Friday

January 30, 2015

January 30, 2015

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*

**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!!**

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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