Tuesday
July 29, 2014

Posts by Steve


Total # Posts: 24,008

Calc 2
you pick your substitutions because of identities sin^2 + cos^2 = 1 cosh^2 = sinh^2 + 1 by dividing by sin^2 or cos^2 you can get the corresponding ones involving tan,sec,cot,csc, etc. as for the answer, recall that the integral of sec is log|sec+tan|, and that the inverse hyp...

Calc 2
(a) would you separate 6^2/√(6^2+1) like that? I think not. use trig substitutions. Let x = tanθ 1+x^2 = sec^2θ dx = sec^2θ dθ and you have ∫tan^2θ/secθ (sec^2θ dθ) = ∫tan^2θ secθ dθ = ∫secθ se...

math
Is the following a linear function? x -2 0 2 4 y -4 0 4 8 My answer is yes.

Algebra
just like any similar equation... (220/x-.05)(x+200) = 220+80 (220/x-.05)(x+200) = 300 (220-x/20)(x+200) = 300x (4400-x)(x+200) = 6000x -x^2 + 4200x + 880000 = 6000x x^2 + 1800x - 880000 = 0 (x-400)(x+2200) = 0

Algebra
If there were normally x tickets sold, the price was 220/x (220/x-.05)(x+200) = 220+80 x = 400

Math word problem
(x-4)(104/x+6) = 104+22 x = 13 So, he bought 13 at 8 cents, and sold 9 at 14 cents

math
What is the slope for the following set of data? x 2 4 6 8 y 1 -2 -5 -8

physics
as usual, F = ma F = qE a = qE/m you have values for q,E,m, so plug 'em in.

math
plot them just like any other number. It just means you have to know how to square fractions and add them. For instance if f(x) = 2x^2-3x+7 f(2/3) = 2(4/9) - 3(2/3) + 7 = 8/9 - 2 + 7 = 5 8/9 = 53/9 or 5.88888

maths, Hmm
for max Q, we need ∂Q/∂x=0 and ∂Q∂y=0 ∂Q/∂x = 4x ∂Q/∂y = 2y+6 so, there's a max/min at (0,-3). Since the 2nd partials are both positive, it's a minimum. So, we need to maximize 2x^2+y^2+6y subject to x+y = 120 Q(0,120) = ...

Math
a vehicle going 60 can never catch up with one going 100, if the faster one has a head start.

add maths
log (3√x / ay^2) = log3 + 1/2 logx - loga - 2logy = log3 + m/2 - 1 - 2n Don't know whether that 3 belongs there, but there you have it. If by 3square root you mean cube root, then I'm sure you can make the fix.

add maths
log√p p = 2, since (√p)^2 = p so, you have 2*2 = 4 because p^2 = (√p)^4

add maths
log √b = 1/2 log 1/a = -1 1/2 - (-1) = 3/2

Calc
using discs, just add up the volumes of tiny slices with radius y and thickness dx: v = ∫[0,0.7] πy^2 dx = ∫[0,0.7] π(e^(5x)+2)^2 dx using shells, you add up the volume of thin cylinders of radius y and height 0.7-x, and thickness dy. Since the thickness ...

Please help with Calc!
first, let u = e^(2x) du = 2e^(2x) dx ∫2e^(2x)sin(e^(2x))dx = ∫sin(u) du I guess you can probably take it from there, no?

math
well, 9^-2 = 1/81 8^-1 = 1/9 81^0 = 1 so, combine the fractions and find your answer. Plain old arithmetic once you get past the powers.

math
substitution or elimination will work fine. Time to review your tools for solving systems of equations.

math
since the solution to the first two equations is x=3 y=4 you should have no trouble evaluating 3x+y

math - ouch!
Did I really say that? How about 10n - 450000 dang!

math
net income is revenue-costs for n units, that is 25n - (450000+15n) = 40n - 450000 extra credit: how many units must they sell before they start making money?

Calc 2
∫(x^2)/((x^2 - 4)^3/2 dx x = 2coshθ dx = 2sinhθ dθ x^2-4 = 4sinh^2θ ∫4cosh^2θ/8sinh^3θ 2sinhθ dθ Keeping in mind that arccoshθ = log(z+√(z^2-1)) I think wolfram's answer is less mysterious. Just as trig substit...

math 1 question pls help asap!!!
3n+5 is ok #8. No clue? really? For any x, f(x) = 3x-2 So, when f(1.5), wherever you see an x, plug in 1.5: f(1.5) = 3(1.5)-2 = 4.5-2 = 2.5 No. The sequence is geometric because there is a constant ration between terms. Multiplication and division are really the same thing. In...

algebra
I assume you mean the field is 140x50. So, that being the length and width, add them up. Now double that, because there are 4 sides, not just 2.

math
#1-4 all ok #5. What's the trouble? Start with 4.5 and start multiplying by 10's. (D) since you get 4.5 45 450 4500 ... (a) is common ratio of 0.1

Calc 2
No, the width is not always 1. Divide the interval into the desired number of intervals. In this case, interval=4, number of divisions=4. If you want 8 intervals on [0,9], each would be 9/8 in width. (b-a)/n is the subinterval width to divide [a,b] into n equal pieces. Don'...

Calc 2
In this case, since the width is 1, you are correct. I would label the rectangles as you did. Make it clear that the curve passes through the upper right corner of each rectangle. A good diagram is at http://www2.seminolestate.edu/lvosbury/CalculusI_Folder/RiemannSumDemo.htm S...

Calc 2
they want you to use rectangles where the top of the rectangle is determined by the value of f(x) on the right side of the subinterval. For [1,5] with 4 subintervals, each subinterval is of width 1, so you rectangles will have heights 2/2, 2/3, 2/4, 2/5 If using left sides, th...

Calc 2
the sums are an approximation of the area under a curve, using rectangles. The area of each rectangle is its width times its height. The width, naturally, is the length of the interval, divided by how may subintervals you use. The height is just the value of the function at so...

Discrete Mathematics
false 6 | 36 but 6 does ∤ either 9 or 4.

Math
.40*1000 + .12x = .32*(1000+x) x = 400

math
the graph of a linear function is just a straight line. Unless the function can be expressed as y = mx+b (a sloping line with slope m) or x = k (vertical line) it is not linear. So, all higher-order polynomials, square roots, etc. are non-linear. Not sure how being a new stude...

math
WHAT IS 25% OF OFF $73.78

geometry
x^2 = 4py, so x^2 = 32y at y=25, x^2 = 800, so x = 20√2 = 28.28 That's the radius, so the diameter is 56.56 cm

Alg
(f-g)(2) = f(2) - g(2) = 2*2^2-2 - (-2*2+4) = 6 - 0 = 6 f(g(2) = 2*g(2) - 2 = 2(4*2-5)-2 = 2*3-2 = 4

Math 2
1230/35 = 35 1/7 1230-35*35 = 25

alferbra
9-x^2 = (3+x)(3-x) so the x+3 factors cancel.

maths
looks like (x+a)(x+b) / (x+a)^2, so ...

maths
(5x)(15y) / (7)(8x) . . .

maths
2(x^2+1) = 5x 2x^2 - 5x + 2 = 0 hint: 2*2 + 1 = 5

maths
x^2-6x+8 = 3x-6 x^2-9x+14 = 0 now just solve for x

maths
a) the -x^2 tells you b) y=(3-x)(x+1) c) vertex at x = 1

maths
who cares what the area of the pool is? One length is 23.5 m he swims 4 lengths. So, ... especially if the dimensions are in meters, why give the area in cm^2 ? You have given the perimeter of a square pool 23.5 cm on a side, yet expressed as an area. Serious review is in orde...

Math
well, sure. 1/3 + 1/6 + 1/9 = 11/18 so, 11/18 x = 22 now just solve for x.

College Algebra & Trigonometry
what's the problem? You have the formula: x(t) = 2cos(5pi t + pi/3) just solve 2cos(5pi t + pi/3) = 3/2 cos(5pi t + pi/3) = 3/4 cos .722 = .75 so, 5pi t + pi/3 = .722 or 2pi-.722=5.560 t = (.722-pi/3)/5pi = -.021 or 6.262 t = (5.560-pi/3)/5pi = .287 see the graph at http:/...

Math
15/35 = 3/7 = 43%

Math
after spoilage, only 410 lbs remain. 500 lbs cost 175.00 30% markup means that the 410 lbs must sell for $227.50 so, ...

Math
if the cost is 1, the selling price is 1.14 So, the markup is .14. .14/1.14 = ?

Math
It appears you could use some carriage returns in there. 2(x-14)+3=7x+5 2x-28+3=7x+5 2x-25=7x+5 2x-7x=30 -5x=30 x=30/-5 x=-6 However, it appears you have solved the equation correctly.

history
Who as the last American Indian to surrender to the US government?

Calculus
just take d/dx(xy-y) y + xy' - y' y+(x-1)y' y+(x-1)(xy-y) y+y(x-1)^2 y(1+(x-1)^2) y" y(x^2-2x+3) to find y, dy/dx = xy-y = y(x-1) dy/y = (x-1)dx ln y = 1/2 (x-1)^2 + c y = ce^(1/2 (x-1)^2) = ce^(1/2x^2 - x + 1/2) = ce^(1/2 x(x-2)) c changes with rearrangement ...

math
.12x = 104 It appears there are some broken beads, since x is not an integer. typo? If the 12% is approximate, then we can take it she has 866 or 867 beads

trigonometry
(h-1.8)/16 = tan 20°

math
His cost for 7 lbs of the mixture is 3*.60 + 2*.70 + 2*.50 = 4.20 a 25% profit requires him to charge $5.25 for that. That's $0.75/lb.

history
Sorry Civil War

history
How did the wartime economies of the North and South compare?

math
you want B/D B/D = (2/3 C)/D = (2/3 (2/3 D))/D = 4/9 A is just noise.

math
((-8+0)/2,(-6+0)/2) = (-4,-3)

history
Did sharecropping restrict the voting rights of African Americans after 1867?

Calculus Help and Check
Hmm. I thought that, using Leibniz' Rule, F'(x) = ln(8+3sinx)*cosx - ln(8+3cosx)(-sinx) Did I miss something there?

math
no idea - how big are the tiles?

math - incomplete
Do you not see that there is a lot of required information missing here?

calculus help
If you want to find F'(x) where F(x) = ∫[cosx,sinx] ln(8+3v) dv then using Leibniz' Rule, F'(x) = ln(8+3sinx)*cosx - ln(8+3cosx)(-sinx)

Calculus Help
The parabolas intersect at x = -c/2 and c/2, so we want ∫[-c/2,c/2] (c^2-4x^2)-(4x^2-c^2) dx = 256/3 4c^3/3 = 256/3 c=4 naturally, c = -4 also works

Calculus Help
the line through (3,1) and (1,8) is 7x+2y = 23 the line through (0,0) and (1,8) is y = 8x the line through (0,0) and (3,1) is y = 1/3 x So, the area is ∫[0,1] (23-7x)/2-x/3 dx + ∫[1,3] 8x-x/3 dx no sweat, eh? See the lines at http://www.wolframalpha.com/input/?i=pl...

trig
tanθ = 8/12 roughly. θ actually needs to be slightly more, because the ball falls some due to gravity. But, a little investigation should convince you that the discrepancy caused by gravity can be eliminated because of the ball's diameter, given proper conditions.

math
232mi/4hr = (232/4)(mi/hr) = 58mi/hr or, using your formula 232 = r*4 and the division proceeds from that

Trig. Math
Hmmm. If the legs are a and b, and the hypotenuse is c, then we have r = (a+b-c)/2 = ab/(a+b+c) Since A = ab/2, that means r = 2A / (a+b+c) with r=2, that means A = (a+b+c) But, since a+b+c = (a+b-c)+2c, we have A = 2r+2c A = 4+2c

MATH HELP ONLY 1 QUESTION!
Looks more like A to me.

Algebra
or, consider this as the usual work problem, where the job is to make 72 copies. 1/1.5 = 1/x + 1/2 = 1/1.5 1/x = 2/3 - 1/2 1/x = 1/6 x = 6 It would have been a little more interesting if the number of copies given for each machine had been different. You might play around with...

Geometry
well, since 4b^3+5b-3 = (2b-1)(2b^2+b+3), I think it's clear...

pre calculus
well, that'd just be 4/2 + 7i/2 = 2 + 7/2 i

calculus 1
f' = 3ax^2 + 2bx + c f'=0 at x = -2 f'=0 at x = 1 sum of roots = -1 product of roots = -2 so, -2b/3a = 1, so 2b = -3a c/3a = -2, so c = -6a f(x) = ax^2 - 3a/2 x - 6ax + d f(-2) = 3 and f(1) = 0, so 4a + 3a + 12a + d = 3 a - 3a/2 - 6a + d = 0 a=2/9 d=7/9, so f(x) = ...

pre calculus
since zt=k is constant, k=3*5 = 15, and we have zt = 15

Math 222
domains of polynomials are all reals for rational functions, exclude points where the denominator is zero. After all, division by zero is not defined.

Math (Functions)
tan -10 -sin 10 / cos -10

Trig functions
cos(kt) has period 2pi/k cos(t) has max at t=0, so -cos(t) has min at t=0 y = 4 - 2cos(pi/6 (t-15)) http://www.wolframalpha.com/input/?i=4+-+2cos%28pi%2F6+%28t-15%29%29+

Math
(-5,4) - (3,-5) = (-8,9) So, you add (-8.9) to the midpoint to get to (-5,4) So, subtract (-8,9) to get to the other endpoint: (3,-5)-(-8,9) = (11,-14)

Trigonometric Functions
as you know, a sin(k(x-h))+b has domain all reals amplitude a period 2pi/k shift h range [b-a,b+a] so, put yours into that form and read off the values

Calculus
at x, the tangent has slope 1/(2√x), so the normal has slope -2√x So, the normal line at (k,√k) is y-√k = -2√k (x-k) Since (2,0) is on that line, 0-√k = -2√k(2-k) 1/2 = 2-k k=3/2 The point is (3/2,√(3/2)) ========================...

Calculus
easy way: d = |(-4)(-5)+(7)(-5)+3|/√(4^2+7^2) = 12/√65 ============================= calculus way: the distance d can be found using d^2 = (-5-x)^2 + (-5-y)^2 = (x+5)^2 + (5+(3+4x)/7)^2 d = 1/7 √(65x^2+794x+2669) dd/dx = (130x+794) / 14√(65x^2+794x+2669...

Math
1/2 * 1/2

social studies 9
What decade did W.E.B. Du Bois write a passage about Charleston South Carolina

Math
visit calc101.com and click on the long division button. See all the details.

elective mathematics
Assuming bag2 contains 3 red and 3 white balls, P(r,r) = 5/9 * 1/2 P(w,w) = 4/9 * 1/2 so, 1/2 seems strange, no? But think. No matter what color ball you pick from bag #1, there is a 50-50 chance that the ball from bag2 will match it. If I got the ball count wrong for bag2, ju...

Math
what, no calculator? #1: 1*2*3*4*5*6*7*8*9 #2: 25*24*23

math 2
65.7 because the next digit, 3 is less than 5

Algebra 2
since loga + logb = log ab, we have log3 6(3x+1) = 2 6(3x+1) = 9 18x = 3 x = 1/6 so, how come, when I worked this out for you, assuming base 10, you didn't just follow the same steps, with a change of base?

math
3y + 2x = 3

Chemistry
mass(g) / molmass(g/mol) = moles So, for each compound, find its mol mass and divide into 100g. HNO3 has mass 1+14+3*16 = 63 So, 100g / 63g/mol = 1.59 moles Suppose I told you to find the number of bean bags in 100 lbs. You'd first have to find out how much one bean bag we...

math - typo?
Assuming the obvious typo, we have 9a+4p = 260 4a+9p = 190 which does not have an integer solution. So, maybe there's something else you need to fix.

Math logarithms
90° clockwise rotation takes (x,y)->(-y,x) so, (x,lg x) -> (-lg x,x) That is, (1/x,e^x) or (x,e^-x) enter those two functions log(x) e^(-x) at http://rechneronline.de/function-graphs/

ALG
(x+8)^2 > 0 This is true for all x ≠ -8, so (-∞,-8)U(-8,∞) (x-4) / (x-1)(x+1) <= 0 (-∞,-1)U(1,4] http://www.wolframalpha.com/input/?i=%28x-4%29+%2F+%28%28x-1%29%28x%2B1%29%29+for+-2+%3C%3D+x+%3C%3D+5

algebra
4 cups of apples

Algebra 2
log 6 + log(3x+1) = 2 log(6(3x+1)) = 2 can't tell what the base is, but if it's 10, 6(3x+1) = 100 18x = 94 x = 47/9

math
(2x)(3) = 5x - 9/4 6x = 5x - 9/4 x = -9/4

Maths
35/14 = x/18

trig
since sec^2-tan^2=1, you can multiply by that: (sec^2+tan^2)(sec^2-tan^2) sec^4-tan^4 but, since tan=sin/cos = sin*sec, that's sec^4-sin^4*sec^4 (1-sin^4)sec^4

Database Queries
I'd go with B (if you use NOT or AND) or C (if you use OR) I see no single best answer without further context. I assume you've done a web search on the phrase -- it will show lots of detailed discussions.

Help with one limit
I'd go with this: (2^n+1)/2^(n+1) = 2^n/2^(n+1) + 1/2^(n+1) = 1/2 + 1/2^(n+1) -> 1/2 as n->∞ The suggestion requires you to multiply top and bottom by 2^-n.

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