Thursday

April 2, 2015

April 2, 2015

Total # Posts: 30,258

**Calculus 1**

f(x)=3 sin x+ln(5x) f'(x) = 3 cosx + 1/x Note that ln(5x) = ln5 + lnx So, the ln5 is just a constant, with zero derivative Of course, you could use the chain rule, so d/dx ln(5x) = (1/5x)*5 = 5/5x = 1/x
*March 11, 2015*

**Math**

(1+0.013)^n = 2 n = log2/log1.013 ...
*March 11, 2015*

**Pre Algebra**

zero
*March 11, 2015*

**Calc**

Use <= for less than or equal. a(t) = cos(t)-sin(t) v(t) = sin(t)+cos(t) + c v(0)=1, so c=0 v=0 when sin(t)+cos(t)=0. That is, sin(t) = -cos(t) sin(t)=cos(t) when t=π/4, so using that as a reference angle, that makes t = 3π/4 or 11π/4 Only 11π/4 is ...
*March 11, 2015*

**Math**

First, I doubt that 960t-5t is correct. If you meant v=960-5t, then clearly 960 is its maximum speed, whence it slowed down. If you meant v=960t-5t^2, that's a bit more interesting. Then the maximum speed is at t=96, and v(96) = 46080 But, if we stop counting at t=10, then...
*March 11, 2015*

**Ap calc**

a = 12t-6 v = 6t^2-6t+c v(0)=3, so c=3, and v = 6t^2-6t+3 s = 2t^3-3t^2+3t+c Since we assume zero distance at t=0, c=0. s(2) = 2*8 - 3*4 + 3*2 = 10
*March 11, 2015*

**math**

If the interior angle is x, then the sum of the other two interior angles is also x. Since they add up to 180, x=90. Also, since the sum of an interior angle and its adjacent exterior angle is a straight line, they sum to 180. So, the largest interior angle has the smallest ...
*March 11, 2015*

**math**

see the 1st related question below
*March 11, 2015*

**Algebra**

a = 49/10 b = 14/9 The reciprocal of b/a is a/b (49/10)/(14/9) = 49/10 * 9/14 = 441/140 = 63/20
*March 11, 2015*

**math**

4x + 5x = 90 x=10 The angles are 40 and 50 The smaller is increased by 10% from 40 to 44 So, the larger is decreased by 4 to 46. 4 is 8% of 50
*March 11, 2015*

**math**

If you meant that Logan is twice as old as Lindsay, then you are correct in setting it up as you did. Your solution, however, is bogus. x-5 + 2x-5 = 30 3x - 10 = 30 3x = 40 x = 40/3 No joy there. If it should have read Logan is 2 years older than Lindsay, then the equation is...
*March 11, 2015*

**math**

h/800 = sin 15°
*March 11, 2015*

**physics**

just see when the distances are equal: 120km/hr = 100/3 m/s, so 100/3 t = 2.5/2 t^2 t = 80/3 Now I expect you can handle the rest . . .
*March 11, 2015*

**Algebra please explain**

each year the boat is worth .85 as much as it was 92000*.85^10 = 18112.45 You are correct. I assume you were guessing between A and C, since the other two are clearly unreasonable.
*March 11, 2015*

**important maths ques**

As usual, draw a diagram. If you draw a line through the center, perpendicular to the chords, you cut them in half. The radius is the hypotenuse of two right triangles. One has a leg of 5, and the other has a leg of 12. So, 5^2 + 12^2 = r^2 12^2 + (17-x)^2 = r^2 5^2 + x^2 = 12...
*March 11, 2015*

**maths please help and explain**

2logx + 1 = log900 since 1 = log10, 2logx + log10 = log900 log x^2 + log10 = log900 log(10x^2) = log 900 10x^2 = 900 x^2 = 90 x = √90 3log(x-2) = 4.714 log(x-2)^3 = 4.714 (x-2)^3 = 51760.68 x-2 = 37.268 x = 39.268 16^(x-3) = 8^(2x+1) since 16 = 2^4 and 8 = 2^3, 2^(4(x-3...
*March 11, 2015*

**MATHS**

this is just like your last problem with the fruits. Try writing down in algebra what they told you. Come back if you get stuck, but show how far you got.
*March 11, 2015*

**maths**

What info did they give? d+p+a = 1134 .75d = a+252 p-96 = a+252 Now you can solve for the amounts.
*March 11, 2015*

**Maths**

Quite an interesting result, new to me. I see you have a typo. This problem is discussed here: http://math.stackexchange.com/questions/364002/prove-that-tan-1-fracyzxr-tan-1-fraczxyr-tan-1-fracxy
*March 11, 2015*

**math**

without trying to go into any existential discussion, let's just say that it is usually written as 1/4 I suspect there is more than that to your question . . .
*March 11, 2015*

**math**

or, if the slope is vertical, there's no derivative there. y = ∛x
*March 11, 2015*

**math**

not so. consider y = |x| Any time there's a cusp, or pointy place, on the graph, f is continuous, but since the slope changes instantly from one value to another, it is not differentiable there.
*March 11, 2015*

**math**

we all know that near x=0, sin(x) = x (or nearly) Since sin(pi-x) = sin(x), sin(pi-x) = pi-x
*March 11, 2015*

**Trigonometry**

just plug the numbers into the sum/difference formulas. Surely you can do that... Since both x and y are less than π/4 (why?), x+y is in QI. Since y > x, x-y is in QIV.
*March 11, 2015*

**MATH**

slope = tan 45°
*March 11, 2015*

**math**

As usual, 42
*March 11, 2015*

**math**

v = 4^3 = 64 ft^3 Now you can easily do (b), yeah?
*March 10, 2015*

**math**

x^2 + (x+7)^2 = 13^2 Looks like a 5-12-13 triangle to me.
*March 10, 2015*

**Pre-Calculus(Trignometry)**

Looks good to me.
*March 10, 2015*

**Calculus**

never come here expecting help "in a couple of minutes." you can't count on anyone's watching every post as it comes up. The first related question below is this exact problem, just with different numbers. Always be sure to check the related questions when ...
*March 10, 2015*

**algebra**

you have two points: (200,6) and (300,15) So, just use the two-point form of the line: y-6 = (9/100)(x-200)
*March 10, 2015*

**Pre-Calculus**

Because of symmetry, the vertex is midway between the roots: x = -13
*March 10, 2015*

**Pre-Calculus**

Looks good to me
*March 10, 2015*

**Calculus**

when the elevator is at height x, tanθ = (x-23)/15 so, sec^2θ dθ/dt = 1/15 dx/dt (1+tan^2θ) dθ/dt = 1/15 dx/dt (1 + ((x-23)/15)^2) dθ/dt = 1/15 dx/dt Now just plug and chug. You have x, and dx/dt=4 ...
*March 10, 2015*

**calculus**

3x^2+y^2 = 7 6x + 2yy' = 0 y' = -3x/y using implicit differentiation again, 6x + 2yy' = 0 6 + 2y'^2 + 2yy" = 0 y" = -(6+2y'^2)/2y = -(6+2(9x^2/y^2))/(2y) = -3(3x^2+y^2)/y^3 = -21/y^3 or, using the quotient rule, y' = -3x/y y" = ((-3)y...
*March 10, 2015*

**Math**

If you add up 22+18, that's 40. But, you counted the 6 who have both twice, so that leaves only 34. So, of the 50 students, 34 have shoes or boards, or both. So, 16 students have neither.
*March 10, 2015*

**math**

room: 8*6 = 48 carpet: 6*4 = 24
*March 10, 2015*

**Math**

(10+7)/(2+10+16+7)
*March 10, 2015*

**Math**

The letter C is not a closed shape. Is it not real?
*March 10, 2015*

**Math**

probably, but I'm not sure what you mean by "wider." All the graphs stretch out both directions infinitely far. However, (B) does so more slowly, so I guess you could say it's wider. See http://www.wolframalpha.com/input/?i=plot+y%3D3x^2%2B2%2C+y%3D3x^2%2B3%...
*March 10, 2015*

**Math questions**

3/4 = 18/24 5/6 = 20/24 8 3/4 = 8 18/24 = 7 42/24 7 42/24 - 5 20/24 = 2 22/24 = 2 11/12
*March 10, 2015*

**math**

4 1/2 yards is 4*36 + 18 = 162 inches She was left with 3 ft 8 in = 36+8 = 44 inches. I think now you can handle the rest, yeah?
*March 10, 2015*

**Geometry**

since volume scales as the cube of the linear scale, the new cone is scaled in every dimension to 3/4 the original cone. So, its volume is (3/4)^3 * 1920 = 810 Note that you don't need the height, just the relative scale factor. 1/3 pi r^2 h = 1920 1/3 pi (3/4 r)^2 (3/4 h...
*March 10, 2015*

**Math**

sorry, no Venn diagrams here.
*March 10, 2015*

**algebra**

If the digits are a and b, then we have a+b = 8 10b+a = 10a+b - 18
*March 10, 2015*

**Arithmetic Progressions**

a+d = 4a a = 10 10+d = 40 d = 30 S12 = 12/2 (2*10 + 11*30)
*March 10, 2015*

**math**

Trick question. At its highest point, the ball changes direction. It has to stop to do that. v = 0
*March 10, 2015*

**Math**

I'll do one, and you can do the other. You can check your work at wolframalpha.com x^3-x = x(x-1)(x+1) so we want A/x + B/(x-1) + C/(x+1) = (3x^2-7x-2)/(x^3-x) So, using the common denominator, we have A(x^2-1) + Bx(x+1) + Cx(x-1) = 3x^2-7x-2 (A+B+C)x^2 + (B-C)x - A = 3x^2...
*March 10, 2015*

**Mathematics**

well, just subtract 6√2 - 6 = 6(√2-1) On the other hand, if you're just asking about the nature of the difference, 6√2 is 6 times √2 6 is just 6 what is the difference between 6*3 and 6? same question, different numbers. Not sure just what is ...
*March 10, 2015*

**maths**

avg speed is total distance/total time time = distance/speed, so (100+200)/(100/40 + 200/60) = 360/7 km/hr
*March 10, 2015*

**math**

2*3*6 sinx*sinx cosx*cosx 36 sin^2(x) cos^2(x) or 9(2 sinx cosx)^2 9 sin^2(2x) 9/2 (1-cos(4x))
*March 10, 2015*

**math**

8 cubes of side 2 have surface 8(6*2^2) one cube of side 4 has surface 6*4^2
*March 10, 2015*

**math**

it appears you want 2^2010 + 2^2012 + 10 --------------------------- 2^2009 + 1 (2^2009*2 + 2^2009*8 + 10)/(2^2009+1) (2^2009*10 + 10)/(2^2009+1) 10(2^2009+1)/(2^2009+1) 10
*March 10, 2015*

**trapezoidal method**

there are many trapezoid rule calculators online, which explain the method and do the math.
*March 10, 2015*

**College Algebra**

if there is x at 10%, the remainder (12000-x) is at 3%. So, add up the interest: .10x + .03(12000-x) = .06(12000)
*March 10, 2015*

**math**

2 min = 8*15sec so, it will double 8 times. 10 * 2^8 = ?
*March 10, 2015*

**Algebra 2**

If you mean the nth term is -4 (1/3)^(n-1) then clearly you have a GP where a = -4 r = 1/3 The terms are -4, -4/3, -4/9, ... The sum is thus a/(1-r) = -4/(2/3) = -6
*March 10, 2015*

**Geometry**

75 at W20°S = <-70.48,-25.65> 125 at N10°W = <-21.71,123.10> Add them up to get the resultant: <-92.19,97.45> Now just convert that back to distance and heading.
*March 10, 2015*

**Elective mathematics**

since there is a common ratio, (2k-4)/(k-3) = (4k-3)/(2k-4) (2k-4)^2 = (4k-3)(k-3) 4k^2 - 16k + 16 = 4k^2 - 15k + 9 k = 7 Now just plug and chug.
*March 10, 2015*

**Analytic geometry**

I don't know what you mean by necessary, but the hyperbola is 9x^2+18x - 4y^2+8y = -41 9(x^2+2x+1) - 4(y^2-2y+1) = -41 + 9*1 - 4*1 9(x+1)^2 - 4(y-1)^2 = -36 or, 4(y-1)^2 - 9(x+1)^2 = 36 (y-1)^2/9 - (x+1)^2/4 = 1 That should tell you what you need to know.
*March 10, 2015*

**Calculus**

exponentials grow faster than any power. So, x^5/e^x -> 0 consider using l'Hospital's Rule. After 5 times, the limit is 120/e^x -> 0
*March 10, 2015*

**math**

Or, if the order is important, 5P3 = 5*4*3 = 60
*March 10, 2015*

**math**

5C3 = 5C2 = 5*4 / 1*2 = 10
*March 10, 2015*

**Please Check My Math Answers. Thanks!**

They all are correct. Good work.
*March 10, 2015*

**Math**

7/8 * pi * 7^2
*March 10, 2015*

**precalculus**

ln2 + lny - ln(2y) ln(2 * y / (2y)) ln(1) 0 If I misread the cryptic 2lN then fix it and follow the rules to get the right answer.
*March 9, 2015*

**precalculus**

decrease of 1.8% is a remaining portion of 98.2% So, the population after t years is 89000 * 0.982^t now just find t when the function = 50000
*March 9, 2015*

**math**

it is the set of products, where each value in each pair is an element of the set described above, with no duplications: {7*8,...9*11}
*March 9, 2015*

**math**

hard to say, without knowing the relationship of the angles. In a triangle? Between parallel lines?
*March 9, 2015*

**precalc**

x^2+3x-10 = (x+5)(x-2) x^2-8x+15 = (x-5)(x-3) So, you want (x+5)(x-2) / (x-5)(x-3) * R = (x-2)/(x-3) So, you have R = (x-2)/(x-3) * (x-5)(x-3) / (x+5)(x-2) R = (x-5)/(x+5)
*March 9, 2015*

**3rd grade fraction**

you sure there are 15 coins?
*March 9, 2015*

**Vectors**

The vector equation for the line is r(t) = x(t) i + y(t) j = (-2-t)i + (4+2t)j r(0) = -2i+4j r(t) = -2i+4j + t(-i+2j)
*March 9, 2015*

**math**

π(2.4^2-2.2^2)cm^2*350cm * 10g/cm^3 = 10.12 kg
*March 9, 2015*

**MATH**

40mm * 25mm * 2mm = 2000mm^3 2000mm^3 * .0005 oz/mm^3 = 1 oz now, why you tell us about a bar of soap and then about the weight of gold, I have no clue...
*March 9, 2015*

**Algebra 1**

since y=2x-1, 2x + 2(2x-1) = 22 6x = 24 x = 4 so, y = 2x-1 = 7 one solution.
*March 9, 2015*

**Math**

you want two partitions of 36 that multiply to between 300 and 350 18x18 = 324 17x19 = 323 16x20 = 320 15x21 = 315 14x22 = 308
*March 9, 2015*

**Trig verifying identities**

oops. That is csc^2(x) - 1 = cot^2(x)
*March 9, 2015*

**Trig verifying identities**

sec(pi/2 - x) = csc x sec^2(x) - 1 = cot^2(x) remember that the co- in cosine, cotan, cosec means the complementary angle. cos(x) = sin(pi/2 - x) and so on
*March 9, 2015*

**preCal help please**

can't figure what you want. 5√-3 / (√5-√3) ? multiply top and bottom by √5+√3
*March 9, 2015*

**Math**

all you have is the difference. You need one more piece of information. normal - storm > 121
*March 9, 2015*

**Math help and check**

1 and 2 are ok 3 is eponential as in (1,2) (2,4) (3,8) (4,16) ... where the common ratio is 2 y = 2^x
*March 9, 2015*

**Math**

correct 80 < t or t > 80
*March 9, 2015*

**FRACTIONS (simplify)**

2m^2-8 = 2(m-2)(m+2) so, that is the common denominator. You end up with (m+2)(m-2)(m+2) - m(2)(m-2) + 2m^2-m^3 ---------------------------------------- 2(m-2)(m+2) m^3+2m^2-4m-8 - (2m^2-4m) + (2m^2-m^3) ---------------------------------------- 2(m-2)(m+2) 2m^2-8 ------------ ...
*March 9, 2015*

**PreCal**

(√2 + 1)/i (√2 + 1)i/i^2 -(√2 + 1)i
*March 9, 2015*

**Calculus 2**

no, that is point-slope form. To me, it's just as good as the slop-intercept form, since it contains all the necessary info. For this kind of problem, you have a point on the curve, and the slope of the tangent. The point-slope form is ideal. x = tcost dx/dt = cost - tsint...
*March 9, 2015*

**MATH**

1.8E-5 = 18E-6 so, sqrt will be √18 E -3 You can do that by hand, or just do some estimating 4^2 = 16 4.2^2 = 17.64 4.3^2 = 18.49 So, you can see it is between 4.3 and 4.3
*March 9, 2015*

**geometry**

no diagram. more data.
*March 9, 2015*

**math**

v = pi r^2 h = 100pi h dv/dt = 100pi dh/dt Now just plug in your numbers to get dv/dt. Note that it does not matter what the height is. Since the cylinder has a constant radius, its volume is directly proportional to its height.
*March 9, 2015*

**math**

the magnitude is clearly √(16^2+18^2) now just figure the angle. Draw a diagram.
*March 9, 2015*

**math**

just use the product rule v = x^2 h dv/dt = 2xh dx/dt + x^2 dh/dt Now just plug in the given values.
*March 9, 2015*

**Math**

avg cost is c(x)/x = .1x + 36 + 90/x now just find x when dc/dx = 0.
*March 9, 2015*

**Trigonometry**

draw a diagram. Use the law of cosines, since you have two sides and the angle between them.
*March 9, 2015*

**calc**

the distance z between the ships after t hours, is given by z^2 = (150-35t)^2 + (30t)^2 at t=4, z=30√5 So, plug in your values, using 2z dz/dt = -70(150-35t) + 1800t
*March 9, 2015*

**Precal**

http://www.wolframalpha.com/input/?i=plot&a=*C.plot-_*Calculator.dflt-&a=FSelect_**Plot-.dflt-&f3=2x%5E2%2F((x-2)(x%2B4))&f=Plot.plotfunction%5Cu005f2x%5E2%2F((x-2)(x%2B4))&f4=x&f=Plot.plotvariable%5Cu005fx&f5=-6&f=Plot.plotlowerrange%5Cu005f-6&f6=6&f=Plot.plotupperrange_6&f7...
*March 9, 2015*

**Functions - Please Help**

the amplitude is (15.28-9.08)/2 = 3.1 Let's say Jun21 is day 172 Dec21 is day 355 The period is clearly 365 days, so y = 3.1cos(2π/365 (x-172)) Now just find x when y=13.5 and figure the dates.
*March 9, 2015*

**math**

f(z) clearly has poles of order 4 at z = 3 order 2 at z = ±√3 i
*March 9, 2015*

**Trigonometry (Identities)**

(cos-(sin-1))/(cos+(sin-1)) (cos-(sin-1))^2/(cos+(sin-1))(cos-(sin-1)) cos^2 - 2cos(sin-1) + (sin-1)^2 ------------------------------------- cos^2 - (sin-1)^2 cos^2 - 2sin*cos + 2cos + sin^2 - 2sin + 1 ----------------------------------------- cos^2 - sin^2 + 2sin - 1 2cos - ...
*March 9, 2015*

**Maths**

can't tell whether you mean 2^x - 1 or 2^(x-1) In either case, see http://www.wolframalpha.com/input/?i=plot+2^x-1%2C+2^%28x-1%29
*March 8, 2015*

**math**

the easy ones are (0,-10/3) and (2,0) Other than that, pick any value for x or y, and then calculate the other.
*March 8, 2015*

**math**

it's already two decimal places. If you mean two significant figures, then that is 7.4
*March 8, 2015*

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