Monday
August 31, 2015

Posts by Steve


Total # Posts: 33,171

Calculus
suppose ∫ f(x) dx = F(x) Then ∫[0,8] f(x) dx = F(8)-F(0) = 4 ∫[0,2] f(4x) dx = ∫[0,2] 1/4 f(4x) d(4x) = 1/4(F(8)-F(0)) = 1 check: ∫[0,8] x^2 dx = 512/3 ∫[0,2] (4x)^2 dx = 16(8/3) = 128/3
May 19, 2015

math please help
the perimeter is just the sum of all the sides. So, for the large triangle, p = 4x+2 + 7x+7 + 5x-4 = 16x+5 Now do the same for the smaller triangle. For (B), just subtract one expression from the other.
May 19, 2015

Calculus
how about |x^2-cosx| or, 2*integral from 0 to 2, since both cosx and x^2 are even?
May 19, 2015

Calculas
the volume of a disc of thickness k is pi r^2 k If the radius is y, it means you are rotating around the x-axis, so the volume of each disc is pi y^2 dx If rotating around the y-axis, each disc's radius is x, so the volume is pi x^2 dy Try drawing a diagram, guys. As you ...
May 19, 2015

Calculas
pi y^2 is used when rotating around the x-axis.
May 19, 2015

Calculas
if you use discs, they have holes. Shells are just like nested cylinders, so there are no holes. Using discs (washers), the calculation is more complex, since the lower portion is bounded by the y-axis (solid discs), and the upper portion is bounded by the two curves (washers ...
May 19, 2015

Calculus
The curves intersect at (±√3,4) So, using the area in the first quadrant, we have, using shells, v = ∫[0,√3] 2πrh dx where r=x and h=(x^2+1)-(2x^2-2)=(3-x^2) v = 2π∫[0,√3] x(3-x^2) dx = 9π/2 Looks more like a bowl than a vase...
May 19, 2015

Calculus
because f(-x) = -f(x) There is equal area above and below the x-axis.
May 19, 2015

Quadratic Functions and Calculus
Holy crap! Have you done anything on this? Have you determined the three data points to use? Have you decided what to do using the ID number? Come back with some input, ok?
May 19, 2015

Quadratic Functions
Not sure what BiQuad is, but if you want to fit a parabola through those three points, you have, assuming that v(t) = at^2 + bt + c, 0a+0b+c = 10000 9a+3b+c = 2025 36a+6b+c = 6400 Somehow I suspect what you really wanted was v(3) = 1000-2025 = 7975, since most stocks don't...
May 19, 2015

math
well, shoot. Which is bigger: a ft^3 or a yd^3?
May 19, 2015

math please help
they are the same. It shows why 11^0 = 1 or why x^0 = 1 for any value of x. (except x=0)
May 19, 2015

math help please!!
3^3/3^6 = 3*3*3 ----------------- 3*3*3*3*3*3 Now you can see that three 3's cancel out in top and bottom, so you are left with 1/(3*3*3) = 1/27 This shows why x^n / x^m = x^(n-m)
May 19, 2015

Math
can you try that again in English?
May 19, 2015

Math
the cars are 360/16 = 22.5° apart. car 16 is 3 positions from car 13. So, a rotation of 67.5° will move car 16 to car 13's position.
May 18, 2015

geometry
in a triangle, angles are opposite sides. Two angles cannot be opposite each other. Using the tan function, the hypotenuse is not used. If the base 12 is opposite the 71° angle, then 12/d = sin 71° 12/c = tan 71° Better review your trig function definitions.
May 18, 2015

Math
you have a rectangle that is 100x(40+20) and a circle that has diameter 40+20=60 so, just add those two areas. If the area inside the circular ends but outside the rectangle does not count, then you have to subtract off the smaller circle of diameter 40.
May 18, 2015

Math
a^2 = 6 b^2 = 5 c^2 = a^2+b^2
May 18, 2015

Math
you want x minutes, where 12+.05(x-500) = 10+.04(x-300) x = 1100
May 18, 2015

math
each interval has width 2, so the midpoints are at 1,3,5,7,9
May 18, 2015

math
16-x^2 is concave down, so you want to use the right endpoints. Each interval has width 1, so you just have 2(f(1)+f(2)+f(3)) = 2(15+12+7) = 68 There are several good online Riemann Sum calculators. You can use them to verify your work.
May 18, 2015

math
see related questions below
May 18, 2015

math
just plug in the values for n: t1 = 7 t2 = 2t1-3(2) = 2(7)-3(2) = 8 t3 = 2(8)-3(3) = 7 ...
May 18, 2015

math
so, did you use the formula?
May 18, 2015

algebra 2 and trig
how many std's away is the 2.5% boundary? The mean is at (78+92)/2 = 85
May 18, 2015

Calculus
Assuming x is not zero, the fractions are zero when the numerators are zero. So, f'=0 when 8x+1 = 0, or x = -1/8 f"=0 when 4x-1 = 0, or x = 1/4
May 18, 2015

Algebra 2
revenue for x hats is y=15x cost is y=0.4(x-150)^2+9000 So, you want x when 15x >= 0.4(x-150)^2+9000 x >= 262.5 so, at least 263 hats
May 18, 2015

Math
if the chord length is 2x, then half the chord subtends half the angle: x/200 = sin 34°
May 18, 2015

please help math
it is that.
May 18, 2015

math please help
after n years, its value is 400(1.07)^n
May 18, 2015

Calculus
it reverses direction when its velocity changes sign. That is, when v(t) = 0. So, find t when v(t) = s'(t) = 3t^2 - 18t + 24 = 0 then plug that value into s(t) and a(t)
May 18, 2015

Math
he used 15.75-10.5 = 5.25 gallons of paint in 1.5 hours. That is 3.5 gal/hr Thus, using the point-slope form of the line, if y is the amount of paint left at x hours after 12:00, then y-10.5 = -3.5(x-2) So, find y when x=0. Or, knowing that he used 3.5 gal/hr, and knowing that...
May 18, 2015

math please
when dividing numbers expressed as powers, you subtract the exponents. Think about it 10^7/10^3 = 10*10*10*10*10*10*10 --------------------------- 10*10*10 Three of the factors cancel, and you are left with 7-3 = 4 multiples of 10. That is 10^(7-3) = 10^4 So, you want (C)
May 18, 2015

Math
216 = 6*6^2 96 = 6*4^2 so, you wind up with 6√6t + 4√6t = 10√6t = √600t
May 18, 2015

Algebra
a = w(w+4) . . .
May 18, 2015

MATH if work is correct
78125 = -5^7 So, starting with 5^-2, the 10th term is -5^7 Note that the 3rd term is 1=5^0. So, you have to multiply by -5 another 7 times to get to -5^7.
May 18, 2015

Math
the full volume is 60*60*45 2/3 of that is still empty. So, divide that volume by 6 L/min (6000 cm^3/min) to get the time needed.
May 18, 2015

Math
In how many different orders can you read 4 books
May 18, 2015

science
a body of mass 5kg is thrown to a height of 100m.what is its potential energy at the maximum height.?
May 18, 2015

math Help!!!!
There are 6 ways you can draw the two marbles to include one red: RB,RY,RW,BR,YR,WR There are 4P2 = 12 ways to draw any two marbles So, P(one red) = 6/12 = 1/2
May 18, 2015

math...Please help!!!!
I think B, but the language is garbled. The SD will not change. Read up on how the SD is figured, and you should see why.
May 18, 2015

Geometry
h^2 + 7^2 = 28^2
May 18, 2015

Math
as you recall, if the axes are rotated through θ, tan 2θ = B/(A-C) so, tan 2θ = 24/7 and cosθ = 3/5 sinθ = 4/5 Now just plug those values into your rotation matrix and crank it out.
May 18, 2015

Math
tan(2θ) = -10/0 2θ = -pi/2 θ = -pi/4 x' = (1/√2)x + (1/√2)y y' = (-1/√2)x + (1/√2)y 13((1/√2)x + (1/√2)y)^2 - 10((1/√2)x + (1/√2)y)((-1/√2)x + (1/√2)y) + 13((-1/√2)x + (1/√2)y)^2 = ...
May 18, 2015

grade (5) math
If the pen has dimensions x and y, with n gates, and assuming there are posts only at the corners and on both sides of the gate(s) and that the gate(s) do not share a corner post, then using up the whole budget, (2x+2y-3n)+2(4+2n)+5n = 50 x+y+3n = 25 and, since the gates are 3...
May 18, 2015

Calculus
since h is not continuous at x=0, h'(0) is not defined.
May 18, 2015

Calculus
cannot say what the limit is. If f(x) is continuous, though, the limit is 7.
May 18, 2015

Calculus
this is true only if f(x) is continuous. Otherwise, all bets are off.
May 18, 2015

Math!!! Please help!!!
x^7 is the 5th term in the expansion, so it is 11C4 x^7 (-3)^4 = 26730x^7 The coefficients are 1 5 10 10 5 1, so (2y-3x)^5 = (2y)^5 + 5(2y)^4(-3x) + 10(2y)^3(-3x)^2 + 10(2y)^2(-3x)^3 + 5(2y)(-3x)^4 + (-3y)^5 Now just expand all those values nCr = n!/[(n-r)!r!] nC(n-r) = n!/[(n...
May 17, 2015

math
compare the sums of the two geometric sequences: (2^30 - 1)/(2-1) vs (3^20 - 1)/(3-1) There's a difference, but either one will set you up for life!!
May 17, 2015

math
not quite. The area is base times height, divided by 2. So, (B)
May 17, 2015

Math
consult your various conversion formulae. One way would be 6.58559 sin(x+0.73169) There are, of course, ways to express that using cosine and other phase shifts.
May 17, 2015

Calculus
See the related questions below. They should help. If not enough, some back and let us know how far you got.
May 17, 2015

Math
for the cards, does the way you arrange your cards make any difference? If not, it's a combination. For the actors, of course it makes a difference who plays which part. So, a permutation. But, if you just want to get four guys, it's a combination.
May 17, 2015

Math
3!
May 17, 2015

math
compare the sums of the two geometric sequences: (2^30 - 1)/(2-1) vs (3^20 - 1)/(3-1) There's a difference, but either one will set you up for life!!
May 17, 2015

Maths
after n years, the interest will be 800(0.02n)
May 17, 2015

math for college readiness
since y=kx, just find k: -30 = k*6 k = -5 ...
May 17, 2015

trigonometry
use your half-angle formula to find sin(15°) Now use your sum formula to find sin(270°+15°)
May 17, 2015

Math
one possible answer: 48
May 17, 2015

math
if the sides are in ratio r, the areas are in the ratio r^2. So, the sides are in the ratio 12:9
May 17, 2015

math
for an angle θ, the chord is 2r sin(θ/2) the arc length is rθ the area of a sector is 1/2 r^2 θ Now use that to find your answers
May 17, 2015

Math
4 * 6 - 2 * 3/2 = 21
May 17, 2015

Math
you give no dimensions of the key's rectangle. Its sides must be in the ratio of 94:50 to be similar to the court. All circles are similar to each other.
May 17, 2015

Math
Well, the standard form is (y-k)^2/b^2 - (x-h)^2/a^2 = 1 and for an hyperbola, c^2 = a^2+b^2
May 16, 2015

algebra
Well, you have the formula. What's the trouble?
May 16, 2015

Maths
f^-1(x) = (x-1)/2 (g◦f)(-2) = g(f(-2)) = g(-3) = 23 (f◦g)(x) = f(g) = 2g+1 = 2(3x^2-4)+1 = 6x^2-7
May 16, 2015

Math
I'd say either can be true, but not all shapes can be inscribed in a rectangle. That is, so that all their vertices touch the sides of the rectangle.
May 16, 2015

Math
thousands of years ago it was learned that the ratio of the circumference to the diameter of a circle is pi = 3.14159265... This is true for all circles: c = pi * d or, c = 2pi * r
May 16, 2015

math
clearly T16 = 1464-1290 = 174 S16 = 16/2 (a+174) = 1464 a = 9 T16 = 9+15d = 174 d=11 S20 = 20/2 (2*9+11*19) = 2270
May 16, 2015

calculus
find y' at the given point (h,k). That is the slope of the tangent line. And then just plug in that slope (call it m) into the point-slope form of the line: y-k = m(x-h) Don't forget your Algebra I now that your'e doing calculus. So, what do you get for y=√(x...
May 16, 2015

calculus
y = x/(x-1) = 1 + 1/(x-1) y' = -1/(x-1)^2 y'(2) = -1 so, the tangent line is y-2 = -1(x-2) see the graphs at http://www.wolframalpha.com/input/?i=ploy+y%3Dx%2F%28x-1%29%2C+y%3D-%28x-2%29%2B2
May 16, 2015

math
clearly T16 = 1464-1290 = 174 16/2 (a+174) = 1464 a = 9 T16 = 9+15d = 174 d=11 S20 = 20/2 (2*9+11*19) = 2270
May 16, 2015

Math
6x4 - (1/2)x2
May 15, 2015

Math
you have 2 complete circles of 12' diameter. Subtract from that area the area of the small circle of radius 2. Now divide the result by 110
May 15, 2015

math
oops. forgot about r. dv/dt = a dr/dt da/dt = 8πr dr/dt So, find r and a when 36π and plug them in to find da/dt
May 15, 2015

math
v = 4/3 πr^3 a = 4πr^2 dv/dt = 4πr^2 da/dt = a da/dt So, find a when v = 36π and plug it in to find da/dt.
May 15, 2015

math
you have two triangular bases, and three rectangular faces. I expect that you know how to find the area of triangles and rectangles ...
May 15, 2015

Math
you need to provide some dimensions of the court. All circles are similar to all other circles.
May 15, 2015

MATH
you have 1/2 of a circle of radius 12 and a rectangle that is 12x19 You just add up those areas.
May 15, 2015

math
If the perimeter is p, the area is A = 1/2 ap. So, since p = ns, what is the side s of an n-gon? The central angle of each of the n isosceles triangles is θ=360/n, so the side is s = 20 tan(θ/2) Thus, the area is A = 1/2 a (ns) = 1/2 (10) (n*20 tan 180/n) = 100n tan(...
May 15, 2015

Calculus
well, we have y' = -1/2 e^(-2t) + 1/ln10 * 1/4 10^(4t) + c y'(0)=0 means -1/2 + 1/(4 ln10) + c = 0, so c = 1/2 - 1/(4 ln10) Now follow the same logic to get y(t)
May 15, 2015

Calculus
T'(6) could be approximated by the value (T(8)-T(6))/2 = 5/2 T'(6) means how fast T is changing at t=6, in °F/hr.
May 15, 2015

geometry
there is no angle opposite the right angle. However, the sides in this triangle are in the ratio 1:√3:2 So, if d is opposite the 60° angle, it is the long side, and the sides are 2, 2√3, 4 If d is opposite the 30° angle, it is the short side, so the sides ...
May 15, 2015

Caclulus
Hmm. I see an extra sin, not cos: 9x sin(6x^2) sin(3x^2)
May 15, 2015

Algebra 1
Z=2 means 2 std above the mean. So, what's 80+2*3?
May 10, 2015

Geometry
one complete circle of diameter 12 and 2 side lengths of 106
May 10, 2015

Trigonometry
Newton's math is correct, but there is certainly no reason to convert to degrees.
May 10, 2015

Maths
b boys, 80-b girls Now add up the total points scored: 75(b) + 65(80-b) = 69(80)
May 10, 2015

maths
avg = totalcost/totalpeople = (2*84 + 6*62)/(2+6)
May 10, 2015

Math
the line through the two given points is y-4 = -7(x-1) Now use that to find the desired values.
May 10, 2015

maths
25^2 = 625 so, figure 26^2, and subtract 630 from that. or, find √630 = 25.099 so, since 25^2 < 630 and 26^2 > 630 as above...
May 10, 2015

maths
well, 1000^2 = 1,000,000, which is the smallest 7-digit number. 10 times that will be 8 digits. √10 = 3.1622, so 3162^2 = 9,998,244 3163^2 = 10,004,569
May 10, 2015

Maths - eh?
apparently the sum of all the shaded areas is less than the shaded area of the triangle. I don't see how that can be.
May 10, 2015

algebra
that will be when 1.05^t = 2 Now add that t to 2000
May 10, 2015

Algebraic Geometry
If the 2nd is x, then we have (x-5) + x + 2(x-5) = 33 x = 12 Now figure the legs.
May 10, 2015

Math
A+B+C = 26 (B+3)+B+(2B-1) = 26 Now you find B, and thus A and C.
May 10, 2015

matrices
well, B^2 = 0 0 1 1 0 0 0 1 0 Now do it again.
May 10, 2015

Math too hard please help
n: C=10n+26 ------------------ 27: 10(27)+36 = 270+36 = 306 and so on with the other values
May 10, 2015

trig
find the angle between the pole and the wire using the law of sines: 35/sin30 = 25/sinθ Now use the law of sines again to find x, since you can now figure the angle opposite x.
May 10, 2015

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