Thursday
December 18, 2014

Posts by Steve


Total # Posts: 27,604

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

Math
x^2+4x = x(x+4) 2x^2+13x+15 = (2x+3)(x+5) x^2-16 = (x+4)(x-4) So, you have x(x+4) (x+5) -------------------- (2x+3)(x+5)(x+4)(x-4) Unless there's a typo, the answer is (e)
December 4, 2014

Math
You started out wanting to simplify y=-15/20.25(x+1.5)^2+0 y=a(x+2)^2+1.5 I assume that means y = -15/20.25 (x+1.5)^2 -15/20.5 (x^2+3x+2.25) = -0.73x^2 - 2.20x - 1.65 Not sure that's any simpler than what you started out with. As for the second, you cannot find a value for...
December 4, 2014

Algebra 1
The population of a city increases by 4,000 people each year. In 2025 the population is projected to be 450,000 people,. What is the equation that gives the city's population p ( in thousands of people) x years after 2010?
December 4, 2014

math
√45 = √(9*5) = √9*√5 = 3√5
December 4, 2014

Algebra 1
I think the answer would be y - 3 = 3/5 (X+6)
December 4, 2014

Algebra 1
What equation represents the line that passes through the points (6,-3)and (-4,-9)?
December 4, 2014

Algebra 1
I think the answer would be (3,-4)
December 4, 2014

Algebra 1
Sorry The possible answers are 1- (-4,-5) 2- (-5,-4) 3- (3,-4) 4- (-3,4)
December 4, 2014

Algebra 1
Which point is located on the line represented by the equation y + 4 = -5(x-3)?
December 4, 2014

Math
the other side is 96/12 = 8 So, now you know both sides, and can easily figure the perimeter...
December 4, 2014

Math
using similar triangles, it is clear that if the tree is halfway to the stake, then it is half as tall as the building. Assuming that the rope touches the top of the tree, that is.
December 4, 2014

Math
h(t) = 75 + 80/√2 t - 16t^2 h=0 when t=4.563 The horizontal speed is a constant 80/√2 = 56.57 ft/s So, the ball travels 258.12 ft Hmm. We differ slightly. What did you do? And of course, check my math.
December 4, 2014

GEOMETRY
the area grows as the square of the radius. So, the radius grows as the square root of the area. Since areaB/areaA = 25, radiusB/radiusA = √25 = 5
December 4, 2014

algebra
domain: all real numbers except holes and vertical asymptotes vertical asymptotes where the denominator is zero and the numerator is not zero holes where the denominator and numerator are both zero horizontal asymptotes at the x-extremes. When x gets huge, you basically have f...
December 4, 2014

Coll Algebra
since time = distance/speed, we have d/(5-1) = d/(5+1) + 2 d = 24
December 4, 2014

5th grade math
Just do regular long division. In the quotient, place the decimal point directly above where it is in the dividend. Then move it to the right the number of decimal places as there are in the divisor. In normal long division with integers, the decimal point is at the right end ...
December 4, 2014

math
well, there are only a few perfect squares: 16 25 36 49 64 100 121 144 169 196 So, check the next numbers for primality. 17 is prime 26 is not and so on
December 4, 2014

Algebra 1
the slope is 2, so use the point-slope form to get y+3 = 2(x-1) or y-1 = 2(x-3)
December 4, 2014

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