Monday
July 28, 2014

Posts by steve

Total # Posts: 24,006

Algebra
they all satisfy x-2y = 1

Math
the park is 150 by 450, making a perimeter of 1200 ft 1200/10 = 120 seconds G

revenue = price * demand = pq = p(300000-15000p) cost for q copies is 4q profit = revenue-cost = p(300000-15000p)-4(300000-1500p) = -15000p^2 + 306,000p - 1,200,000 maximum profit is thus at p = 306000/30000 = 10.20

Geometry
Just a guess: 3/5?

math
solve for x in 150*1.03^x = 300 1.03^x = 2 x log1.03 = log2 x = log2/log1.03 = 23.45 years

science
(2^x ln2 - e^x)(2^x+e^x) - (2^x-e^x)(2^x ln2 + e^x) --------------------------------------------------------------- (2^x+e^x)^2

science
just plug and chug, using the quotient rule (2^x ln2 - e^x)(2^x+e^x) - (2^x-e^x)(2^x ln2 + e^x) ---------------------------------------------------------------            (2^x+e^x)^2 You can "simplify" that to

science
just plug and chug, using the quotient rule (2^x ln2 - e^x)(2^x+e^x) - (2^x-e^x)(2^x ln2 + e^x) ------------------------------------------------------- (2^x+e^x)^2 You can "simplify" that to

math
Excuse me? You developed your own function. The price after r rate increases is 6.40 + 0.1r so, for r=0, the price is 6.40 for r=8, the price is 6.40+.1*8 = 7.20 Between those two prices, she'll make at least \$1500. Take a look at http://www.wolframalpha.com/input/?i=plot+...

math
Your equation looks good. So, just solve it and you get (250-5r) (6.40+0.10r) >= 1500 -.5r^2 - .7r + 1600 >= 1500 .5r^2 + .7r - 100 >= 0 Now, solve the left side using the quadratic formula, and you find that .5r^2 + .7r - 100 = 0 at x = -22.8 and 8.8 Between those tw...

Delcambre High
r:m = 4/15:1/3 = 4/15:5/15 = 4:5

math
well, you know that 1/3 pi r^2 * 8 = 250 So, now just solve for r.

math
23010(1+.029/2)^(2*9) = 29816.29

math word problem
If he buys x packs of batteries, we wan to find out how many packs it takes to cost more than the price of the charger and batteries. 7x > 15.39 x > 2.2 So, after using the rechargeable batteries 40 times, they will be the better buy.

Algebra/not sure what to do Thank You
just pick any value for x and evaluate y at that point. x=0: y=2*0-1 = -1 So the point is (0,-1) x=-5: y=2(-5)-1 = -11 So the point is (5,-11) x=17: y=2*17-1 = 33So the point is (17,33) and so on for any x value you want. You can also pick y, but then you have to work backward...

geometry
Can't tell. The two bases are equilateral triangles, but the three lateral faces are rectangles of area 6. But is the prism tall and skinny, or short and fat? You must know either the height of the prism, or the side length of its bases. If the bases are of side 2s, then e...

Trig
55° + 360k are all coterminal for any integer k. 9/5 π + 2kπ are all coterminal for any integer k. So, pick a positive and negative k

math(log)
since 81 = 3^4, we have 3^-4 = 3^(2x-1) -4 = 2x-1 x = -3/2 logx + 3/logx = 4 log^2(x) - 4logx + 3 = 0 (logx-1)(logx-3) = 0 logx = 1,3 x = 2,8 check: 1+3/1 = 4 yes 3+3/3 = 4 yes

Math
us always, draw a diagram. Label one of the acute angles θ. The side opposite is 4 and the side adjacent is 3. (Note: the hypotenuse is not a side!) The hypotenuse is 5, since 3^2+4^2=5^2 Now, review your trig definitions. sinθ = opposite/hypotenuse = 4/5

geometry
sin 40° = x/80

math
sin 70° = 25/x As usual for trig problems, draw a diagram. In this case, label the angle at the ground 70°. You want the hypotenuse (x), and have the side opposite the angle (25).

math
Not sure what "compounding amount" means. If you mean the final amount after adding the interest, just apply the usual formula, which you surely have. A = 700(1+.015/12)^(12*8) = 789.19 To find just the interest, subtract the original \$700, leaving just \$89.19

maths
if the bot has speed b, and the stream has speed s, then since time=distance/speed, 12/(b-s) + 40/(b+s) = 8 16/(b-s) + 32/(b+s) = 8 b=6 s=2 check: 12/4 + 40/8 = 3+5 = 8 16/4 + 32/8 = 4+4 = 8

math algebra?
You forgot the minus sign. -4p < 36 p > -9 That's just shorthand for switching sides of the inequality: -4p < 36 -36 < 4p -9 < p

maths
3000/(pi*75) = ?

10
What happens if the square does not share sides with the triangle? If the vertices of the triangle are at (0,0),(6,0),(0,12), then if one side of the square is on the hypotenuse, and one corner is at (s,0), another is at (0,2s), so the hypotenuse has length √5 s. Now, we...

trig angle of elevation
The rim is only 4 feet above his eyes, so 4/x = sin 12.5° we don't really care how far horizontally he is from the basket. All that stuff about 15 feet and stepping back is just noise. The final picture is just a 12.5° angle with a 4-ft height difference.

don't let those fractional exponents confuse things. What you have is just (x^1/5)^2 + x^1/5 - 6 = 0 That's just like u^2+u-6=0 So, just factor it to be (x^1/5 + 3)(x^1/5 - 2) = 0 x^1/5 = -3 or 2 x = -243 or 32

Math
18% compounded 12 times per year give 1.5% per month. So, 6 years = 72 months.

MATH
3(x+2) = 3*x + 3*2 = 3x+6 an identity 3(x+4) = 3*x + 3*4 = 3x+12 ≠ 3x+4 not only not an identity, but not even conditional. There is no value of x which makes it true!

math
√32 = 4√2, so we have 4x*4√2xv^2 + v√2x^3 16x√2x√v^2 + v√2x√x^2 16xv√2x + vx√2x 17vx√2x

math
2:3 = 4:6, so draw the picture with 4 pencils and 6 pens

Math
38*34 = 1292 you are correct

math
var=25 means std=5 113 is 12 below the mean, or 2.4 std So, what's P(Z < -2.4)

Math
5^1 * 5^10 5^5 * 5^6 5^20 * 5^-9 In each case the sum of the powers is 11.

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 ...

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/22...

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

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

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

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 amb...

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...

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

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

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°

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 ...

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)

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

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,...

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

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

algebra - incomplete
no idea - how long did it fly?

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 - ...

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.

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.

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 o...

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...

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

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

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!)

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?

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 ...

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 shou...

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&#...

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 ...

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.

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...

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.

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.

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.

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%2...

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...

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 look...

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)

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://davidmla...

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 whe...

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 ...

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 = ±...

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.

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 + ...

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

algebra math
9pts/6wks = 3/2 pts/wk

check set up trigonometry
Nope. cot28 = x/360

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 cosine...

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

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

Math
1.5km/16km = 3/32

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

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°)

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

Geometry
(25/35)^3 = (5/7)^3

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 ...

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.

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.

Geometry
9 edges Euler's formula: V-E+F = 2

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 . . .

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

math 1 question!!!!!!