Monday

July 27, 2015

July 27, 2015

Total # Posts: 32,481

**calculus1**

sin u sec^5 u = tan u sec^4 u = sec u * tan u * sec^3 u du if v = sec u, then that is v^3 dv So, you have ∫ sin2x sec^5(2x)dx 1/2 ∫ sin2x sec^5(2x) 2 dx = 1/2 ∫ sec^3(2x) d(sec(2x)) = 1/8 sec^4(2x) + C There are lots of good Riemann sum calculators online. ...
*June 10, 2015*

**math trigonometry**

can you not use the same name for all your posts? cos(-200) = cos(200) = -cos(20) = -m work with the other angles in a similar way. Draw triangles on the axes to help see the transformation formulas.
*June 10, 2015*

**math trigonometry**

it's just an expression. Nothing to prove. But, in the spirit of the previous post, reduce all the angles to QI reference angles and see what drops out.
*June 10, 2015*

**math trigonometry**

what's the problem? cos 180 = -1 sin 225 = -sin 45 = -1/√2 sin 170 = sin 10 = cos 80 tan 135 = -tan 45 = -1 and you have (-1)(-1/√2)(cos 80) / (cos 80)(-1) = -1/√2 or -(-sin 45) / -tan 45 = -cos 45 = -1/√2
*June 10, 2015*

**Physics 11th**

h(t) = x + 4.9t - 4.9t^2 if h=0 when t=3, then x + 4.9(3) - 4.9(9) = 0 x = 29.4
*June 10, 2015*

**Algebra**

4! = 24
*June 9, 2015*

**Alg 2**

y-4=2(x+3) is the line parallel to y=2x-5 You want the line perpendicular. So, your equation is y-4 = -1/2 (x+3) you can massage that as you will.
*June 9, 2015*

**Physics**

it takes 120/200 = .6 seconds to reach the target. So, how far does the bullet fall in .6 s?
*June 9, 2015*

**calculus1**

f(x) = cosx+x-2 f'(x) = 1-sinx start with, say, x=3 x -> 3 - f(3)/f'(3) = 3-.01/.8588 = 2.98835 and proceed as needed
*June 9, 2015*

**math trigonometry**

that's theta, not theter. tan(180+θ)*cos(90+θ) + sin(360-θ)*tan(180-θ) = (tanθ)(-sinθ) + (-sinθ)(-tanθ) = 0
*June 9, 2015*

**algebra 2**

clearly, a = 13 d = -2 -25 = 13+19(-2), so -25 is A20 S20 = 20/2(13-25) = -120
*June 9, 2015*

**math**

no ideas on any of the? Review the distributive property -2r(8r+5) (-2r)(8) + (-2r)(5) -16r^2 - 10r Do the others the same way
*June 9, 2015*

**pre-calculus 11**

x^2/2 - 1 = x+3 x^2 - 2 = 2x+6 x^2 - 2x - 8 = 0 You multiplied x by 2, but not the 3.
*June 9, 2015*

**solving two-step inequality**

the difference between 5 times a number and 6 is less than 14.
*June 9, 2015*

**Algebra**

the slope is (2-4)/(6+2) = -1/4 So, in point-slope form, you have y-5 = -1/4 (x-2) Now massage that into slope-intercept form.
*June 9, 2015*

**need ratio**

(3/2):(9/2) = 3:9 = 1:3
*June 9, 2015*

**physics**

well, geez. The wall is 2m high. At the end the bug slides down 1 cm. So, he ends up 199cm from the foot of the wall. Not much of a physics problem.
*June 9, 2015*

**math**

540(1+.06)^3
*June 9, 2015*

**Economic**

even more important: who says so? Is it even true?
*June 9, 2015*

**Algebra**

or, just use the point-slope form of the line. You know the slope is 1/5 and it goes through (-3,-6). So, y+6 = 1/5 (x+3) You can massage that as you will.
*June 9, 2015*

**Calc 1**

Not at all. Just because the limit exists, that does not mean the function at x=a has the value L. It might not even be defined at all. recall your previous example, f(x)=(x^2+x-2)/(x^2-1), where the limit as x->1 was 1.5, but the function was not defined there. There was a...
*June 9, 2015*

**math trigonometry**

Not only that, I'm not sure what the sin^3x is even doing there. I will note that sin/cos^2 = tan/cos
*June 9, 2015*

**Math - still no question**

apparently you either did not read, or did not like my work on your previous posting. So, just what is your question? You have presented some data, but don't say what it is you want to know! You might also indicate how the semi-circles are arranged. Just in a long snaky ...
*June 9, 2015*

**Geometry - incomplete**

depending on the labeling, any one of those could work.
*June 9, 2015*

**math**

100x + 200y <= 1400 0.6x + 0.8y <= 7.2 x/y >= 2/3 volume is .8x+1.2y Now just follow the usual optimization steps.
*June 9, 2015*

**gwalior glory school**

1st digit is 4 ones digit is 2 tens is 2+4 the number is 462 or, 451 if you only have one eye ...
*June 9, 2015*

**math**

3n+p = 70 n+3p = 50 add them together and you have 4n+4p = 120 so, 2n+2p = 60
*June 9, 2015*

**Algebra**

Just realize that a negative exponent switches the factor between numerator and denominator. (c^-3)^2d^4/d^-2 = c^-6 d^4/d^-2 = d^6/c^6 (e^4)^-3f^-5/f^-2 = e^-12 f^-5/f^-2 = e^-12 f^-3 = 1/(e^12f^3) (8^-7/8)^-2 = (8^-8)^-2 = 8^16
*June 9, 2015*

**MATH**

(ar)(ar^3) = 2ar^4 a^2r^4 = 2ar^4 ar^4 = 2r^4 a = 2 a(r^4-1)/(r-1) = 80 1+r+r^2+r^3 = 40 r = 3 So, the GP is 2,6,18,54,162,... (6)(54) = 2*162 2+6+18+54 = 80
*June 9, 2015*

**Algebra**

-5c^-3 = -5/c^3 So, (-5/c^3)^4 = 625/c^12
*June 9, 2015*

**Algebra**

here's one way. You want the concentration to be reduced by a factor of 15/25 = 3/5 So, the volume must be increased by a factor of 5/3. 5/3 * 120 = 200 ml So, if you add 80ml of water, the concentration is reduced from 25% to 15% Or, you can solve the equation .25*120 + ...
*June 9, 2015*

**maths**

factor out the x and you have (5/3 - 3/5)x = (25-9)/15 x = 16/15 x
*June 9, 2015*

**calculus1**

The graphs intersect at (0,-1) and (0,1). If this area is spun around the y-axis, you can think of the solid as a bunch of thin discs, of thickness dy, each with a hole in the middle. So, the area is a = ∫[-1,1] π(R^2-r^2) dy where R = 2-2y^2 and r = 1-y^2 a = &#...
*June 9, 2015*

**Calc 1**

true If the perimeter is p, then 2x+2y = p y = (p-2x)/2 = p/2 - x The area is a = xy = x(p/2-x) = p/2 x - x^2 This is just a parabola, with vertex at x = p/4 so, y = p/4 as well, and you have a square to get max area.
*June 9, 2015*

**science**

I believe it is C water can act as either a polar or nonpolar solvent.
*June 9, 2015*

**Calc 1**

what do you mean you "tried 0.5"? Tried for what? In my solution, the slope is 2, not 1/2.
*June 9, 2015*

**Calc 1**

clearly, s(0) = 0 s(1/2) = 1 So, the line is y=2t. since t is time and y is position, say, cm, then the slope of the line (cm/s) is the average velocity during the interval [0,0.5] See http://www.wolframalpha.com/input/?i=plot+y%3Dsin%28pi*x%29%2C+y%3D2x
*June 9, 2015*

**Kainantu sec..science(chemistry)**

PV=kT That is, PV/T is constant. (10)(1.93)/(273+100) = 1V/273 so just solve for V.
*June 9, 2015*

**Kainantu sec..science(chemistry)**

1 mole at STP is 22.4L 2.00g of CS2 is 2/76.14 = 0.0263 moles CS2 CS2+3O2 = CO2 + 2SO2 so, each mole of CS2 produces 2 moles of SO2. I expect you can take it from there...
*June 9, 2015*

**Maths**

assuming you measure the 12m along the ground, we have the horizontal distance from the base of the building is 12cos5° = 11.95 So, from eye level, the vertical distance to the top of the building is 11.95tan35°15' = 8.45 Add to that the 1.6m of your height, and ...
*June 8, 2015*

**math**

65*3 = 5x x = 39
*June 8, 2015*

**Physics**

since s = 1/2 at^2, the truck moved for t seconds, where 42 = 1/2 * 2.15 t^2 t = 6.25 seconds The car moved 1/2 * 3.47 * 6.25^2 = 67.77 meters so, it was 25.77 m behind the truck v = at, so you can figure out the speeds, I expect.
*June 8, 2015*

**Physics**

h(t) = 22.0 + 17.0t - 4.9t^2 v(t) = 17.0 - 9.8t So, find t when h=0, and use that to find v at that instant.
*June 8, 2015*

**Physics**

x(t) = 2.17+4.80t^2−0.100t^6 v(t) = 2.17+ 9.60t - 0.600t^5 a(t) = 9.6 - 3.0t^4 As you say, v(2) = 0, so a(2) = -38.4
*June 8, 2015*

**algebra**

x/(x-5)-3=5/(x-5) x/(x-5)-5/(x-5)=3 (x-5)/(x-5) = 3 1 = 3 not true for any value of x.
*June 8, 2015*

**Maths**

since the circumference is πd, just find d where πd*480 = 1200 m
*June 8, 2015*

**geometry**

clearly AD and BC are horizontal, and thus parallel. since B is 1 to the left of A, and C is one to the left of D, BA || CD. since AD and AB are not the same length, ABCD is a parallelogram and not a rhombus.
*June 8, 2015*

**Math**

can't see the diagram, but the area of a semi-circle is π/2 r^2 So, the area between two semi-circles of radii r and R is π/2 (R^2-r^2) You have circles of radii 14 and 16. So, plug in your numbers.
*June 8, 2015*

**statistics**

there were 15 cards, 5 of them diamonds. So, the chance of getting a diamond is 5/15 After that, having drawn a diamond, there are only 14 cards left, 4 of them diamonds. So, the chance that the 2nd draw is another diamond is 4/14.
*June 8, 2015*

**pre calc**

y = kx 9 = 12k, so k = 3/4 y = 3/4 x
*June 8, 2015*

**physics**

you have a right triangle, with the hypotenuse = 9 (his actual speed), and one leg=2 (the current) so, his resultant velocity must be upstream at an angle x such that sin(x) = 2/9 and the actual resultant speed s (due north) is √(9^2-2^2) Having gotten his speed s, the ...
*June 8, 2015*

**maths**

One subset is {1,3} I expect you meant to ask a little more . . .
*June 8, 2015*

**Calculus**

the revenue function is price * quantity, so R(x) = x(50-.01x) profit is revenue less cost, so P(x) = R(x)-C(x) = x(50-.01x) - (10+2x) = -0.01x^2 + 48x - 10 Now just set dP/dx=0 and evaluate P there. Or, just use your Algebra I skills and find the vertex of the parabola.
*June 8, 2015*

**math**

d/1400 = 8/450
*June 8, 2015*

**Math**

The digits are, as explained above, going right to left, 2 3 4*2=8 2+3=5
*June 8, 2015*

**math**

Grrrr! The Greek letter is pi The dessert is pie! Here is the graph. I expect you can use it to help with the other questions. http://www.wolframalpha.com/input/?i=-1800cos%289%CF%80%2F6+t%29%2B1800+for+0+%3C%3D+t+%3C%3D+10
*June 8, 2015*

**science**

at deceleration a, the velocity is v = 20-at so t = 20/a the distance traveled by the car is s = 20t + 1/2 at^2 = 20(20/a) - 1/2 a (20/a)^2 = 200/a So, to stop in 50 meters, 200/a = 50 a = 4 m/s^2 check: v = 20-4*5 s = 20*5 - 2*5^2 = 100-50 = 50
*June 8, 2015*

**speed time distance**

180 km/hr = 50 m/s the front of the train arrives at t=0. The front of the train leaves the platform at t = 365/50 = 7.3 The back of the train whose length is x leaves the platform at t = 7.3 + x/50 So, solve for x in 7.3 + x/50 = 21
*June 8, 2015*

**math**

Neither can I. You never asked a question.
*June 8, 2015*

**math**

The volume is x(30-2x)^2 The area is (30-2x)^2 + 4x(30-2x)
*June 8, 2015*

**Math**

also recall that cos(x) is negative in QII and QIII
*June 7, 2015*

**Pre-Algebra**

direct: y = kx, so k = y/x inverse: xy = k If y varies directly with x, find the constant of variation with x = 4 and y = -24 k = y/x = -24/4 = -6 If y varies inversely with x, find the constant of variation with x=5 and y = 10 k = xy = 5*10 = 50 and do the others in like wise.
*June 7, 2015*

**calc**

y is concave up if y" > 0 By the 2nd FT of Calculus, y' = -f(x) = -6/(x+1)^2 y" = 12(x+1)^3 so, where is y" positive?
*June 7, 2015*

**Inequalities**

Hmmm. I get (x-3)/(x-2) + 12/(x^2-x-2) > 8/(x+1) (x-3)(x+1) + 12 > 8(x-2) x^2-2x-3+12 > 8x-16 x^2-10x+25 > 0 (x-5)^2 > 0 So, all x except x = 2,5 and -1 Oddly enough, it appears that the real solution is x < -1 or x > 2 and x not 5. See http://www....
*June 7, 2015*

**Math (PLEASE HELP!)**

Evidently you do not understand the concept of a range. Your temperature is somewhere in 27±3 24 = 27-3 and 30 is 27+3 So, clearly the range is 24-30
*June 7, 2015*

**math**

as usual, maximum area is achieved in a square pen. To show this, note that if the dimensions are x and y, we have 2x+2y=200, so y = 100-x The area a = xy = x(100-x) = 100x-x^2 This is just a parabola, with its vertex at x=50. So, the pen is 50x50, or a square. Hmm. I see I ...
*June 7, 2015*

**Math**

you want m where 50 < 15+.10m
*June 7, 2015*

**Math**

total socks: 7 so, P(blue,red) = 2/7 * 2/7
*June 7, 2015*

**calc**

not sure what you mean by evaluate 4-x and 2x-8 Maybe a look at the graphs will help clarify your thinking: http://www.wolframalpha.com/input/?i=plot+y%3D4-x%2C+y%3D2x-8
*June 7, 2015*

**Walk two moons need help**

1st question: have you read it?
*June 7, 2015*

**statistics**

1569/23652 = 0.06633 You can do the rounding.
*June 7, 2015*

**statistics**

176/232 = 0.75862 You can round that as needed.
*June 7, 2015*

**Statistics**

since the yearly salary amounts to 2080*13.50 the benefits amount to 24% of that amount.
*June 7, 2015*

**algebra**

y = (10x+7)/(6x+3) now solve for x: (6x+3)y = 10x+7 6xy+3y = 10x+7 (6y-10)x = 7-3y x = (7-3y)/(6y-10) now x is y^-1, so to express f^-1(x), that is f^-1(x) = (7-3x)/(6x-10)
*June 7, 2015*

**Algebra**

for the survey, (b) looks better to me for the poems, you have (4/13)(2/12)
*June 7, 2015*

**Algebra**

(1.4*8)x10^(1+4) = 11.2x10^5 = 1.12x10^6
*June 7, 2015*

**Math**

if the base is x and the height is z, then x^2z = 4 The surface is the base and 4 sides, so a = x^2 + 4xz = x^2 + 4x(4/x^2) = x^2 + 16/x da/dx = 2x - 16/x^2 = (2x^3-16)/x^2 da/dx = 0 when x=2, so the container is 2x2x1
*June 6, 2015*

**Math (PLEASE HELP!)**

T = 27±3 |T-27| <= 3 Surely you can figure the range.
*June 6, 2015*

**Math**

1/7 = 3/(4x-1) 1 = 21/(4x-1) 4x-1 = 21 4x = 22 x = 11/2
*June 6, 2015*

**Math/Physics**

just given arbitrary vectors of some magnitudes, there is no way to compute their sum or difference. Unless you know the x- and y-components, you are stuck.
*June 6, 2015*

**Algebra**

x(x+18) <= 175 x^2+18x-175 <= 0 (x+25)(x-7) <= 0 So, -25 <= x <= 7 Or, for real-world tables, 0 <= x <= 7 There is probably a minimum positive width for a useful table.
*June 6, 2015*

**math**

The 4th row of Pascal's Triangle is 1 4 6 4 1 That is, (a+b)^4 = a^4 + 4a^3b + 6a^2b^2 + 4ab^3 + b^4 So, (3+b)^4 is 3^4 + 4(3^3)b + 6(3^2)b^2 + 4(3^1)b^3 + b^4 = 81 + 108b + 54b^2 + 12b^3 + b^4 That's all very nice, but if your question is to solve for b in (3+b)^4 = 1...
*June 6, 2015*

**algebra**

when you raise to powers, you multiply exponents. Consider: 2^3 = 2*2*2 (2^3)^4 = (2*2*2)*(2*2*2)*(2*2*2)*(2*2*2) = 2^(3+3+3+3) 2^(3*4) = 2^12 So, (x^4 y^5)^5 = x^20 y^25
*June 6, 2015*

**Math**

1/4 + 1/s = 1/3 Now just solve for s.
*June 6, 2015*

**algebra**

6C3 = (6*5*4)/(3*2*1) = 20
*June 6, 2015*

**math**

Draw radii to the points of tangency. Draw a line connecting the centers. Draw a parallel line, 2 units closer to the tangent points. Now you have a right triangle with legs 10 and 6, with the tangent line forming the hypotenuse.
*June 6, 2015*

**math**

It won't seem hard after you've done a few dozen of them... I assume you meant 9^(x+2)=240+9^x That is the same as 9^2*9^x = 240 + 9^x 9^x(81-1) = 240 80*9^x = 240 9^x = 3 x = 1/2
*June 6, 2015*

**Math**

make that 2n/10 + 5n/7 + 303 = n
*June 6, 2015*

**Math**

"several" sevenths? What kind of nonsense is that? Anyway if that means 5/7, then 2/10 + 5n/7 + 303 = n n = 3535
*June 6, 2015*

**math**

angle ADB is an exterior angle to triangle ACD. So, it is equal to angles ACD+CAD. Thus angle C is 45 degrees.
*June 6, 2015*

**Math**

In the absence of any other information about how the amplitude changes, I'd just use a linear rate of change. For instance, y = (2+0.3x) sin(x) Or, if you insist on a constant amplitude, then averaging them seems like a good option.
*June 6, 2015*

**Math**

Assuming even change in height, the rate is 0.5 m/hr So, at what time t do you have 1.4 + 0.5t = 1.71 ??
*June 6, 2015*

**Math**

see your original post.
*June 6, 2015*

**math derivatives - eh?**

The given information says nothing about the height or width of the building. Without that, we do not know enough to work the problem.
*June 6, 2015*

**Math**

see your previous post.
*June 6, 2015*

**Math**

come on, man! The common difference is A2-A1 or A3-A2, which they gave you. The difference is shown above: -2p+10 or -3p-13 In either case, it is 56. Now do you think you can write the sequence?
*June 6, 2015*

**Math**

since the difference is constant, (5p+12) - (7p+2) = (2p-1) - (5p+12) -2p+10 = -3p-13 p = -23 Now you can find the difference, and write the terms of the sequence.
*June 6, 2015*

**Algebra II**

that it is.
*June 6, 2015*

**math**

you want, for m miles, 26+.12m = 24+.19m
*June 5, 2015*

**math**

a quadratic has x^2 as its highest power. So, A. Note that y decreases by 3 when x increases by 1. So, it will look like y = -3x But, when x=0, -3x=0, and y is -8. So, y = -3x-8 again, A
*June 5, 2015*