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February 1, 2015

Posts by Steve


Total # Posts: 28,522

Math
what do you mean simplify? You can distribute the fraction, and you get -15/20.5 = 0.73 so you could write -.73x^2 - 2.20x - 1.65 but that's only approximate. SO, again, what do you mean by "simplify"? I will note that x^2+3x+2.25 = (x+1.5)^2 if that helps You ...
December 8, 2014

Math
12x^12/4x^3 = 3x^9 x^8/24x^6 = x^2/24 3x^9 * 24/x^2 = 72x^7
December 8, 2014

Homeschool
each 1.5 cm represents 3m So, how many times bigger is 8 than 1.5? There will be that many 3m lengths. So, the real length is 8/1.5 * 3
December 8, 2014

trig
you can't solve it. It's just a function definition. But, the graph is at http://www.wolframalpha.com/input/?i=r+%3D+3%281-sin%CE%B8%29 Now, if you want to see its equation in rectangular coordinates, r = 3 - 3sinθ r^2 = 3r - 3r sinθ x^2+y^2 = 3r - 3x x^2+y^2...
December 8, 2014

math
40*40 = 1600 So, the cost is (800/9)*25 + 800*2.50
December 8, 2014

math
if $x at 8%, then the rest (8000-x) is at 12%. So, .08x + .12(8000-x) = 650 Now do the math.
December 8, 2014

Algebra 2
clearly there are (2y^2+6)/(y^2-1) notebooks. So, plug in y=3 to find how many.
December 8, 2014

Math
you get the y-intercept when x=0 You get the x-intercept when y=0. So, 1/6 x^4 - 2x^2 + 4 = 0 x^4 - 12x^2 + 24 = 0 x^2 = (12±4√3)/2 = 6±2√3 So, take each of those values and get its ± square roots.
December 8, 2014

fundamental to programing
read x,y,z if (x<y & x<z) {print x} else if (y<x & y<z) {print y} else {print z}
December 8, 2014

Math (TRIG)
Review the equation for a hyperbola in polar coordinates. #2 Hint: sec^2 = 1 + tan^2 #3 y = 500 sin70° t - 16t^2 Solve for t when y=0 to find the time in flight The x-velocity is constant at 700 cos70° So using the time from step 1, distance = speed * time
December 8, 2014

Trig (math)
#1 in polar form, -1+√3i = (2,2π/3) So, the two square roots of that are (√2,π/3) and (√2,4π/3) #2,#3 just plug in x = r cosθ y = r sinθ #4 8x - 7y = -10 7y - 8x = 10 7r sinθ - 8r cosθ = 10 r = 10/(7sinθ-8cosθ)
December 8, 2014

math
well, 2 2/3 = 2.66 2.75 = 2.75 5/2 = 2.50 So, which is least?
December 8, 2014

math
24 = 6*4 42 = 6*7 So, 6 people each clean 4 small and 7 large cages. No other larger number divides both 24 and 42, since 4 and 7 have no common factors.
December 8, 2014

Algebra
If there are n games, you want .40*.80n + p*.20n = .50n .32 + .20p = .50 .20p = .18 p = .18/.20 = .9, or 90% Check. If there are 100 games, you have won 32 already. So, there are 20 games left, and you need to win 18 of them, or 90%
December 7, 2014

Trig (math)
#1 You have y = 9 x = 9√3 So, tanθ = 1/√3 r = 18 You should be able to recognize a 30-60-90 right triangle... #2 (4*5)cis(30°+120°) #3 is just the same. #4 is the same, but divide r, and subtract angles.
December 7, 2014

calculus
Just plug in the numbers you have, and you get (20)(10)(5) + (20)(15)(3) + (10)(15)(8) = 3100 How did you come up with 265?
December 7, 2014

Math
the distance s = 1/2 at^2 So, 500 = 4.9t^2 Now you have the time. You need to say what the velocity's direction is. As you recall, s = vt + 1/2 at^2 It makes a big difference whether v is positive or negative. In 5 seconds it will fall 4.9*5^2 meters.
December 7, 2014

L'Hopitals Rule
sin(x^2-4)/(x-2) --> 2xcos(x^2-4)/1 --> 4 ln(x-3)/(x-5) --> (1/(x-3))/5 -> 0 (x-pi/4)tan(2x) = (x-pi/4)/cot(2x) --> 1/(-2csc^2(2x)) = -1/2 sin^2(2x) --> -1/2
December 7, 2014

linear approximation
f'(x) = -24x sin(3x^2) f'(0) = 0 So, you want the line with slope=0 through (0,4). Duh. y=4 Kind of a dumb place to approximate, eh? With a horizontal tangent, and all that.
December 7, 2014

Pre Calc Take 2
Hmmm. Let's try that again without the typo... log (x-6)*(x+3) = 1 x^2-3x-18 = 10 x^2-3x-28 = 0 x = (3±11)/2 x = -4 or 7 The only real solution is x=7 Check: log(1)+log(10) = 1 yes
December 7, 2014

Pre Calc
well, work it out... log(x-6)+log(x+3) = 1 log (x-6)*(x-3) = 1 (x-6)*(x-3) = 10 x^2-9x+18 = 10 x^2-9x+8 = 0 (x-1)(x-8) = 0 x = 1 or 8 x=1 does not work, because then x-6 < 0 and the log is not defined. So, the only real solution is x=8 Check: log(2)+log(5) = 1 log(10) = 1 ...
December 7, 2014

Algebra 1
Describe how the graphs of y =IXI nand ym = IXI -15 are related. 1- the graphs have the same shape,. The y intercept of the 2nd graph is -15 2-the graphs have the same y intercept. The 2nd graph is steeper than y= absolute x 3- the 2 graphs are the same 4- the graphs have the ...
December 7, 2014

Algebra 1
Graph y= absolute x -2
December 7, 2014

solve
since time = distance/speed, if the speed was x, 168/(2x) = 168/x - 3 x = 28
December 7, 2014

Advanced Algebra
Since we have a geometric series, Sn = A * (e^knt - 1)/(e^kt - 1) So, plug in the numbers and we have S5 = 0.5 (e^(-0.853*4*5)-1)/(e^(-0.853*4)-1) = 0.517
December 7, 2014

math
23 min * 100/3 rev/min = 766.666 rev So, divide the distance between the 1st and last grooves into 767 grooves, and you get 4/766.666 = 0.0052 inches between grooves So, you have an arithmetic sequence with a = 5.75*2π d = 0.0052*2π and you want S767 Just plug and chug
December 7, 2014

problem solving
If there were n bricks at price p, then we know that 1.05np = 315 (n+6)p = 315 Now just eliminate p and solve for n.
December 7, 2014

Maths
There is a lot of missing information here. I can easily devise a scenario where the assertion is false. Suppose A is 1 cm above L and B is 10 cm above L. If D and E are on L, clearly CD < CE.
December 7, 2014

AP CALC. AB
#2 (a) is correct #3 f' = lnx + 1 The only extremum is at x = 1/e f" = 1/x, which is positive at 1/e, so f(1/e) is a minimum. Looks like (c) is the answer See the graph at http://www.wolframalpha.com/input/?i=x*lnx Ignore tha part where x<0, since lnx is not real ...
December 6, 2014

Pre calculus
look up the half-life of C-14. If it is k years, then the amount left after t years is (1/2)^(t/k) So, you want to solve for t in (1/2)^(t/k) = 0.289
December 6, 2014

math
a + c = 8 3.5a + 2.5c = 23 Now just solve for a and c.
December 6, 2014

math
the LCD(2,3) is 6. So, multiply the whole equation by 6: 3x-30 = 2
December 6, 2014

Algebra
Heck, they gave you an example, so that makes it easy. Just pick any values for a,b,c: 9-3=6 ==> 9*6<+>-3*6=9*-3 or 54<+>-18=-27 Who cares what <+> really means?
December 6, 2014

programming urgent
just loop on the indexes. If the arrays x and y have m rows and n columns, then for (i=1..m) for(j=1..n) z(i,j) = x(i,j)*y(i,j) next j next i
December 6, 2014

Physics: need detailed answer
It means there is a horizontal force of 100N applied to the mower.
December 6, 2014

trig
well, you know that x = -2029 y = 2129 so, r = 2941 So, now you just have to review your basic trig functions for angles in standard position. I was a bit confused by the double minus sign, but if I have it right, you're ready to move along.
December 6, 2014

Algebra 1
Which equation is the equation of a line that passes through (-10,3) and is perpendicular to y=5x-7? 1- y=5x+53 2- y=-1/5x -7 3- y= -1/5x +1 4- y= 1/5x +5
December 6, 2014

Math
correct
December 6, 2014

Math
the easiest way is indeed to use the slope-intercept form. It saves having to memorize another formula. If ax+by=c, then by = -ax+c y = -a/b x + c/b and you can see that the slope is -a/b
December 6, 2014

Math
as in any scenario, it is rise/run. More precisely, it is the change in the dependent variable -------------------------------------- the change in the independent variable
December 6, 2014

MATH
not at all. x(t)=3t+5 You have to write the function using the independent variable as the parameter. In this case, t is the independent variable. However, referring to your previous posts, if you are using x and y, yes, x is usually the independent variable. Try reading your ...
December 6, 2014

MATH
no way to tell. However, it is usually x, given the choice between x and y.
December 6, 2014

MATH
plug in y=0 10x+0=500
December 6, 2014

Math
(1.4*2.5)x10^(3-6) 3.5x10^-3 multiply the numbers, add the exponents
December 6, 2014

Math
given the vertex, you know that y = a(x-2)^2 - 1 Now plug in the point to find a: a(4-2)^2 - 1 = -3
December 6, 2014

MATH
the intercept in slope-intercept is the y-intercept; what you get when x=0. I just told you how to find the x-intercept: set y=0 and solve for x.
December 6, 2014

MATH
well, what is x when y=0? 30x+20 = 0
December 6, 2014

Math
well, think about it. Every 15 ft of the field is 1/2 in in your drawing. So, if the field is 150ft long, that is (1/2)*10 = 5in in the drawing. So, find out how big the field is, divide both dimensions by 15, and use that many 1/2-inches in the drawing.
December 6, 2014

Maths
correct. So, what is n?
December 5, 2014

Algebra 1
you want slope = -1/5 So, the point-slope form of the line is y-3 = -1/5 (x+10) Now massage that into one of the choices.
December 5, 2014

Algebra 1
Which equation is the equation of a line that passes through (-10,3) and is perpendicular to y=5x-7? 1- y=5x+53 2- y=-1/5x -7 3- y= -1/5x +1 4- y= 1/5x +5
December 5, 2014

Calculus
f'(x) = (1-x)e^-x f is increasing when f' > 0 e^-x is always positive, so f is increasing when 1-x > 0 See the graph at http://www.wolframalpha.com/input/?i=x+e^-x%2C+0%3C%3Dx%3C%3D2
December 5, 2014

Calculus
e^e^2 is a constant. Fix the typo and try again. f is increasing when f' > 0 f is concave up when f" > 0
December 5, 2014

Algebra 2/Trigonometry
f(x) has 3 sign changes, so 3 or 1 positive roots f(-x) has no sign changes, so no negative roots There might be two complex roots.
December 5, 2014

Calculus
I think we can assume arccos. If so, then recall that d/dx (arccos(u)) = -1/√(1-u^2) du/dx Now just plug and chug.
December 5, 2014

Calculus
and you would be wrong. You have it exactly backwards. f is increasing where f' > 0. Better double-check your derivative.
December 5, 2014

Calculus
If f = √u, f' = u' / 2√u. You have u=3x, so f'(x) = 3 / 2√(3x) f'(3) = 3 / 2√9 = 1/2
December 5, 2014

Intermediate Algebra
√(40x^3) = √(4x^2)√(10x) = 2x√(10x) √(3/4) * √(4/7) = √(3*4 / 4*7) = √(3/7) √6 + √20 = √6 + 2√5
December 5, 2014

Algebra 1
What equation has a graph parallel to the graph of 9x + 3y = -22? 1- y = 3x -22 2- y = -3x + 8 3- y = 1/3 x + 12 4- y = - 1/3 x - 2
December 5, 2014

maths
Don't give much away on the line and point, do you? For the other, just draw a 3-circle Venn diagram, and start filling in the pieces.
December 5, 2014

Math
Good idea, but you don't need x. There are n sides and n angles. Since you already have 4 angles, there are n-4 remaining. So, (n-2)180 = 125+220+40+295+20(n-4) n=6
December 5, 2014

Math
Doesn't matter. I'm full!
December 5, 2014

math
(2/3)/3 * 36 = 2/9 * 36 = 8
December 5, 2014

Algebra
height=39 length = height+21 = 39+21 = 60
December 5, 2014

Algebra
review your equation of motion. the distance is s = 1/2 at^2 You know s=435 and a=-9.8 So, just find t.
December 5, 2014

Math
If he borrowed $x from his friend at 8%, then the rest (170000-x) is at 4%. So, now you have .08x + .04(170000-x) = 9800 x = 75,000
December 5, 2014

Calculus
The graphs intersect at (-4,20) and (5,25) So, consider the area as a bunch of thin strips, each of width dx, and height equal to the distance between the curves. The area is thus ∫[-4,5] (x+20)-x^2 dx = 1/2 x^2 + 20x - 1/3 x^3 [-4,5] = 243/2
December 5, 2014

Math
Grrr! It's pi, not pie! ∫[0,π/2] cos^2(3x) dx Now, you know that cos(2u) = 2cos^2(u)-1, so cos^2(u) = (1+cos(2u))/2 and the integral becomes ∫[0,π/2] (1+cos6x)/2 dx = x/2 + 1/12 sin6x [0,π/2] = π/4
December 5, 2014

math
40:blue = 8:9 blue = 45
December 5, 2014

math Subtraction equation
x - 25 = 45
December 4, 2014

algebra
if the given zeros are a,b,c,... then the polynomial is y = (x-a)(x-b)(x-c)...
December 4, 2014

Math
If x,y,z are all positive, then the sum is 1+1+1+1 = 4 If any are negative, then u/|u| becomes -1, and the total is less. I guess you can list the possibilities, eh?
December 4, 2014

math
If you mean (32x^3y^4)/(24x^3y^2) * (3x)/(9y) multiply top and bottom to get (96x^4y^4)/(216x^3y^3) = (24x^3y^3)(4xy) / (24x^3y^3)(9) = 4xy/9 Or, you could simplify each fraction first, getting (8x^3y^2)(4y^2) / (8x^3y^2)(3) * (3)(x)/(3)(3y) = 4y^2/3 * x/3y = 4xy/9
December 4, 2014

Math
I will underline instead of overlining. 0.3 = 0.3333333333333333 It is clear that If both numbers are the same, there is no difference. Otherwise, there is a difference. 3.3 = 3.333333333... 3.34 = 3.3434343434343434... Surely your text has explanations and examples of this ...
December 4, 2014

NEED Math HELP please!!!
8x - 4xy = 3 8x-3 = 4xy (8x-3)/4x = y -2x-5y = 10 5y = -2x-10 y = -(2x+10)/5
December 4, 2014

Math
If you go x miles, then you want 1.00 + 0.20(6(x-1)) = 5.00
December 4, 2014

Algebra My bad
Dr Bob, you are correct. I solved it correctly earlier, and got impatient when it popped up again. My bad.
December 4, 2014

Algebra B PLEASE HELP
15000(1+r)^2 = 16099.44 r = 0.36
December 4, 2014

pre-calculus
just for readability, suppose u = cosx Then you have 6u^2-5u-6=0 (3u+2)(2u-3) that means cosx = -2/3 cosx = 3/2 I guess you can take it from there, ok?
December 4, 2014

Math
If x>=3, |x-3| = x-3 |3-x| = x-3 So, 2x-6 = 1 2x = 7 x = 7/2 If x < 3, |x-3| = 3-x |3-x| = 3-x So, 6-2x = 1 2x = 5 x = 5/2 In either case, |x-3| and |3-x| are the distance of x from 3. Twice that distance = 1, so x is 1/2 away from 3, in either direction.
December 4, 2014

Math
3√(3-x) = -3/2 √(3-x) = -1/2 3-x = 1/4 x = 11/4 But, that does not fit the original equation. Maybe you meant ∛(3-x) = -3/2 3-x = -27/8 x = 51/8
December 4, 2014

Algebra B
15000(1+r)^2 = 16099.44 (1+r)^2 = 1.073296 1+r = 1.036 r = 0.036 So, the rate is 3.6%
December 4, 2014

Calculus
First, it's pi, not pie!!! e/x^4? That's very unusual. As written, it's e/x^4 + π^2/√x I doubt that's what you meant, so try again, and maybe include some parentheses, ok?
December 4, 2014

Math
max height when t = -b/2a. That is, when t=2 Solve for t when h=0 to find when it hits the ground. So, where is the ball when t=0? That is, where does it start?
December 4, 2014

Calculus
y = 6x^6 + 4x^13 - 9x^7 + 3 for large x, it's just 4x^13
December 4, 2014

college algebra
I assume we're doing a G.P. here. a12 = a1*r^11 = 5*(-2)^11 = ?
December 4, 2014

Math calculous
There's no guarantee that a single parabola will pass through all four points. So, let's pick the fitrst three and see what happens. If y = ax^2+bx+c, then a+b+c = 7 4a+2b+c = 20 9a+3b+c = 43 3a+b = 13 5a+b = 23 2a = 10 a = 5 b = -2 c = 4 y = 5x^2-2x+4 Luckily, (4,76) ...
December 4, 2014

math
f(-3) = 3^6 - 2*3^4 - 81*3^2 + 162
December 4, 2014

Math
for x-intercept, solve for x when y=0 for y-intercept, solve for y when x=0
December 4, 2014

Math
Does each person buy just one cookie? if so, then the profit y on a month of 4 weeks is y = 2*30*4 - 100 For x people per week, that would be y = 8x-100
December 4, 2014

Calculus
P'(x) = 60x^3 + 30x^2 So, P(x) = 15x^4 + 10x^3 + c If you meant the profit is -50 when no cheese is sold, then P(0) = -50, and c=50. So, P(x) = 15x^4 + 10x^3 - 50 Now plug in x=3 to find P when 300 lbs are sold.
December 4, 2014

Math
the perimeters are also in the ratio of 2:7 So, find the perimeter of the smaller triangle, and multiply it by 7/2
December 4, 2014

Math
check to see whether there is a constant term. If not, meaning that the function is just a multiple of x, then it's direct variation.
December 4, 2014

Math
a car rental costs a daily fee of $20 plus 10 cents per mile. A driver starts from 100 miles away and drives at 20 mph. How far away is he after x hours? You need a constant term and a term with x. For a direct variation, there is no constant term.
December 4, 2014

Math
3^5 = (3)(3)(3)(3)(3) = 243
December 4, 2014

Math
Draw your triangle x = -3 y = 1 r = √10 Now use the definitions of the trig functions to fill in the table.
December 4, 2014

Math Question
it's clear you are in QII, since y>0 and x<0. So, draw your triangle. The hypotenuse is √2, so now you can fill in the table.
December 4, 2014

Simple math
state: .8/2.69 = 0.297 = 29.7% federal: .18/2.69 = ?
December 4, 2014

Math
What, your keyboard doesn't have || characters? If x<5, x-5 < 0 So, |x-5| = -(x-5) = 5-x 5x - (5-x) = 6x-5
December 4, 2014

algebra
However, if you want a polynomial with real coefficients, you need another zero: the conjugate of 1-i = 1+i SO, your polynomial is then (x-(1-i))(x-(1+i))(x-2) ((x-1)+i)((x-1)-i)(x-2) ((x-1)^2+1)(x-2) (x^2-2x+2)(x-2) ...
December 4, 2014

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