>0 and b<0, then ab<0 so there's no way that n can be positive if a and b have different signs.
June 2, 2014

Simplify Polynomials
18x^2+6+4x-15x^2-4+13x (18-15)x^2 + (4+13)x + (6-4) 3x^2 + 17x + 2 3x^2+6-2x+5x-4x^2+9 (3-4)x^2 + (-2+5)x + (6+9) -x^2 + 3x + 15 3x^2+3x-7x+3-5x^+2 (3-5)x^2 + (3-7)x + (3+2) -2x^2 - 4x + 5 -5 is the coefficient of x -4 is the coefficient of x^2 (m^2-m-4)+(m-5) m^2 + (-1+1)m...
June 2, 2014

Algebra Math
the 3 movies use 3.6+2.8+4.1 = 10.5 GB So, his available space will be 8.25+2.3 = 10.55 GB
June 2, 2014

algebra math
9pts/6wks = 3/2 pts/wk
June 2, 2014

check set up trigonometry
Nope. cot28 = x/360
June 2, 2014

Math
Hmmm. I don't see an obvious application of the law of sines here. However, if we consider the distance directly to the plane, and call the first one x and the second one y, then 1000/x = sin52° 1000/y = sin16° Then we want the distance z given by the law of ...
June 2, 2014

check my set up please, trig
(105-5)/x = sin43°
June 2, 2014

algebra
1/2 (2x+4)(x+3) = 56 x^2+5x-50 = 0 (x+10)(x-5) = 0 ...
June 2, 2014

Math
1.5km/16km = 3/32
June 2, 2014

Calculus
e=2.718 so, the abs error is 2.718-2.68 = 0.038 as a % error, that is .038/e = 1.39%
June 1, 2014

Geometry
If the point directly below the top of the tree is x feet from the base, then we have h/(x+10) = tan61° h/x = tan78° eliminating x, we get the height h/tan61° - 10 = h/tan78° h = 10(cot61°-cot78°)
June 1, 2014

Math
csc60° * cot 30° * tan 60° = 2/√3 * √3 * √3 = 2√3 2sec^2 45° cos30° = 2*2*√3/2 = 2√3
June 1, 2014

Geometry
(25/35)^3 = (5/7)^3
June 1, 2014

math
4D coefficients require a variable. The 6 is just a constant, not a coefficient of x. 7A Total is just the sum: 6t+2 + 9t-6 = (6+9)t+(2-6) = 15t-4 15A (1.8 x 10^1)(7 x 10^5) = (1.8x7)x10^(1+5) = 12.6x10^6 = 1.26x10^7 18D -x(5x-4) = -x*5x -x(-4) = -5x^2 + 4x Look again at your ...
June 1, 2014

Algebra
If x is the smaller voltage, then x+32 is the larger one. x + x+32 = 126 Now find x, and you have the smaller voltage.
June 1, 2014

Maths
since the right side of the intervals are at 9,10,11 just add up (1)* f(9)+f(10)+f(11) Again use the right sides, of width 2/3 each, to get (2/3)*(f(-7/3)+f(-5/3)+f(-1)) Do the left sums similarly, using the appropriate widths.
June 1, 2014

Geometry
9 edges Euler's formula: V-E+F = 2
June 1, 2014

math(urgent)
.75p = 1200, so the original price p=1600 Since the profit was 10% of 1200, the cost was 1080. At 1600, the profit would be 520, or 32.5% of the selling price. I gotta admire you syntax on that (c) part. That simply cannot be how the question was worded . . .
May 31, 2014

MATH GEO URGENT
Since opposite angles are supplementary, we have 2x+4x = 180 x = 30 and the angles are 60,90,120,90
May 31, 2014

math 1 question!!!!!!
May 31, 2014

Statistics/ is this how I do it.
add and divide by 5 gives the mean, not the range the range is hi-low = 103-83=20 The mean is 96.4 To find the std, (1) take the difference of each value from the mean (2) square that difference (3) add up all those squares (4) take the square root. That is the std. Better ...
May 31, 2014

Math
X is 5 by 10 Y:x = 4/3, so Y is 20/3 by 40/3 and its perimeter is thus 40 or X is 5 by 10, so its perimeter is 30 Y:X = 4:3, so its perimeter is 40
May 31, 2014

math
6b/3a + b/a = 6b/3a + 3b/3a = 9b/3a = 3b/a or 6b/3a + b/a = 2b/a + b/a = 3b/a
May 31, 2014

math
well, what's 1000000/600 * 14 ?
May 31, 2014

math
just multiply by the dimensions: 60m * 25m * 7m = 10500 m^3
May 31, 2014

math
Looks like this question has been done several times. Check the Related Questions links below.
May 31, 2014

Algebra 1
Same old parenthesis-free exposition. Surely by now you can factor the expressions and eliminate common factors. Take a look at http://www.wolframalpha.com/input/?i=%28%283h^3+-+6h%29%2F%2810g^2%29%29+*+%28%284g%29%2F%28g^2+-+2g%29+%29 and notice how the parentheses make ...
May 31, 2014

math
how many from 11:35 to 12:00? how many from 12:00 to 12:50? Now add them up...
May 31, 2014

math
34/d = cos 72° now just solve for d.
May 30, 2014

HELP!!!!
correct
May 30, 2014

Math HELP
Just read the words and write as symbols. The number of apples in an apple tree n after subtracting by 6, n-6 multiplying by 6, (n-6)*6 dividing by 6, (n-6)*6/6 equals 6. (n-6)*6/6 = 6 n-6 = 6 n = 12 books = x a = x/2 + 1 b = (x-a)/2 + 2 c = (x-a-b)/2 + 3 x-a-b-c = 3 make all ...
May 30, 2014

MATH
LCD = (k-3)(k+3) = k^2-9
May 30, 2014

math
well, clearly, a is 11 or 18 b is 5 Now pick the correct answer.
May 30, 2014

trig
you are correct
May 30, 2014

Geometry
well, you know that each sphere holds 3392.92/30 = 113.097 so, now you know that 4/3 pi r^3 = 113.097, so r = 3
May 30, 2014

math
4770(1+r/4)^(4*3) = 8233 (1+r/4)^12 = 1.726 1+r/4 = 1.0465 r/4 = .0465 r = .186 = 18.6%
May 30, 2014

Math
6700(1+.046/2)^(2*15) = 13253.90
May 30, 2014

algebra
Do you mean (x^10 + 5x^9 + 4x^8)/(x+2) ? If so, then you have x^8(x^2+5x+4)/(x+2) x^8(x+1)(x+4)/(x+2) but I don't see what that has to do with the Binomial Theorem.
May 30, 2014

Math
Draw a Venn diagram. Look for the intersections. For this problem, let the two circles represent how many people eat meat an d fish, respectively. In this case, 2 eat both. So, put a 2 in the place where the two circles intersect. Now, since we know that 6 eat meat, and we'...
May 30, 2014

#1 I get 2n^2/(n-6) #2 (2x^2 + 8x + 6)/x / (2x^2 + 2x)/(x^3 - x^2) 2(x+1)(x+3)/x / 2x(x+1)/x^2(x-1) (x+3)/(x-1) #3 8b^3c/b^2c / (4b^2 + 4b) 8b / 4b(b+1) 2/(b+1) Next time, show your steps. You are evidently taking some wrong turns.
May 30, 2014

Man, you gotta start using parentheses. Can't you see how hard it is to separate the terms and factors? #1 and #2 are ok #3 3h(h^2-2)/10g^2 * 4g/g(g-2) I suspect a couple of typos, so I will say it's (3g^2-6g)/10g^2 * 4g/(g^2-2g) 3g(g-2)/10g^2 * 4g/g(g-2) 3(g-2)/10g * ...
May 30, 2014

Trig
If you measure the temperatures and plot them, the curve is sinusoidal. This is mainly because the earth is a sphere rotating in space, relative to the sun. As the sunlight hits the surface, it causes the temperatures to rise, but then the earth turns away, and they fall again...
May 29, 2014

Algebra
6e^-x = 3 e^-x = 1/2 e^x = 2 x = ln 2 32(1.5)^x = 640 1.5^x = 20 x ln 1.5 = ln 20 x = ln20/ln1.5 and similarly for the others. If you get stuck, come on back and show what steps you took. Just remember that log and exponents are inverse operations. Just as with roots, if you ...
May 29, 2014

algebra
speed = distance/time So, you want 20/1.2 - 20/1.6 = ?
May 29, 2014

geometry
The slope of a line does not change. The length expands by the dilation factor.
May 29, 2014

algebra
so, how many watts per decibel? Divide that into 2.42*10^-5 what's this "cross"? Can't you say "times", or use the multiplication symbol?
May 29, 2014

math
(1) The sides are x and y, so y = 400-x The area is thus a = xy = x(400-x) (2) If the side x is parallel to the water, x+2y = 400, so y = (400-x)/2 and the area is a = xy = x*(400-x)/2 (3) x+y=200, so the area is a = xy = x(200-x) If you need to find the maximum area, just ...
May 29, 2014

algebra
3 = x-3 6 = x As for the other, I can't quite decode your weird text. I can say that ln e = 1 ln √n = 1/2 ln n ln a - ln b = ln(a/b) If you have ln e = ln √6 - 3ln x 1 = ln√6 - ln x^3 1 = ln √(6/x^6) e = √(6/x^6) 6/x^6 = e^2 x^6 = 6/e^2 x = (6...
May 29, 2014

Precalculus
y=2*pi*x*(25-x)^2
May 29, 2014

college algebra
If the numbers are x-1,x,x+1, then 3x = 651 x = 217 So, the numbers are 216,217,218 Don't know what was all that stuff with factors of 651. Looks like you need to study what "sum" and "consecutive" mean. The two paychecks are p and .75p. So, p + .75p = ...
May 29, 2014

Algebra
Reference angles are always measured from the x-axis. So, since 3pi/4 = pi - pi/4, the reference angle is pi/4. Better go back and review that topic some.
May 29, 2014

college algebra
you are mixing up all kinds of unrelated numbers, and then throwing darts at the calculations. If x is the slower rate, then 3x is the faster rate. So far so good. Now consider that distance = time * speed, and the total distance covered is 64 miles. Since the time for both ...
May 29, 2014

MATH
a rational number can be written as a fraction. Any terminating or repeating decimal is also rational. √5 is not rational. There is no fraction which is exactly equal to √5. The decimal value goes on forever and never repeats. It is easy to prove that √5 is ...
May 29, 2014

Math - incomplete
don't you see that there's something missing here?
May 29, 2014

Algebra 2
OK. You do understand that if the sides of the rectangle are x and y, then the area is a = xy right? Given the equation of a parabola, can you find the vertex? If y = ax^2+bx+c, then the vertex is at x = -b/2a So, in each case, figure out what x and y are, express the area a ...
May 29, 2014

Algebra 2
(1) The sides are x and y, so y = 400-x The area is thus a = xy = x(400-x) (2) If the side x is parallel to the water, x+2y = 400, so y = (400-x)/2 and the area is a = xy = x*(400-x)/2 (3) x+y=200, so the area is a = xy = x(200-x) If you need to find the maximum area, just ...
May 29, 2014

Geometry
the car moves as far as 10 times the circumference of the wheel. C = pi*d, so C = 22pi = 69.11 inches so, the car moves 691.1 inches, or 57.6 ft
May 29, 2014

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