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January 30, 2015

Posts by steve


Total # Posts: 28,495

Problem Solving: Draw Picture
draw a line 22.5 inches long mark a spot every 1.5 inches
November 25, 2014

math
just solve for y in: 1500 + (7500-1500)y = 7080
November 25, 2014

English
They all look good to me.
November 25, 2014

English
#1 is correct. Extra credit: what is bad about #2?
November 25, 2014

English
#1
November 25, 2014

Geometry
the three medians intersect at the centroid, which is where the triangle will balance.
November 25, 2014

Calculus
the average value of f(t) over the interval [a,b] is ∫[a,b] f(t) dt ------------------ b-a So, for this problem, that would be (∫[0,5] .96t^2+25 dt)/(5-0) = (.32t^3 + 25t [0,5])/5 = 165/5 = 33
November 25, 2014

Algebra math Question
well, you have 2(w + 2.4w) = 20.4 Now just solve for w, and the length is 2.4 times that.
November 24, 2014

math
Oh, please. You provide no numeric details at all -- how do you expect an answer? Since 42 is the answer to the ultimate question of life, the universe, and everything, I thought surely it was the answer to your obfuscated question!
November 24, 2014

math
42
November 24, 2014

math!!
algebraically, you want 8m >= 3m+25 or, just note that Sam saves an extra $5/month. SO, it will take 5 months to gain $25.
November 24, 2014

MATH
P(1+0.01375/4)^(4*3) = 15000
November 24, 2014

calculus
So, looks like C to me.
November 24, 2014

calculus
since (arctan(u))' = 1/(1+u^2) u', we have d/dx arctan √(3x) = 1/(1+3x) (√3)/(2√(3x)) = √3 / (6x+2)√x
November 24, 2014

Pre-Calc/Trig
well, that would depend on n, don't you think? multiples of 2 are even; otherwise, odd
November 24, 2014

Algebra
the domain is all the values of x where f(x) is defined. f(x) = 4 if -6 <= x < -2 |x| if -2 <= x < 8 ∛x if 8 <= x <= 14 So, clearly the domain is [-8,14] since f(x) is defined everywhere inside the interval, and nowhere outside it. Doesn't matter ...
November 24, 2014

Math
Ya got me. I don't find any rational roots at all. Makes factoring kinda tricky. You sure it's not 2y^4-y^3-10y+5 ? That could be done by grouping y^2(2y-1) - 5(2y-1) (y^2-5)(2y-1) For your function as given, I don't see any way. Wolframalpha confirms this: http://...
November 24, 2014

maths
If you want the radius r of the circle, just draw a diagram and note that (4/2) = r sin(60°/2)
November 24, 2014

math
(7/2)mi / (221/4) min = 7/2 * 4/221 mi/min = 14/221 mi/min
November 24, 2014

algebra
Nope. As you state it, it makes no sense. One does not add and subtract denominators.
November 24, 2014

algebra
I'm guessing you meant y/(y-5)+5/(5-y) = y/(y-5) - 5/(y-5) = (y-5)/(y-5) = 1
November 24, 2014

math - eh?
1/a + 1/b = 1/60 12/a + 36/b = 1 You sure there's no typo? I get a negative value for a.
November 24, 2014

Calculus
Let u^2 = x+9 Then √(x+9) = u x = u^2-9 dx = 2u du Then the integral becomes ∫(u^2-9)/u (2u du) = ∫2(u^2-9) du = 2/3 u^3 - 18u = 2u/3 (u^2-27) = 2/3 √(x+9) (x-18) For other problems, you can check your results at http://www.wolframalpha.com/input/?i=%E2...
November 24, 2014

Calculus
u=5x du = 5dx and the integrand becomes 1/5 sec(u) tan(u) du That should look familiar
November 24, 2014

Calculus
let u = x^9 then du = 9x^8 dx and the integrand is now 1/9 e^u du
November 24, 2014

math
distance gone will be 45*4 = 180 km poles/km = 1000/50 = 20 So, 180*20 = 3600 poles
November 24, 2014

Calculus
let u = 7sinx+35 du = 7cosx and the integrand now becomes 1/7 du/u
November 24, 2014

Math
gee - why not follow the hints? Use cross products: if a/b = c/d, then ad = bc So, for the first, try each pair: 1. 24/96 , 27/108 ? 24*108 = 96*27 YES 2. 17/102 , 12/70 ? 17*70 = 102*12 NO 3. 21/51 , 35/85 ? 21*85 = 51*35 YES 4. 45/75 , 63/105 ? 45*105 = 75*63 YES Try the ...
November 24, 2014

Math
sinB/b = sinA/a sinB = 9(sin28)/15 = 0.2817 B = 16° or 164°
November 24, 2014

Math
since the distance s = rθ the object travels 8.1*10 = 81 cm/s Curious how you got 47
November 24, 2014

Calculus
or, 4 + 4/x^2 :-)
November 24, 2014

Calculus
just do a long division (4x^2+4)/x^2 = 4 + 2/x^2
November 24, 2014

math,trigonometry
well, you know that y/35 = cos 20° x/35 = sin 20° This problem is slightly sly, since most of the time they give you the angle with the ground!
November 24, 2014

caculus
let u = arcsin(x) du = 1/√(1-x^2) dx and the integrand is u^6 du
November 24, 2014

math
q = 2d 25q+10d = 360
November 24, 2014

physics
1W = 1J/s = 1N-m/s Just look at the units. You have 100,000N * 250m/s = 25,000,000N-m/s = 25MW
November 24, 2014

math
you asked it much better the first time. Why garble the question and post it again?!?!?
November 24, 2014

math
we are told that d = 2q 10d+25q = 135 now just solve for q 10(2q)+25q = 135 45q = 135 q = 3
November 24, 2014

math
2 A's out of 16 letters. P(A) = 2/16
November 24, 2014

algebra
If she started with d dollars, and bought y yards, then we are told 29.50y + 12.00 = d 19.75*2y = d+28.00 So, she started with $130 and bought 4 yards. check: 29.50*4 = 118, leaving 12 left over 19.75*8 = 158, $28 too much
November 24, 2014

Trig
Remember, it's sinA/a = sinB/b What you have is sinA = 5.74, not A=5.74 There is no angle with sine of 5.74. Clearly there will be no triangle here. Sin 88 is almost 1, so 23/4 that will be much more than 1.
November 23, 2014

algebra
c = 4b+1 .12b + .10c = 2.18 Now just solve for b and c
November 23, 2014

Calculus
v(t) = h'(t) = -32t + Vo Now just plug in t=5 and whatever Vo was.
November 23, 2014

Trig- math
how did you get sinA? Also, the area = (bc sinA)/2, not (ab sinA)/2 849^2 = 930^2 + 1301^2 - 2*930*1301 cosA A = 40.6° area = b*c*sinA/2 = 930*1301*0.651/2 = 393,879
November 23, 2014

Trig
-6u-3v = -6(2i-5j) - 3(-i+3j) = -12i+30j+3i-9j = -9i+21j |-6u-3v| = √(81+441) = √522 x = |v| cosθ and y = |v| sinθ Since cos60° = 1/2 and sin60° = √3/2 v = (4(1/2),4(√3/2)) = (2,2√3) I assume that (u)(v) means u•v If so, ...
November 23, 2014

Calc
See the first related question below. Just change the numbers as needed
November 23, 2014

Basic Math (Check my answer)
It is C width = area ÷ length
November 23, 2014

algebra
If the speed of the plane and the wind are p and w, then since distance = speed * time, 3(s+w) = 390 5(s-w) = 390 s = 104 w = 26
November 23, 2014

Math
do you know how to plot points? If so, just plot the four points above. Then you can measure the length and with of the rectangle. And surely you know how to wind the area of a rectangle, given its length and width ...
November 23, 2014

Trigonometry
since cos pi/6 = √3/2, sec pi/6 = 2/√3 Now just finish it up.
November 23, 2014

math
just solve for a: 14.7 e^(-0.21a) = 11.11 e^(-0.21a) = 0.7558 -0.21a = ln 07558 = -0.28 a = 4/3
November 23, 2014

Algebra 2
x^2 = 6y+10 (6y+10)^2 + y^2 = 2 37y^2 + 120y + 98 = 0 now just solve for y, then x. I hope you're looking for complex solutions... See http://www.wolframalpha.com/input/?i=solve+x^2%2By^2%3D2%2C+x^2-6y%3D10+
November 23, 2014

Math
4(x+2)+3x+2(x-y) 4x+8+3x+2x-2y 9x-2y+8 Not real sure just what you're asking for.
November 23, 2014

Maths
lots and lots. Clearly, 4 by 5 But also √20 by √20 1 by 20 7 by 3 (21 rounds to 10) Just pick any numbers that multiply to give a value between 19.5 and 20.5
November 23, 2014

Math
32(2)^2x-12(2)^x+1=0 Recall that 2^2x = (2^x)^2, so you have 32(2^x)^2 - 12(2^x) + 1 = 0 Now, just to make things easier to read, let u = 2^x and you have 32u^2 - 12u + 1 = 0 (8u-1)(4u-1) = 0 u = 1/8 or 1/4 So, that means we have 2^x = 1/8 ------> x = -3 2^x = 1/4 ------>...
November 23, 2014

math
we have a/c = 7/3 a+90 = 3c a = 315 c = 135 but, that's only 3/4 of the seats, so the total is 4/3 (315+135) = 600
November 23, 2014

Algebra
lazy way: try the points to see whether they fit. algebraic way. Plug in the values for x and y to get 9a-3b+c = -22 a-b+c = 2 9a+3b+c = 2 Either way, it's -2,4,8
November 23, 2014

Calculus
try this site: http://mathworld.wolfram.com/RiemannSum.html
November 23, 2014

Maths
just plug in values for n, from 1 to 5. Tn is the nth term. So, for the first one, T1 = 3(1^2)-2 = 3*1-2 = 3-2 = 1 T2 = 3(2^2)-2 = 3*4-2 = 12-2 = 10 and so on
November 23, 2014

Chemistry
Just using estimates, it look like you have about 0.5 moles of O2 0.3 moles of N2 1.2 moles of H2 So, the fraction of the total represented by O2 is 0.5/2.0 = 25% Now you can refine that by using the real mole values.
November 23, 2014

Chemistry
Since each mole of HCl neutralizes 1 mole of NaOH, .025L * .288M = 0.0072 moles HCl So, for the NaOH, 0.0072 moles / 0.150M = .048L or 48 ml
November 23, 2014

Algebra 2
It's better if you show your work first, but here goes. Since y = x-3, x-3 = 3x^2-5 3x^2 - x - 2 = 0 (3x+2)(x-1) = 0 x = 1 or -2/3 and you can now evaluate y for each x. as shown at http://www.wolframalpha.com/input/?i=solve+y%3D3x^2-5%2C+x-y%3D3
November 23, 2014

math
No, that can't be right. The balloon is rising at 15 m/s. Aha. d^2 = 381.25t^2 + 6000t + 40000 2d dd/dt = 762.5t + 6000 dd/dt = 15.7 m/s
November 23, 2014

math
after t seconds, the distance d is d^2 = (200+15t)^2 + (12.5t)^2 d^2 = 381.25t^2 + 960t + 6400 So, 2d dd/dt = 762.5t + 960 At t=1, d=215.36 So, at t=1, dd/dt = 4.0 m/s
November 23, 2014

Calculus
y=0 is part of the boundary. y>=0 restricts us to the area above the x-axis.
November 23, 2014

Calculus
The curves intersect where -y^2/2 = 2-y^2 That is, at (-2,2) So, we have the left boundary is x = -y^2/2 and the right boundary is x = 2-y^2 The vertices of the region are at (-2,2),(0,0),(2,0) So, using shells, v = ∫2πrh dy where r = y and h = (2-y^2)-(-y^2/2)=2-y^...
November 23, 2014

Algebra
15P2 = 15*14
November 23, 2014

Trig
|v| = √(5√2)^2 + (5√2)^2) = √(50+50) = 10 tanθ = y/x = -5√2 / 5√2 = -1 θ = -45° Plot the point and you can easily see that this is so.
November 23, 2014

Math (trig)
Since the diamond's diagonal is along the direction of travel, the angle between the direction and the baseline is 135°. The distance from 2nf base to dcf = 409-90√2 Now use the law of cosines to find the unknown distance: d^2 = (409-90√2)^2 + 90^2 - 2(409-...
November 23, 2014

math
Assuming that coins of equal vale cannot be distinguished from each other, (2+3+4+5)! / 2!3!4!5! = 2522520
November 23, 2014

MTH LIBERAL ARTS
7C4 = 7C3 = 7*6*5 / 1*2*3 = 35 The number of choices is 10*10*9 10*10*9 * 21 = 18,900 seconds That's only 5 hr 15 min
November 23, 2014

Calculus
As usual, you can use shells or discs (washers). I think shells is easier here. Each shell has the line y=1 as its axis, and height the distance between the curves. We integrate on y, since the shells have thickness dy v = ∫2πrh dy where r = (1-y) and h = √y-y...
November 23, 2014

Algebra
√6+2 + √6-2 = 2√6 (√6+2)(√6-2) = 6-2^2 = 2 Now do the math
November 22, 2014

Algebra
No idea how the lines are laid out. But if it's perimeter you want, just add stuff up. Just as a start, I'd say 10√150 = 10√25√6 = 10*5√6 = 50√6 9√96 = 9√16√6 = 9*4√6 = 36√6 7√54 = 7√9√6 = 7*...
November 22, 2014

Math
Hello i am doing assignment in my math 20-2 class. The question is: data collected of cars passing on the road revealed that the average speed was 90 km/h with a standard deviation of 5 km/h and the data which is normally distributed a policeman is assigned to set photo radar ...
November 22, 2014

word problem
94 + 5*44 = ?
November 22, 2014

Algebra
It would be nice if you used standard notation for stuff. -5a^-2/b^3 = (-5)(1/16)/8 = -5/128 (-5a)^-2/b^3 = (20)^-2/8 = 1/3200 How did you arrive at 1/10? -16^(-1/2) = -1/4 Negative exponents mean reciprocals (2-3)√14 is indeed -√14 5/√20 - 2/√45 = 5/(2...
November 22, 2014

Math
ever heard of arccos(x) or cos -1x
November 22, 2014

Calculus
f(x) increases means that f'(x) > 0 f'(x) = 2(x+3)(2x-11)/(4x-5)^2 So, just find the intervals where f'(x) is positive
November 22, 2014

AP Calc
hmmm. better see my solution to your previous posting. the distance should have (x-8)^2 + 4x, not (4x)^2, since 4x is already y^2!
November 22, 2014

AP Calc
one way to tell whether you did it right, is to show your work! Then we can see how you arrived at your result.
November 22, 2014

AP Calc - PS
Ignore the comment about the length of the normal line. The question did not actually ask for the distance, just the point on the curve. We just wanted to find the point where the normal to the curve passes through (8,0)
November 22, 2014

AP Calc
One way is to find the length of the line normal to the curve which passes through the point. The tangent at any point has slope 1/√x, so the normal line has slope -√x. The line through (8,0) and (x,2√x) has slope 2√x/(x-8), which we want to be -√...
November 22, 2014

algebra
#16 and #18 are correct though I must say the typesetting needs work The others, no idea. No diagrams or graphs here.
November 22, 2014

AP Calc
yep. nice feeling when it clicks, no?
November 22, 2014

AP Calc
the max or min area occurs where dA/dx = 0 dA/dx = 2(5x^4-6x^2+1) = 2(5x^2-1)(x^2-1) So, dA/dx = 0 at x = ±1/√5, ±1 Naturally, A=0 at x=1, so the obvious choice is x = 1/√5. Thus, the maximum possible area is 2/√5(1/5-1)^2 = 32/(25√5)
November 22, 2014

Physics
the tension is just the weight of the iron, minus the weight of the water displaced.
November 22, 2014

Chemistry
there are .03716*0.510 = 0.01895 moles of HCl Each mole of HCl neutralizes 1 mole of NaOH So, there were .01895 moles of NaOH in 0.025L of solution. Thus, the solution was 0.01895mol/0.025L = 0.758M
November 22, 2014

statistics
I found that the inversenorm is 83.5922, what do i do after this?
November 22, 2014

statistics
Ok but before we start we usually write downwhat the mean equals, standard deviation and X. Im still confused on which one would be the mean.
November 22, 2014

statistics
Hello i am doing assignment in my math 20-2 class. The question is: data collected of cars passing on the road revealed that the average speed was 90 km/h with a standard deviation of 5 km/h and the data which is normally distributed a policeman is assigned to set photo radar ...
November 22, 2014

maths
2score=40 2dozen=24 so, the cost will be 24/40 * 280
November 22, 2014

mechanics
stone 1: height is 40 + 20t - 9.8t^2 stone 2, 3 seconds later: 30(t-3) - 9.8t^2 they meet (or pass closely) when the heights are equal: 40 + 20t - 9.8t^2 = 30(t-3) - 9.8(t-3)^2 So, just solve that for t, and then plug that value into either equation.
November 22, 2014

Algebra 2
OK. But this is Algebra I, which you have presumably already passed. But, moving right along, 5x^2 - 16x + 6 = 0 The quadratic formula says that the roots of ax^2+bx+c are x = (-b±√(b^2-4ac)/2a So, for this problem, that means x = (16±√(16^2-4*5*6))/...
November 22, 2014

Algebra 2
Hmmm. By algebra 2 you should surely know how to solve quadratic equations... x^2+(4-2x)^2=10 x^2+16-16x+4x^2-10 = 0 5x^2 - 16x + 6 = 0 ...
November 22, 2014

Math
Review your text on partial fractions. You know that the sum will be (Ax+B)/(x^2+1) + C/(x-2) + D/(x-2)^2 If you put all that over a common denominator, you get (Ax+B)(x-2)^2 + C(x-2)(x^2+1) + D(x^2+1) ------------------------------------------------ (x^2+1)(x-2)^2 Expand ...
November 22, 2014

Math
I get (27x+14)/(x^2+1) - (27/25)/(x-2) + (8/5)/(x-2)^2
November 22, 2014

calc
I will assume you meant f'(0) = 3 in that case, f"(x) = 10 f'(x) = 10x+c 3 = 10*0+c -----> c = 3 f'(x) = 10x+3 f(x) = 5x^2+3x+c 1/3 = 5*0+3*0+c c = 1/3 f(x) = 5x^2 + 3x + 1/3 I figure you can now find f(1).
November 22, 2014

calc - typo
Sorry. If f'(x) is a constant, f"(x) = 0 Fix the typo and try again.
November 22, 2014

Fencing Applicatio
Clearly, P(f) = 500+20f There are lots of good graphing web sites. Or, heck, you can get out the old graph paper and a pencil!!! Imagine!!
November 22, 2014

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