Tuesday
August 4, 2015

Posts by Steve


Total # Posts: 32,564

Trigonometry
sinθ = 20/130
May 31, 2015

math
the mean of two values lies between them. So, (√2+√3)/2 does the job. Or, just note that √2 = 1.414... √3 = 1.732... Now pick any value in between them.
May 31, 2015

math
I assume you want to solve for a and b in (√2+√3)/(3√2-2√3) = a+b√6 get rid of the radicals in the bottom by recalling that (x-y)(x+y) = x^2-y^2. So, multiply top and bottom by 3√2+2√3 and you have (√2+√3)(3√2+2√...
May 31, 2015

Calculus
just use the power rule: A' = 2x - 128/x^2 A" = 2 + 256/x^3
May 31, 2015

physics
you want mass. So, since density = g/cm^3, you need to multiply density times volume to get mass. So, do the math...
May 31, 2015

geometry
on the vertical line x=7, you could have (7+55,-2) or (7-58,-2) On the horizontal line y = -2, you could have (7,-2+59) or (7,-2-51) Of course, you could pick any points on the circle (x-7)^2 + (y+2)^2 = r^2 where r is between 50 and 60.
May 31, 2015

Math
a sphere has area 4πr^2. You have half a sphere, so just solve for r in 2πr^2 = 1062 r^2 = 1062/2π ...
May 31, 2015

Maths
4b+4c=4 3b = 2c, so substitute that into the first equation 4b+6b=4 10b=4 b=$0.40 3b= $1.20, so 2c=$1.20, and c=$0.60
May 31, 2015

Math
note that each term is 6 less than the previous one. So, the 100th term is 6*99 less than the 1st term. . . .
May 30, 2015

Math
start listing the powers of 7. Just the last digits are important: 7 49 343 ...1 ...7 Every 4th power starts a new cycle of digits. 40 = 4*10, so the final digit of 7^40 is 1. Now you know how to get the final digit of 7^42.
May 30, 2015

algebra
4p^3 + 20p^2 - 9p - 45 = 0 4p^2(p+5) - 9(p+5) = 0 (4p^2-9)(p+5) = 0 (2p+3)(2p-3)(p+5) = 0
May 30, 2015

maths - eh?
is there a question in there somewhere?
May 30, 2015

Physics
s = v^2/2a, so 4.2^2/2a = 2.1 a = 4.2 m/s^2 F=ma, so 100 = (20+m)(4.2) m = 3.8 kg
May 30, 2015

Math please help!!
as always, draw a diagram. Note that if the tower's height is h, you have h cot45° - h cot55° = 40 Now just solve for h.
May 30, 2015

Math - eh?
I guess that would depend on the table, no?
May 30, 2015

math
if the price is p, then the price for all 5 items is 3p. So, each costs 3/5 p, or 60% of the original price, regardless of what it was.
May 30, 2015

Math
the two diagonals d1 and d2 can be found using the law of cosines: d1^2 = 78^2 + 90^2 - 2(78)(90)cos35° d2^2 = 78^2 + 90^2 - 2(78)(90)cos145° = 78^2 + 90^2 + 2(78)(90)cos35°
May 30, 2015

math
what is ^x ? square root? If so, we have (√x - 1/x)^2 = x - 2/√x + 1/x^2 3+2^2 = 3+4 = 7, so we have 7 - 2/√7 + 1/49 That's kind of strange, so maybe you can clarify the notation and the grouping. Some parentheses would be helpful in that regard.
May 30, 2015

math
(2n+5) > 1 2n > -4 n > -2 -(2n+5) > 1 2n+5 < -1 2n < -6 n < -3 Think of the shape of |x| -- it is a V-shape. So, if |x| > n, it will be where the graph is above the line y=n. That means there will be two intervals, not one. See http://www.wolframalpha....
May 29, 2015

Algebra
f(x) = 4|x-7| To get f(x+1), just replace every x with x+1: f(x+1) = 4|(x+1)-7| = 4|x-6|
May 29, 2015

math
Are you asking us or telling us? In any event, B is correct.
May 29, 2015

math
s = b/2 s+7 = 2/3(b+7) now just solve for s and b. You should get Sam is 7 years old now.
May 29, 2015

Math
(42,42)
May 29, 2015

polar form precalculus
r sinθ = rcosθ r(sinθ-cosθ) = 1 r = 1/(sinθ-cosθ) or, r = 1/(√2 sin(θ-π/4)) = 1/√2 csc(θ-π/4)
May 29, 2015

precal
9x^2+36=y^2+36x+6y 9x^2-36x -y^2-6y = -36 9(x^2-4x) - (y^2+6y) = -36 9(x^2-4x+4) - (y^2+6y+9) = -36 + 9*4 - 9 9(x-2)^2 - (y+3)^2 = -9 (y+3)^2 - 9(x-2)^2 = 9 (y+3)^2/9 - (x-2)^2 = 1 That's a standard form, so you should be able to provide its description now.
May 29, 2015

algebra
just add like terms: 5x^8 -5z^4+5z^2+3 +3z^6+4z^4-9z ----------------------------- 5x^8 + 3z^6 - z^4 + 5z^2 - 9z + 3 I suspect you meant z^8 and not x^8.
May 29, 2015

geometry
the desired locus is the perpendicular bisector of the line segment. So, its slope is -1 and it passes through (5/2,7/2) y - 7/2 = -1(x - 5/2)
May 29, 2015

Maths
ahhhh. I did the solution, but I failed to notice the three-day time difference. So you'll have to analyze the graph several periods later.
May 29, 2015

English
Which pf the following, would not always require a citation in a research paper? a- quotation of a phrase b- quotation of a sentence c- thesis statement d- sentence paraphrased from a book
May 29, 2015

English
in which of the following resides the irony in the short stories the gift of the magi and the necklace
May 29, 2015

English
Which specific word choices from the lottery best impacts the stories tone.
May 29, 2015

English
Which quote from The Morning of June 28 1948 best supports the conclusion that the public strongly disliked the Lottery
May 29, 2015

English
what poetic device is suddenly there came a tapping as of someone gently rapping rapping at my chamber door.
May 29, 2015

Algebra
Seem so to me.
May 28, 2015

science
power is in Watts, by the way. Work is Joules.
May 28, 2015

science
Power = work/time = 900N*40m/45s
May 28, 2015

Algebra
unless you have some parentheses, multiplication and division come first. So, 13+3*6/9-7 = 13+18/9-7 = 13+2-7 = 15-7 = 8 18-6/3+12*3 = 18-2+36 = 16+36 = 52
May 28, 2015

Algebra
mosey on over to this web page and you can see all the details: http://www.calc101.com/webMathematica/long-multiply.jsp Just type in your polynomials and it will do all the work.
May 28, 2015

Physics
96 cos 15.3° Think about it. Full weight at 0° (cos=1) and no weight at all at 90° (cos=0)
May 28, 2015

Maths
Don't really need to do it. I was just showing the logical steps I followed. As for the conversion to hours and minutes, well, duh: 60 minutes in an hour, so .2673 hours is .2673*60 or about 16 minutes.
May 28, 2015

Maths
ok. you have y = 1.05 sin(2π/11.72 x) + 1.55 So, when does y=1.7? 1.05 sin(2π/11.72 x) + 1.55 = 1.7 1.05 sin(0.5361x) = 0.15 sin(0.5361x) = 0.1428 .5361x = 0.1433 or 2.9982 That means that x = 0.2673 or 5.5926 So, y >= 1.7 when 0.2673 <= x <= 5.5926 Or, ...
May 28, 2015

trig
The wind is blowing to the SE. That will make the resultant speed less than 500 km/hr. That will make your final course a little more eastward than your calculation.
May 28, 2015

Algebra 2
x^2+6x+8 = (x+2)(x+4) x^2-2x-8 = (x+2)(x-4) The other one is (x-6)(x+6) * x^2(x+4) -------------------------------- x(x+6) * (x-6)(x+2) Now you should be able to cancel factors and figure any excluded values (where the denominator is zero)
May 28, 2015

maths
pick any two points on the graph. Connect them with a straight line. Two easy choices are when x=0 or y=0. x=0 means y=2, so one point is (0,2) y=0 means x = -2, so the another point is (-2,0) Plot those two points and draw a line though them. If you cannot plot a point, you&#...
May 28, 2015

Algebra 1
what you got aginst standard math notation? x/(x^2-9) - x/(x+3) + 3/(x-3) once you get the common denominator of (x^2-9), the numerator is x - x(x-3) + 3(x+3) = x-x^2+3x+3x+9 = -x^2+7x+9 so the final fraction can be written as -(x^2-7x-9)/(x^2-9)
May 27, 2015

Algebra 1
You have (5a^2+21a)/(2a^2+6a) ÷ (a+4)/(4a^2) ÷ (5a^3+11a^2+2a)/(a+3) a(5a+21)/2a(a+3) ÷ (a+4)/4a^2 ÷ a(5a+1)(a+2)/(a+3) I suspect a typo: the 5a^2+21a ought to be 5a^2+a. If that is so, then we have a(5a+1)/2a(a+3) ÷ (a+4)/4a^2 ÷ a(5a+...
May 27, 2015

Algebra 1
(3z^2-z-2)/(6z^2-11z-10)(4z^2-25)/(2z^2+11z+15) (3z+2)(z-1)(2z-5)(2z+5) ---------------------------------- (3z+2)(2z-5)(2z+5)(z+3) (z-1)/(z+3) You had a typo: it was (2z+5)(z+3)
May 27, 2015

college geometry
Or, you can stop at: 3.5^2 = (3 - 3)^2 + (7 - b)^2 and you have (b-7)^2 = 3.5^2 b-7 = ±3.5 b = 7±3.5
May 27, 2015

Math
verified here: http://www.wolframalpha.com/input/?i=parabola+y%3D-1%2F24+x%5E2
May 27, 2015

Math
I agree.
May 27, 2015

Mathematics
draw the radius which bisects the chord, and another to the end of the chord. Now you have a right triangle with legs 5 and 12. So, the hypotenuse (the radius of the circle) is 13.
May 27, 2015

Math
two ships collided at sea. One was carrying red dye, and the other was loaded with blue dye. All the sailors were marooned... ba da bing!
May 27, 2015

Algebra 1
the side of r√2 clearly indicates the cube's base diagonal is the diameter of the cylinder. So, geez, pretend the cylinder is standing up already. I think my result is correct. Just simplify it some.
May 26, 2015

Algebra 1
can't see the picture, but it sounds like the cube lies flat on the bottom of the cylinder, and it touches all four corners on the cylinder. Then the ratio of volumes is (r√2)^3/(pi r^2 (2r+4)) Plug in your value of r for a numeric value.
May 26, 2015

Math
Don't see why you set them up differently. I'd say you want 0.96x+1.032y=x+y-11.2 0.96y+1.032x=x+y+3.2 Now just solve for x and y as usual, and you get x = 600 y = 400 If you don't like decimals, just multiply everything by 1000.
May 26, 2015

Math
(6*3/8.2)x10^(7-8+20) = 2.195x10^19
May 26, 2015

XXX
after w weeks more, we have (3+3w)/(17+w) = .65 w = 3.4 check: after 3 more weeks, the win/loss ratio will be (3+9)/(17+3) = 0.60 after 4 more weeks, it will be (3+12)/(17+4) = 0.71
May 26, 2015

Math
since the image is 3 times the actual size, you want 14.4/3 = 4.8 for the actual size The other two are correct.
May 26, 2015

math
y(-5) = (1/2)(3^10) = 29524.5 You will get no negative values for any exponential.
May 26, 2015

Math
The center of the circle lies on the intersection of the perpendicular bisectors of the sides. Since one side lies on the line x=1, its perpendicular bisector is the line y = -6 Now find the midpoint of one other side, and see where its bisector intersects y = -6.
May 26, 2015

Math
see the related questions below
May 26, 2015

Math
a = (5/6)(3*5/6) = 25/12 yd^2 = 25/12 * 9 = 75/4 ft^2
May 26, 2015

geometry
it is well known that the altitude of a right triangle is the geometric mean of the two parts of the hypotenuse. See, for example, http://jwilson.coe.uga.edu/emt668/emat6680.folders/brooks/6690stuff/righttriangle/rightday3.html
May 26, 2015

geometry
How far is the library from the park? x^2 = 6*8 I don't see that as a choice. ??
May 26, 2015

math
If you mean ∫ 1/(t^2-1)^2 dt try using partial fractions: 1/(t^2-1)^2 = 1/4 (1/(t+1) + 1/(t+1)^2 - 1/(t-1) + 1/(t-1)^2) each of those is easy to integrate.
May 26, 2015

Math
a+5d = 5a a+10d = 2(a+4d)+3 Now you can find a and d, and then a+7d.
May 26, 2015

math
Draw a Venn diagram. You will see that 28 like some sport. So, 2 like none of them.
May 26, 2015

DIFFERENTIATION
if the base has side x and the tin has height y, then x^2 y = 864 y = 864/x^2 The surface area a is a = x^2 + 4xy = x^2 + 4x(864/x^2) = x^2 + 3456/x da/dx = 2x - 3456/x^2 = (2x^3-3456)/x^2 da/dx=0 when x=12. Now find the area.
May 26, 2015

precal
just start with -4pi/3 and start adding 2pi. You will run into two of the other three values. The remaining one is a different angle.
May 26, 2015

precal
4sin^2 = 4cos + 1 4 - 4cos^2 = 4cos + 1 4cos^2 + 4cos - 3 = 0 (2cos-1)(2cos+3) = 0 so, cosx = 1/2 or -3/2 -3/2 is not a choice, so just find where cosx = 1/2.
May 26, 2015

Precalculus
Review your trig function definitions. For this triangle, tanθ = 7/5
May 26, 2015

Precalculus
it's exactly 60/√(60^2+85^2)
May 25, 2015

algebra
nope. is 2(3+4) = 2*4? Review the distributive property: (-2)(x-3) = (-2)(x)+(-2)(-3) = -2x+6 You cannot combine x-3 into -3x
May 25, 2015

Algebra
that would be correct.
May 25, 2015

Algebra
well, what is the smallest number which is a multiple of 2,4,8 and 12?
May 25, 2015

Algebra
2 is the only number which divides both terms.
May 25, 2015

Algebra
well, 7*3 = 21, so think again
May 25, 2015

Math
so, where did the 3 come from? One side of ABC is 20. So, if a scale factor of 0.5 is applied, the corresponding side of CDE is 0.5*20 = 10 Now do the same for the other two sides.
May 25, 2015

Math
How can that be your answer? It asks for the lengths of all the sides of CDE. What the heck is 1.5 supposed to be?
May 25, 2015

Math
when you say "related" it's not quite clear which way the scale factor is applied. if ABC is .5 CDE, the all the sides of ABC are 0.5 as big as those of CDE. if CDE is 0.5 ABC, then all the sides of CDE are .5 as big as those of ABC. So, pick the right one, and ...
May 25, 2015

Algebra
find the highest power of primes and variables that divide both terms: 14abc = 14abc 28a^2b^2c^3 = 14abc * 2abc^2 So, the GCF is 14abc It divides both terms, but no higher powers of anything will do so.
May 25, 2015

Math
5^2 = 5x5 5^9 = 5x5x5x5x5x5x5x5x5 5^11 = 5x5x5x5x5x5x5x5x5x5x5 = (5x5)x(5x5x5x5x5x5x5x5x5) So, when you multiply powers, you just add the exponents.
May 25, 2015

Math
so are you saying it could be stratified?
May 25, 2015

Math
Identify the sampling,method. You want to determine the number of text messages students at your school send in a month. You go to the cafeteria and ask every 4th student that walks in. a- random b- systemic c- stratified d-m none of these My answer is none of the these ...
May 25, 2015

Algebra 1
What are the solutions to the system? y=x^2+5x-9 y+2x+1
May 25, 2015

Algebra 1
Since opening night, attendance at Play A has increased steadily, while Play B first rose then fell. Equations modeling the daily attendance y at each play are shown below, where x is the number of days since opening night. On what day(s) was the attendance the same at both ...
May 25, 2015

Math
my answer is 208.02 meters
May 25, 2015

Math
A model rocket is launched from a roof into a large field. The path the rocket can be modeled by the equation y=-0.04x^2+8.3x+4.3 where x is the horizontal distance in meters, from the starting point on the roof and y is the height in meters, of the rocket above the ground. ...
May 25, 2015

Math
Sorry I think that it is 439.20 meters in 9.2 seconds
May 25, 2015

Math
A catapult launches a boulder with an upward velocity of 92 m/s. The height of the boulder, h, in meters after 1 seconds is given in the function h= -5t^2+92t+16. How many seconds does it take to reach maximum height? What is the boulders maximum height?
May 25, 2015

math
I don't see any way. The number of yellow birds must be a multiple of 20 less than 100. So, if there are 20 yellow, b+g=80 7b+5g=99 If 40 yellow, b+g=60 7b+5g=98 If 60 yellow, b+g=40 7b+5g=97 If 80 yellow, b+g=20 7b+5g=96 None of those setups has positive integer solutions...
May 25, 2015

math
recall the formula for the circumference of a circle of radius r: c = 2πr Now just plug in your numbers.
May 25, 2015

Math
4k+1 = 5n+2 4k = 5n+1 So, what multiple of 4 is 1 more than a multiple of 5? k=4, n=3 So, 17 students.
May 25, 2015

Algebra
If each tray originally had n muffins n + 5 >= 20 n >= 15 so, there were originally 6n >= 90 muffins
May 25, 2015

Algebra
if the prices are n and s, then we have 14n + 4s = 250 7n + 4s = 170 now just find c and s. Just looking at the numbers, I suspect a typo, but go with what you have written.
May 25, 2015

algebra (check my work)
yes, as could could check: .60 * 40 = 24
May 25, 2015

math
s = rθ where θ is in radians. So, since π radians is 180°, s = 9 * 69 * π/180
May 24, 2015

Coordinate Graphing
3x+2 = 5 x = 1 so, plot (1,5)
May 24, 2015

combinatorics
first, how many edges are there on an icosohedron? Then, since there are duplicates, you will have 30Pn/(10!10!10!) ways to arrange the toothpicks. But, there are rotational symmetries which make multiple solutions really the same thing.
May 24, 2015

Math
v = x(20-2x)^2
May 24, 2015

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