Wednesday

March 4, 2015

March 4, 2015

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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