Thursday
February 11, 2016

Posts by Steve

Total # Posts: 37,565

calculus
or, you can integrate over dy, and avoid the split: In this case, the two lower bounding curves are x = y^2/4 x = 3-y ∫[2,4] y^2/4 -(3-y) dy = 14/3 Checking with Damon's method gives ∫[-1,1] 4-(3-x) dx + ∫[1,4] 4-2√x dx = 2 + 8/3 = 14/3 So, each ...
December 9, 2015

algebra
y = (6/3)x
December 9, 2015

Geometry
Complete the 2 column proof. Given m<rst = 5x and m<uvw = 7x <rstand <uvw are supplementary. Prove x=15 m<rst=5x and m<uvw=7x <rst and <uvw are supplementary given m<rst + <uvw = 180 definition of supplementary angles 5x+7x = 180 ? 12x=180 ? x=15 ?
December 9, 2015

Math
expand parentheses to get 36w+24+17+9w collect like terms to get 45w+41
December 8, 2015

Algebra
25*35 - (25-4)(35-4) =
December 8, 2015

Physics
clearly the angle is x (from directly ahead), where sin(x) = 25/31 If it takes t hours, then 0.3^2 + (25t)^2 = (31t)^2
December 8, 2015

alegbra 2
(7y+6)/(20x^2+20) = (21y+18)/(60x^2+60) just multiply top and bottom by 3
December 8, 2015

Math
what is 1/2 divided by 3?
December 8, 2015

math
c = 40.00 + .05m
December 8, 2015

Geometry
correct, if somewhat murky.
December 8, 2015

Grover Cleveland high school
study the equation of motion. If he indeed fell, starting at 10 m/s downward, then his height after t seconds was h(t) = 400 - 10t - 5t^2 But I doubt he pushed off with such a downward speed. Maybe you can modify h(t) to reflect the actual scenario.
December 8, 2015

precalc
I'll do a freebie for you. Maybe you can attempt the rest and show your work. The major semi-axis half the distance between the major vertices. Similarly for minor. #1: maj semi = 3 min semi = 2 x^2/4 + y^2/9 = 1 #3 is similar, but the center has been translated. Recall ...
December 8, 2015

Math
#1. Each nested side is 1/√2 as long as the previous side. Use that to find the length of the nth nested side. #2. Since the last digit is 8, there are 80 of them: 18,28,...808 Now you know the sum of the numbers from 1 to 80 is 80*81/2. So, you have 10 times that sum, ...
December 8, 2015

Math
I'll get you started with A. Its cost for n years is A(n) = 12500 + 300n + 3(36000/25)n do the same with B, changing the numbers as needed. Then you can make the table and compare costs for 2 years.
December 8, 2015

Math
right on.
December 8, 2015

Math
correct.
December 8, 2015

Mulitvariable Calculus
any text on vector analysis or differential geometry will discuss this topic. And google is your friend.
December 8, 2015

math
√x+y=11 x+√y=7 can't you think of some nice simple numbers that fit? The only perfect squares less than 11 are 4 and 9.
December 8, 2015

math
If those are supposed to be exponents, try 110(0.70^x) and so on The base of the exponent is the rate of change. So, 1.2^x indicates a 20% growth rate. Now it should be simple to sort by rate of growth (as a percent, not an absolute $$ amount)
December 8, 2015

math
No, it's B! Why not show your work, so we can see what's going on? How did you evaluate .01 * 2^17?
December 8, 2015

math
Nope. You want f(17)-f(10) --------------- 17-10
December 8, 2015

algebra 2 trig
One way to do this is to set up coordinates. Let A = (0,0) B = (-9,0) When A has sailed 5 miles, it lies on the circle x^2+y^2 = 25 The line through B with slope 0.4877 is y = .4877(x+9) This line intersects the circle at two places: (-4.5,2.2) and (1.0,4.9) So, you gotta be ...
December 8, 2015

math
cost(1+.20) = 40
December 8, 2015

Algebra 1
If the walkway has outside length of x, the inside length (the side of the garden) is x-8 SO, the garden has area (x-8)^2
December 8, 2015

Math
The ratio of ages of P and Q in 1996 was 2:3 and in 2001 it was7:10 What will be the ratio in 2011? in 1996: P/Q=2/3, so Q=3P/2 in 2001: (P+5)/(Q+5)=7/10 (P+5)/(3P/2+5)=7/10 P=30 so, Q=45 In 2011, (30+15)/(45+15)=3/4
December 8, 2015

11U Functions Identity
-sinx - cosx*cotx -sinx - cos^2x/sinx (-sin^2x - cos^2x)/sinx -1/sinx -cscx
December 8, 2015

maths - incomplete
how far is she from the building? It appears to have been omitted.
December 8, 2015

Math
p(~rain) = 1-p(rain)
December 8, 2015

Trigonometry
where sinA = 0, cscA is not defined.
December 8, 2015

Calculus
when she is x meters from the light, and her shadow has height y, then 2/x = y/24 -2/x^2 dx/dt = 1/24 dy/dt When she is 2m from the building (22 m from the light), -2/22^2 * 0.6 = 1/24 dy/dt dy/dt = -0.06 m/s
December 8, 2015

Math
assuming you mean the dot product, and the 2.3 should be 2,3 then we have 2*4 + 3*3 = 17
December 7, 2015

physics
well, you know the equation of the altitude of the trajectory is y = x tanθ - g/(2 v^2 cos^2θ) x^2 So, just solve for θ in 12000tanθ - 9.8/(2(800cosθ)^2) = 3000 θ = 14° Better check my math.
December 7, 2015

Math
So, finish the diagram. If the man enters the water at point C, x meters upstream from A, and lands at point D, y meters downstream from B, then we have distances of land: (d^2+x^2) water: √(x+y)^2+d^2) land: √(y^2+(2d)^2) The time it takes to cross the river is ...
December 7, 2015

Math
if you can't answer that one, you have not read anything about the sine function. Just as a hint, remember that sin^2 + cos^2 = 1
December 7, 2015

Algebra
since distance = speed * time, 6(b+s)=90 10(b-s) = 90
December 7, 2015

st augustine/math
5x + 10(50-x) = 350
December 7, 2015

geometry
find the slope m of the line joining the two points. All parallel lines have the same slope m All perp. lines have slope -1/m Check out the point-slope form of a line.
December 7, 2015

Trig
square the previous equations and add them up. Recall that sin^2θ + cos^2θ = 1
December 7, 2015

Trig
If the plane is flying on heading NθE, then we want 100sinθ-50 = -v/2 100cosθ = v √3/2 100sinθ = 50-v/2 100cosθ = v√3/2 (50-v/2)^2 + 3/4 v^2 = 100^2 v = 115.14 So, cosθ = .997 θ = 4.3º and the heading is N4.3ºE
December 7, 2015

trigonometry
review the tangent function. Draw a diagram. You can see that if the pole has height h, then h cot15°20' + h cot10°52' = 50 That is if A and B are on opposite sides of the pole. If they are on the same side, then B is farther away than A, and h cot10°52'...
December 7, 2015

PreCalculus - Need help, due tonight
#1: ln[√(x-6)*(x+1)^3] #2: ln∛(x/(1-x)^2)
December 7, 2015

trigonometry
As I see from the diagram, if the tree's height is h, and the distance to the point is x, then (h-3)/x = tan30°40' x = h cot65°10' + 3tan65°10' Now just plug and chug.
December 7, 2015

trigonometry
h/55 = tan15°
December 7, 2015

calculus
we have 18√x + 5√y = 14 9/√x + 5/(2√y) y' = 0 You have x and y, so plug 'em in to find y'
December 7, 2015

precalc
#1 vertical because y's denominator is greater. center: (-4,0) a = 10 b = 8 c = 6 I give the semi-major axes and focal distance. You can easily convert yo coordinates. Do #2 similarly
December 7, 2015

trig
ever hear of pi? sec pi/4 + 2 csc pi/3 √2 + 2*2/√3 √2 + 4/√3 4+tan 2pi/3 4+(-√3) 4-√3 Using 3.14, you cannot evaluate exactly, even with a calculator.
December 7, 2015

Calculus
Nope. You only integrated 2πx √(1+4x^2) Each strip of the surface has radius y=x^2, so ∫[0,4] 2πy ds ds^2 = 1+y'^2 = 1+4x^2, so A = ∫[0,4] 2π x^2 √(1+4x^2) dx That's a bit more complicated: http://www.wolframalpha.com/input/?i=%E2...
December 7, 2015

math
45/5 = 9
December 7, 2015

math
so, did you try some of the math? Surely you can work with the numbers. 4x2=8 9x3=27 ...
December 7, 2015

Math
x/80 = .275 Looks like you need multiplication here.
December 7, 2015

lsue
y=3x+11 x+y=59 x+3x+11=59 4x=48 x=12 y=47
December 7, 2015

Math
1A 2B 3C 4A -- you want total points 5A 6C 7A 8A 9B -- you obviously did not check the equation to see whether it was correct. 10A 11A 12A n >= 50 13A 14B -- you obviously did not check some value to see whether it fit 15D 16 x = 238.2 - 10*5.8 17 12.50 + 6x = 71.00
December 7, 2015

Math please help
yes, it is correct except that the Greek letter is pi not pie!!
December 7, 2015

CHEMISTRY
42
December 7, 2015

Math
We have the point (15,450) and a slope of 4. So, using the point-slope form of the line, we choose (b)
December 7, 2015

Math
If the shortest side is x and the middle length is y, then x + y + 2x = 19 But 2x is also x+y-3, so y=x+3, and x + x+3 + 2x = 19 x = 4 and the sides are 4,7,8
December 7, 2015

physics
since work = force * distance, which is greater fd or (2f)(3d) ??
December 7, 2015

computer
rats. The above loop will include the terminating 999 in the sum. It is a simple change to stop before including it.
December 7, 2015

computer
as the numbers are accepted, keep track of the smallest. That way there is no need to do a sort later on. read least sum=least val=least WHILE val ne 999 DO   read val   sum += val   least = val if val < least DONE print least,sum Of course, an...
December 7, 2015

Math trigonometry
Looks good to me.
December 7, 2015

math
34m+14 = 30m+22
December 7, 2015

Maths
(2sin+1)/cos = 4cos 2sin+1 = 4cos^2 2sin+1 = 4 - 4sin^2 4sin^2 + 2sin - 3 = 0 Now just solve the quadratic for sin x, and you can then get x.
December 7, 2015

Math
V = 1/3 Bh If the base has side x, then we see that h=x-2, so 1/3 x^2(x-2) = 25 You can solve the cubic, but it's easier just to note that 5*5*3 = 75
December 7, 2015

Math
all you really need is the $85 price. A 15% discount gives $72.25 No mention is made of adjusting for profit or costs.
December 7, 2015

Calculus
if u = e^x you have du = e^x dx ∫√(1+u^2)/u du Now you can use a trig substitution to get around that mess.
December 6, 2015

Calculus
A more general solution is found below; you can plug in your numbers. http://www.freemathhelp.com/forum/threads/70982-surface-integrals-spherical-cap
December 6, 2015

Calculus
the cone intersects the sphere where x^2+y^2+(x^2+y^2) = 81 x^2+y^2 = 81/2 that is a circle of radius 9/√2 in the plane z=9/√2 That means the spherical cap has a height of 9(1-1/√2). There are many sites which can give you the formula for that. As for the ...
December 6, 2015

Applied Calc
everything is just perfect. -1/5 is just a number. Since du = -5x^4 dx, the x^4 dx in the integrand becomes -1/5 du Now just do the integral, and you have -1/5 ln(u)+C
December 6, 2015

Math
72.25 is what I get.
December 6, 2015

gk
how can more than all of the students do anything?
December 6, 2015

gk
1/4 * 1/2 * 2/3 = 1/12
December 6, 2015

trigonometry
6m * 50 * pi/180 = ?
December 6, 2015

Algebra
(21^2 + 9^2) = 22.847 But your screen has diagonal of 65. So, just multiply 9 and 21 by 65/22.847
December 6, 2015

calculus
A satellite is free falling from a distance "d" of the surface of the moon with radius "r", with zero initial velocity. At what rate does the area of the portion of the moon visible to the satellite decrease at a time "t" after the free fall ...
December 5, 2015

Math
avg speed = (total distance)/(total time) (3*45 + 5*55)/(3+5)
December 5, 2015

math
nope - direct variation direct: y=kx inverse: xy=k
December 5, 2015

y
a = Δv/Δt = (-18m/s) / (4.2s) = -4.86 m/s^2
December 5, 2015

Math(analytic geometry)
At a point (h,4√h) the parabola has slope 2/√h At a point (k,√(8-k^2)) the circle has slope -k/√(8-k^2) (Assume top branch of both curves.) We want the two slopes to be the same, and we want the slope to be ∆y/∆x, so 2/√h = -k/√(...
December 4, 2015

Algebra
low coefficient means the data do not cluster close to the line. So, not much confidence.
December 4, 2015

Algebra
numerator must be 1,2,3,4,6,12 denominator must be in 1,2,3,6 + or - also possible look for the easy ones first. I usually eschew fractions, so some trial and error produced 6x^3+13x^2-41x+12 = (x+4)(6x^2-11x+3) Now you can solve the quadratic by factoring or formula.
December 4, 2015

Algebra
What's wrong with using || symbols? Your keyboard surely has them. #1 ok #2 C |x+3| has x-intercept at -3, but y-intercept is +3.
December 4, 2015

Algebra 2
this one will not factor into rational roots 9r^2-5r-10 = 0 9r^2-5r = 10 (3r-5/6)^2 = 10 + (5/6)^2 = 385/36 3r - 5/6 = ±√385/6 3r = (5±√385)/6 r = (5±√385)/18
December 4, 2015

math pleaz help quick
((6.6×10^17)−(9.2×10^14))/(4×10^16) (6600x10^14 - 9.2x10^14)/(4x10^16) (6590.8x10^14)/(4x10^16) 1647.7x10^-2 16.477
December 4, 2015

Trigonometry
p: lbs of peanuts a: lbs of almonds c: lbs of cashews work with the weights: p+a+c = 140 p = 2a now, work with the values: 3p+4a+8c = 6*140 Now go for it
December 4, 2015

math help azap
as written, none of them. 17^5÷(17^6)(17^−3)/17^−2 = 1/17^2 17^5÷((17^6)(17^−3)/17^−2) = 1 so, (a) or (e) Put in some other parentheses and you might get other answers.
December 4, 2015

Algebra 2
well, x^2+2x-8 = (x+4)(x-2) that help?
December 4, 2015

Geometry
|MA| + |AT| + ... That is, the sum of the lengths of all the sides. But there's an easier formula, since MATH is a parallelogram...
December 4, 2015

algebra
The cost (c) for (m) minutes is: c = $25.00 + .45m If you think on it a minute, you'll see why this is so.
December 4, 2015

math
no, y = mx+b has slope m, and y-intercept at y=b You have it backwards. To find a point on the line, pick any value for x, and then find the corresponding value of y. Clearly the easiest value to try is x=0.
December 3, 2015

pre-cal
clearly that would be 3/8 of the area of the entire circle. I'm sure you know how to find the area of a circle... On the other hand, 3 consecutive seats subtend only two angles, so the area should be 2/8 of the circle, no?
December 3, 2015

pre-cal
clearly, that would be 20π/8
December 3, 2015

Math
the co- in the trig functions means co-mplementary angle. cos(x) = sin(90-x) cot(x) = tan(90-x) csc(x) = sec(90-x) #2 true. review the dot product. #3 eh? a vector and a scalar? #4 2*4 + 3*3 if * means dot product #5 <2+4,6+5> for the last one, use the law of sines to ...
December 3, 2015

MATH
solve what? replace x with whatever you want. So, f(t) = 6t-2
December 3, 2015

Geomertry
holy smoke! Where to start? The angles on a spherical triangle sum to more than 180, vs 180 in the plane. pick up any text on spherical trig and you can easily list a dozen things right off the bat.
December 3, 2015

Math
The enlarged rectangle has a new strip of 1/8 inch wide, meaning it is 5 inches long. If x grows by 1 inch (8 times as much), the area will also grow by 8 times as much, or 5 in^2. This assumes that y does not change in all the manipulations.
December 3, 2015

Math
not tricky at all, if you take the time to draw a diagram. Label the 4 base corners ABCD and the vertex P. Drop an altitude to the center of the pryamid's base, point Q. Draw a perpendicular line from Q to the center of one of the base sides. It meets at point R. Then, ...
December 3, 2015

Math
The above is gibberish. Why not post the question as it was given to you? The closest thing I can think of to your posting is Hora aderat briligi. Nunc et Slythia Tova Plurima gyrabant gymbolitare vabo; Et Borogovorum mimzebant undique formae, Momiferique omnes exgrabure Rathi.
December 3, 2015

Mathematics
assuming x-1 > 0, 4x+3 <= 2x-2 x <= -5/2 But we assumed x>1, so no joy there. If x-1 < 0, or x < 1, 4x+3 >= 2x-2 x >= -5/2 So, f(x) <=2 on the interval [-5/2,1) See this at http://www.wolframalpha.com/input/?i=%284x%2B3%29%2F%28x-1%29
December 3, 2015

Math
it will be 7/2 as big, since all the numbers to be added are 7/2 as big.
December 3, 2015

Math!
assuming the same f, f(t) = 6t-2 f(2) = 6*2-2 f(-3) = 6(-3)-2 and so on I am confused as to just what your question is. What's to solve?
December 3, 2015

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