Wednesday
March 4, 2015

Posts by Steve


Total # Posts: 29,335

Calculus 2
∫ e^x √(1+e^(2x)) dx Note that if u = e^x, you have ∫ u√(1+u^2) du Now, if v = 1+u^2, dv = 2u du, and you have 1/2 ∫ √v dv That I think you can handle, eh?
February 4, 2015

Math
#1 x^2 = 2x-1 x = 1 #2 2(x-1) = 3x+1 x = -3
February 4, 2015

Math
(2+2+2)/2 - 2 = 1 2+2+2 - 2/2 = 5 2+2+2 + 2/2 = 7 2*2*2 + 2/2 = 9
February 4, 2015

Math
1 false a^x is exponential, for any positive a. #2 false, since 1^x is constant.
February 4, 2015

Calculus 2
(x^3+5x^2+12)/((x^2)(x^2+4)) = (x+2)/(x^2+4) + 3/x^2 So, ∫(x^3+5x^2+12)/((x^2)(x^2+4)) = ∫ (x+2)/(x^2+4) + 3/x^2 dx = 1/2 log(x^2+4) + arctan(x/2) - 3/x + C
February 4, 2015

Math
Nope. try 4n-6 < 0.5(-n) "opposite" is a vague term. Usually it means negative. You have interpreted it as reciprocal. In either case, "the product of four and a number" is 4n six less than that is 4n-6, not 6-4n.
February 4, 2015

physics
both are 3 significant digits.
February 4, 2015

Math
why divide? Just add up all the times. Dividing by 4 will give the average time per activity, but no one asked for that. Dividing 4 by the sum is meaningless. It gives the number of activities that can be done in a second, but that's of no use to anyone.
February 4, 2015

math
2/5 + 1/6 + 1/3 = 12/30 + 5/30 + 10/30 = 27/30 So, what's not covered?
February 4, 2015

Algebra
23 nickels is right, but that wasn't what you were asked to find.
February 4, 2015

From Theory to practice
Q: What's the difference between theory and practice? A: In theory, there is no difference, but in practice, there is!
February 4, 2015

algebra
(4x+6)(4x-6) = 16x^2-36
February 4, 2015

Math - Absolute Value Inequalities
B is correct. |x-2| means the difference between x and 2. That difference must be less than 3, so 2-3 < x < 2+3 -3 < x-2 < 3
February 4, 2015

math
4^2 = 16 5^2 = 25 so, 4.5 is a good first guess. 4.5^2 = 20.25 too big 4.4^2 = 19.36 4.45^2 = 19.80 4.46^2 = 19.89 4.47^2 = 19.98 4.48^2 = 20.07 So, you want something between 4.47 and 4.48 keep going.
February 4, 2015

College Alegbra
w(2w-7) = 400
February 4, 2015

trig
who is r? If x is the angle between p and q, then 12^2 = 8^2+10^2-160cos(x) Now subtract x from q's heading (not bearing!)
February 4, 2015

geometry
since the linear scale has doubled, the volume has grown by a factor of 8.
February 4, 2015

Algebra 1B
surely your text has examples and explanations. And remember that google is your friend.
February 4, 2015

algebra
for F(x) = ax^2+bx+c, the vertex lies on the axis of symmetry, at x = -b/2a. so, for your function, that is at x = -2/-2 = 1 f(1) = 7 so, the vertex is at (1,7). See the graph at http://www.wolframalpha.com/input/?i=-+x^2+%2B2x+%2B+6 Recall that the quadratic formula says that...
February 4, 2015

algebra
there are oodles of online graphing utilities. wolframalpha.com desmos.com come to mind. Just type in your function.
February 4, 2015

algebra
to find the y-intercept, set x=0: f(0) = 1 To find the x-intercept(s) use the quadratic formula.
February 4, 2015

Calculus II
use integration by parts. Let u = x, du=dx v = e^-4x dx, v = -1/4 e^-4x ∫ udv = uv - ∫v du so, ∫(x)(e^-4x dx0 = -1/4 xe^-4x + 1/4 ∫e^-4x dx = -1/4 xe^-4x - 1/16 e^-4x = -1/16 e^-4x (4x+1) + C
February 4, 2015

math
f(g) = 3g+4 = 3(bx-4)+4 = 3bx-8 g(f) = bf-4 = b(3x+4)-4 = 3bx+4b-4 Clearly, b = -1
February 3, 2015

Geometry
I get 7/2
February 3, 2015

Math - Operations with Algebraic Vectors
|i+3j-k| = √(1+9+1) = √11 Better go back to where it shows how to figure the length of a vector.
February 3, 2015

MATH
If there are n terms, n/2 (5+61) = 957 n = 29
February 3, 2015

Math
12x-6y=21 3x+6y=9 now add them up and the y's are eliminated. Should be easy going from there.
February 3, 2015

math (geometry)
42
February 3, 2015

calculus
y' = x-3 P0 = (1,4) ∆y = y'(x0)*∆x = (-2)(0.1) = -0.2 P1 = (1.1,3.8) ∆y = y'(x1)*∆x = (-1.9)(0.1) = -0.19 P2 = (1.2,3.61) ∆y = y'(x2)*∆x = (-1.8)(0.1) = -0.18 P3 = (1.3,3.43) Read the fine article at wikipedia, which shows a ...
February 3, 2015

calculus
(√(x+4)-2)/x using l'Hospital's Rule, that gives (1/(2√(x+4)))/(1) = (1/(2*2))/2 = 1/4
February 3, 2015

Math
Note that the last digit of 3^n repeats: 3,9,7,1,... 3^997 = 3^996*3, so it ends in 3 so, ...
February 3, 2015

Math Work
4(1/2)(sin(pi/3+5pi/6)-sin(pi/3-5pi/6)) Now just add the fractions and plug in the values.
February 3, 2015

geometry
the area is a = πr^2 + 2πrh So, πr^2+100πr = 3000 r^2+100r = 955 r = 8.779 So, r is about 9
February 3, 2015

Geometry
CZ extended to AB is a median. The centroid is 2/3 of the way from the vertex to the opposite side. So, you have an isosceles triangle with base=6 and altitude=6
February 3, 2015

Math
I'd use (4-1)/(1+1) = (3+1)/(3+1) Don't know why all the choices have a -2 in them, since none of the points contains a -2.
February 3, 2015

Math Help - DQ?
I interpret the instruction to use the Half-Angle formula as sin(15°) = √((1-cos30°)/2) = √((1-√3/2)/2 = √(2-√3)/2 = (√6-√2)/2 Granted, the half- and double-angle formulas are two sides of the same coin, but ...
February 3, 2015

math
If you mean f(x) = (x^2-4)/(x-2) if x<2 then since x<2, (x^2-4)/(x-2) = x+2 So, f(x) = x+2 if x < 2 ax^2-bx+3 if 2 <= x < 3 4x-a+b if x >= 3 So, as x->2-, f(x)->4 That means we must have 4a-2b+3 = 4 at x=2 9a-3b+3 = 12-a+b at x=3 a = 7/2 b = 13/2 f(x...
February 3, 2015

math
(6p+4b+3c)(1.2)=(3p+8b+6c)=3p+2(4b+3c) So, if Mohan spent 2x on puffs and y on the others, (2x+y)(6/5)=x+2y 6(2x+y)=5(x+2y) 12x+6y=5x+10y 7x=4y y = 7x/4 Now, we want x/(2x+y) = x/(2x+7x/4) = x/(15x/4) = 4/15 Mohan spent 8/15=53.3% of his money on puffs. check: (8/15+7/15)(6/5...
February 3, 2015

algebra
(2/5)x + x = 21 (7/5)x = 21 x = 15 The two numbers are 6 and 15
February 3, 2015

algebra
just plug in -2 for all the x's: f(-2) = 2(-2)+1
February 3, 2015

math
all are functions. For #4, suppose that u and v produce the same y value. That is, mu+b = mv+b then that means that mu = mv u = v In other words, if you have the same y-value, it can only be produced by one x-value. That means that you have a function.
February 3, 2015

math
correct. but stop guessing.
February 3, 2015

math
(c)
February 3, 2015

math
y"=6x-24 = 6(x-4) you want y"=0
February 3, 2015

math
they are where y' = 3x^2-12x+9 = 0
February 3, 2015

math
.42x = 210
February 3, 2015

Pre-Calculus
x-axis: (x,y)->(x,-y) y-axis: (x,y)->(-x,y) but, since h(x) is an odd function h(-x) = -h(x) reflecting h(x) through either axis flips it to the same thing. (x,x^3)->(x,-x^3) (x,x^3)->(-x,x^3) = (-x,-(-x)^3)
February 3, 2015

Pre-Calculus
swap x and g and then solve for g: x=(g+7)^3+4 x-4 = (g+7)^3 ∛(x-4) = g+7 g = ∛(x-4) - 7 check. If h is g inverse, g(h(x)) = h(g(x)) = x g(h) = (h+7)^3+4 = ((∛(x-4) - 7)+7)^3+4 = (∛(x-4)-7+7)^3+4 = ∛(x-4)^3+4 = x-4+4 = x and similarly for h(g)
February 3, 2015

math
and you'd be correct. But why guess? A brief check on the definition of a function would make it certain.
February 3, 2015

Pre-Calculus
nothing. x^2 is an even function. Reflecting it about its axis changes nothing. (x,y)->(-x,y) since f(x) = f(-x), the graph is unchanged.
February 3, 2015

Pre-Calculus
you surely know that this is a parabola which opens up, so there is no local maximum. So, find the f values at the ends of the interval, and pick the larger for the global max. No interval? No maximum.
February 3, 2015

Pre-Calculus
x then y: (x,y)->(x,-y)->(-x,-y) y then x: (x,y)->(-x,y)->(-x,-y) f(x) -> -((-x)^3+2(-x)^2-(-x)+5)
February 3, 2015

Pre-Calculus
reflect: (x,y)->(-x,y) f(x) -> -x^3+2x^2+x+5 shift: (x,y)->(x+4,y) f(x) -> -(x+4)^3+2(x+4)^2+(x+4)+5 = -x^3-10x^2-31x-23 see the graphs here: http://www.wolframalpha.com/input/?i=plot+y%3Dx^3%2B2x^2-x%2B5%2C+y%3D-x^3-10x^2-31x-23 the shift isn't real clear, but...
February 3, 2015

math
you need to divide the interval into 1/8 pieces, since the loaf holds 8 slices. Then shade in 6 of those pieces for the sandwiches.
February 3, 2015

mathematic
same as prob that it's not green: 1-3/8
February 2, 2015

science
likely a noble gas, since the others form molecules of more than one atom.
February 2, 2015

Math
a 50% profit margin means that the price is 2 times the cost. So the cost:profit ratio is 1:1 If the cost of raw material is doubled, then the ratio becomes 1.25:1 = 5:4, with the profit being only 4/9 instead of 1/2.
February 2, 2015

vectors
recall that every 5 minutes covers 30° That will give you the angle traversed.
February 2, 2015

calculus
cos(3π) is also -1, so x = 3π/2
February 2, 2015

math
14=-16-10n n=-3 the others look good.
February 2, 2015

Algebra
when it hits the ground, the height is zero. So, just solve -16t^2 + 1000 = 0 16(62.5-t^2) = 0 t = √62.5 = 7.9
February 2, 2015

math
27(1/8)
February 2, 2015

Math
you are right on.
February 2, 2015

Physics
momentum is conserved. In this case, we are considering only the horizontal motion, since the wagon cannot move vertically. So, the basic problem is that of what happens when the wagon's mass is suddenly increased by the addition of the bird's mass. To conserve ...
February 2, 2015

Math Help
that is not an answer. It is a restatement of the problem, using only sines. 2sin^2x-sinx-1 == 0 (2sinx+1)(sinx-1) = 0 sinx = -1/2 or 1, so x = π/2, 4π/3, 5π/3 http://www.wolframalpha.com/input/?i=cos2x%2Bsinx%3D0+for+x%3D0..2pi
February 2, 2015

math
where f'=0 and f"<0. So, what do you think?
February 2, 2015

math
y" = 4/(5-x)^3 f is concave up when f" > 0 So, what do you think?
February 2, 2015

Grammar and Context
I fail to see how this has anything to do with physics or chemistry. Maybe you have some ideas in that regard. when you say "would have" done, do you mean you want to know things that it failed to do?
February 2, 2015

math
1500 <= i+200 <= 2000
February 2, 2015

algebra
yes it is Though, to me, saying 3(4w+5)^2 is just as good. It is clear what the factors are. I wrote 4w+5 instead of 5+4w just because the polynomial was given in descending powers of w, so I made my factors read the same way.
February 2, 2015

mathematics
fractions are ratios 2/3 = 2:3
February 2, 2015

Algebra 2!!!!
checking the graphs at wolframalpha.com, http://www.wolframalpha.com/input/?i=4x^3-8x^2-15x%2B9 http://www.wolframalpha.com/input/?i=2x^3-5x^2-4x%2B10 it is clear that #1 has a root at x = 3 #2 has a root at x = 5/2 So, divide through and you can use the quadratic formula to ...
February 2, 2015

maths..g.p
a=5 d=4 n=(131-5)/4 = 31 check: 5+31*4=129 S = 31/2 (5+129)
February 2, 2015

maths..a.p
there are 49 of them, so 49*50/2
February 2, 2015

math
not possible. 1-4 is negative.
February 2, 2015

maths
a = 2r, so r = a/2 a/(1-r) = 8 a/(1-a/2) = 8 a = 8-4a a = 8/5 So, the sequence is 8/5, 32/25, 128/125, ...
February 2, 2015

acceleration
amazing. a = (Vf-Vi)/t
February 2, 2015

Math
As usual, draw a figure. If we start at the right angle and label the vertices clockwise, then we see that BD is the hypotenuse of an isosceles right triangle, with length 12√2. If the 4th side is x, then we have from the law of cosines, (12√2)^2 = 8^2 + x^2 - 2(8...
February 2, 2015

math
Sorry. 24 does not divide into 5 equal parts. You probably mean that there are 24 boys, or that there are 24 girls. If boys, then 24/g = 2/3 g = 36 If there were 25 total students, then (25-g)/g = 2/3 75-3g = 2g g = 15
February 2, 2015

maths
start distributing: (-2)(2x)(3x+1) + (-2)(-5)(3x+1) = -4x(3x+1) + 10(3x+1) I think you can probably take it from here, eh?
February 2, 2015

maths
Use a little synthetic division to find that the remainder is 4m+6 So, m = 1/2 x^3 + (1/2)x^2-5x+4 = (x+2)(x^2-(3/2)x-2)+8
February 2, 2015

algebra
you are correct
February 2, 2015

algebra
they are exactly the same. The * is optional, as you prefer.
February 2, 2015

algebra
correct
February 2, 2015

math
AP: 10,10+2d,10+6d GP: (10+2d)/10 = (10+6d)/(10+2d) d = 5 check: AP: 10,15,20,25,30,35,40 GP: 10,20,40
February 2, 2015

math
cone: v = 1/3 pi r^2 h using that v, then for the sphere, find its radius and then area: v = 4/3 pi r^3 a = 4 pi r^2
February 2, 2015

math
4 minutes is 240 seconds. So, the water will rise (27*240)/(60*30) cm I expect you can use that to answer the question.
February 2, 2015

math
as always, distance = speed * time. (x-20)(3.25) = 2x+30 x = 76 So, 56 km/hr * 3.25 hr = 182 km
February 2, 2015

Math
If 30 spoke E&F and 10 spoke E&F but not S, then that means 20 spoke E,F,S. So, in your Venn diagram, the small triple intersection in the center has a 20 in it. But, since only 20 spoke French and Spanish, and all of them also spoke English, there are 0 who spoke no English.
February 2, 2015

Calculus
y^2 = (x^2−1)^2 y = ±(x^2-1) That is, y = (x^2-1) or y = (1-x^2) The area between two functions f(x) and g(x) is ∫ f(x)-g(x) dx. hat is, it is the sum of all the thin strips whose height is the difference between the curves.
February 2, 2015

Calculus
I get for the area ∫[-1,1] (1-x^2)-(x^2-1) dx = ∫[-1,1] 2-2x^2 dx = 2(x - x^3/3)[-1,1] = 8/3
February 2, 2015

Precal
The names monomial, binomial, etc, are usually reserved for polynomial functions, where all the terms are just powers of x (or other variables). The above function, with its 5^x factor is not a polynomial, as generally used. The terms of a polynomial are separated by + and - ...
February 1, 2015

Math
h(t) is just a parabola. The max height is reached at the vertex. For the parabola ax^2 + bx + c the vertex is at x = -b/2a. So, for h(t), the vertex is at t = 3. h(3) = 152 It hits the ground when h=0. To find that, just use the quadratic formula.
February 1, 2015

Math
c(x) = 25 for 0 < x <= 6 25 + 4⌊x-6⌋ for x>6
February 1, 2015

Algebra 2
√(79-5x) = 6x+4 79-5x = (6x+4)^2 = 36x^2+48x+16 36x^2+53x-63 = 0 (4x+9)(9x-7) = 0 x = -9/4 or 7/9 but, you have to check for spurious roots: √(79-5(-9/4)) = √(79+45/4) = 9.5 but, 6(-9/4)+4 = -9.5 This is the spurious root. If you square both sides, it becomes...
February 1, 2015

Math
GCF(32,40) = 8 so there are 4 rows of irises and 5 rows of tulips, all rows with 8 bulbs.
February 1, 2015

Physics
The horizontal and vertical speed are both 19.8/√2 = 14 m/s At that speed, it takes 35/14 = 2.5 seconds to get to the goal. The height of the ball is y = 14t-4.9t^2 y(2.5) = 4.375 m Looks like it will clear the bar by 1.325 m I'll let you decide the vertical velocity...
February 1, 2015

Physics
the height of the ball as a function of time is y = 31.1*sin37.0°*t - 4.9t^2 = 18.7t - 4.9t^2 So, you want to find t when y = 5.5 (and is on its way down). t=3.5 s Since the horizontal speed is constant, just multiply it by 3.5 to find the distance. v = 18.7 - 9.8t and ...
February 1, 2015

Geometry
Look. You had x^2+6x If you consider that as x^2+2ax, a=3. to complete the square, you have to add a^2, which is 9. Just follow the steps I took in my solution. I assume you can take the square root of 25 when you get that far...
February 1, 2015

Geometry - ahem
(x+a)^2 = x^2+2ax+a^2
February 1, 2015

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