Monday
January 26, 2015

Posts by Steve


Total # Posts: 28,370

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

Algebra 1
What is an equation in slope-intercept form for the line that passes through the point (1,-3) and (3,1)
December 4, 2014

chemistry
find the atomic wt of Ca figure the mol wt of CaCO3 So, the mass of Ca is just wt(Ca)/wt(CaCO3) * 1.229g
December 4, 2014

Chemiry 11
figure how many moles. Then, each mole contains Avogadro's Number of sulfur atoms.
December 4, 2014

Algebra 1
y = -2x so, k = -2
December 4, 2014

Algebra 1
For the equation -4y =8x, what is the constant of variation?
December 4, 2014

math
the given line has slope 5 So, you want a line with slope -1/5 That line is thus (recall the point-slope form): y-3 = -1/5 (x+10) and you can massage that into whatever form you like.
December 4, 2014

Calculus
I suspect a typo. Why write "1 sqrt(t)"?
December 4, 2014

Algebra
the distance s = 1/2 at^2 You have s and a, so just find t.
December 4, 2014

Algebra 1
thank you
December 4, 2014

Algebra 1
Suppose y varies directly with x and y = 24 when x =8. What is the value of y when x = 10?
December 4, 2014

algebra
The vertices involving y>=x are clearly (-2,-2) and (3,3) The rest you can surely find... What did you try? See the solutions at http://www.wolframalpha.com/input/?i=solve+x+%E2%89%A5+%E2%88%922%2C+x+%E2%89%A4+3%2C+y+%E2%89%A4+5%2C+y+%E2%89%A5+x+
December 4, 2014

math
what, no calculator? .01 is around 1/100, so the answer should be somewhere near 3 or 4
December 3, 2014

Math Help
The increase is 20 20/50 = 40% (of 50)
December 3, 2014

Math
Since √5 = 5^(1/2), log √5 = 1/2 log5 Not sure what all the other mumbo jumbo means.
December 3, 2014

Math
√(2-3x) = 9 2-3x = 81 3x = -79 x = -79/3 Remember: (a-bx)^2 is NOT NOT a^2 - b^2x^2 Not that that matters here, anyway, since √(stuff)^2 is just stuff, whatever stuff you have. (√x)^2 = √(x^2) = x. There is no reason at all to square what's inside ...
December 3, 2014

math
assuming the x side is parallel to the wall, then 2x+4y = 120 The area is 2xy = 2x(120-2x)/4 = 60x - x^2 The maximum area is thus where x=30 As usual with such problems, the maximum area is achieved when the fencing is divided equally among lengths and widths.
December 3, 2014

Algebra 1
What is an equation in slope-intercept form for the line that passes through the points (1,-3(), (3,1)?
December 3, 2014

Algebra 1
Thank you trying to help my grandson with his homework
December 3, 2014

Algebra 1
What is an equation for the line with slope 2/3 and y intercept 9?
December 3, 2014

Algebra 1
Suppose y varies directly with x and y = 24 when x =8. What is the value of y when x = 10?
December 3, 2014

Algebra 1
For the equation -4y =8x, what is the constant of variation?
December 3, 2014

Algebra 1
What is the slope of the line that runs through points (1,1), (0,3)?
December 3, 2014

Pre-Calc/Trig...
Since An/An-1 = r (1/An)/(1/An-1) = An-1/An = 1/r so, the ratio between terms is still constant.
December 3, 2014

College Algebra
If the amounts are x,y,z then we have x+y+z = 14000 .03x + .04y + .05z = 539 z = 3y Now just solve for x
December 3, 2014

Algebra 1
thank you
December 3, 2014

Algebra 1
the point 12,9 is included in a direct variation. what is the constant of variation
December 3, 2014

Algebra 1
Thank you, I'm a grandfather trying to help my grandson.
December 3, 2014

Algebra 1
suppose y varies directly with x and y = 14 when x = -4 what is the value of y when x = -6
December 3, 2014

Algebra 1
The ordered pairs 1,4 - 2,16 - 3,64 - 4,256 - 5, 1024 represents a function. What rule represents this function. 1- 4 x power 2- 4x 3- xto the 4th power 4- x+4 my answer is 4x
December 3, 2014

trig
zero. Why? try drawing the triangle...
December 3, 2014

maths
20
December 3, 2014

mathematics
If you mean 2 2/4, that's 10/4 1/4 / 1/4 = 10 yet, who actually writes 2 2/4 instead of 2 1/2? I suspect a typo. And lose the \\\'s. Try /// for fractions.
December 3, 2014

algebra
w*4w = 392 That gives you w. Now, you want p = 2(w + 4w)
December 3, 2014

AP CALC. AB
clearly the tangent is horizontal when x^2-2 = 0 h"(x) = (x^2+2)/x^2 And you know that f(x) is concave up when f"(x) > 0 See that graph at http://www.wolframalpha.com/input/?i=integral+x+-+2%2Fx
December 2, 2014

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