# Posts by Steve

Total # Posts: 52,248

you don't want any maxima or minima, because that means the graph bends back on itself, meaning it fails the horizontal-line test. (A) is what you want. the domain is [0,pi]

Calculus I
Let t=0 at the given instant. The slope of the line is tan? (with ? measured clockwise from the x-axis) tan? = (7-3t)/(5+2t) = 7/5 sec^2? d?/dt = -29/(5+2t)^2 74/25 d?/dt = -29/25 d?/dt = -29/74 ------------------------------ second method ------------------------------ The ...

looks good to me.

maths
well, tan? = (24-1.5)/15 as seen from the man's eyes (assuming they are on the top of his head!)

looks good to me. Or, using shells, v = ?[0,1] 2?(y+1)(e^y-1) dy

Math
These are all easy, since the line segments are all horizontal or vertical. Just figure the lengths and compare. For example, AB = 2-(-4) = 6 They will be very easy to do if you just plot the points.

Calculus
Huh? There's nothing to do next. I gave you the first integral. The 2nd one was just for extra credit.

Calculus
The curve is maybe a bit easier to visualize if you write it as x = 4sin(y). The area is ?[0,?/2] (4-x) dy = ?[0,?/2] (4-4sin(y)) dy = 2?-4 ?4-4sin(y) dy = 4y + 4cos(y) This is a bit easier than using vertical strips, where the area is ?[0,4] arcsin(x/4) dx since integrating ...

Maths
Sorry. There's still a typo. Now you have two x terms. Don't you read what you post? As typed, your two circles do intersect. http://www.wolframalpha.com/input/?i=plot+x%5E2+%2B+y%5E2+-+10x+-+8y+%2B+18+%3D+0+,+x%5E2+%2B+y%5E2+-+8x+-+4y+%2B+14x+%3D+0 Rather than just ...

Calculus
well, f(x) is continuous, so the MVT applies. (f(1)-f(-1))/(1-(-1)) = (-8-8)/2 = -8 So, you want c where f'(c) = -8 3c^2-9 = -8 c = ±1/?3 Note that at f'(0) = -9, so it is too steep. You were just guessing, there, right? Just to show that our c values work, note...

Math
I don't know, but I'm sure google does ...

Maths
I suspect still a typo, since there are two x terms. Sorry, friend.

Math
5?700 = 5?(100*7) = 5(?100)(?7) = 5*10 ?7 = 50?7

Maths
are you ever going to fix the typo? Why keep wasting time with the same flawed posting? x^2 + y^2 - 8y - 4y + 14 = 0

T > -15 it doesn't get much simpler than this. Better review the section in your text... or google inequalities

Calculus
?3/4 (x^5/5 - x^4/2 + x^3/3) [0,1] = ?3/4 (1/5 - 1/2 + 1/3) = ?3/4 * 1/30 = ?3/120

Calculus
Not quite. You have figured the volume consisting of squares. For the triangle, the base is x-x^2, so the altitude is (x-x^2)?3/2. The volume is then ?[0,1] (1/2)(x-x^2)(x-x^2)?3/2 dx = ?[0,1] ?3/4 (x-x^2)^2 dx = ?3/120

Algebra
You know the sides are in the ratio 1:?3:2 Just switch angles to figure sin60

MATH HELP PLZ
what question? In any case, I'm sure it will mainly involve counting how many data fit the criteria, and then dividing by the total.

Math
2sinx + cosx = 0 2sinx = -cosx tanx = -1/2 Now you know there will be two solutions, in QII and QIV

Algebra check plz
Hmmm. What does they need to add a base shipping charge of \$5 mean to you?

math
well, count up the ones with 4 C's and divide by the total number.

Maths
Or, try this way. The tangent line must be perpendicular to the radius which meets it. Also, the distance from the center to the line must be r. Since the center of the circle is at (a,b), if it touches the line at (h,k), we have m = (a-h)/(mh+c-b) That must have a single ...

Maths
If the line is tangent, the solution to the system of equations has a single solution. (x-a)^2 + (y-b)^2 = r^2 (x-a)^2 + (mx+c-b)^2 = r^2 x^2 - 2ax + a^2 + m^2x^2 + 2m(c-b)x + (c-b)^2 = r^2 (m^2+1)x^2 + (2mc-2mb-2a)x + a^2+(c-b)^2-r^2 = 0 To have a single solution, the ...

Maths
x^2 + y^2 - 10x - 8y + 18 = 0 x^2-10x + y^2-8y = -18 x^2-10x+25 + y^2-8y+16 = -18+25+16 (x-5)^2 + (y-4)^2 = 23 The second equation has a typo. Fix it and complete the squares to find its center. Then compare the distance between centers to the sum of the radii.

Maths
(a) 4/9 * 3/4 = 1/3 (b) 1 - 1/4 - 1/3 = 5/12

math
x = 2/10 x + 1/2 x + 12 6/20 x = 12 x = 40

math
since the scale ratio remains constant, x/135 = 1/20

math
(10/12 - 2/3) / (1/6) = 2 days

If M = bL^3/12 replace b by 1.015b and L by 0.98L and you have (1.015b)(0.98L)^3/12 = (1.015*0.98^3)bL^3/12 = 0.955M so, M has decreased by 4.5% I see no reason to resort to binomial approximation. But, if you want to try it, and compare results, feel free.

math
in 10 days, A does 10/12 of the work In 2 days, B destroys 2/3 of the work 10/12 - 8/12 = 1/6 Since A does 1/12 each day, it will take 2 more days to finish.

geography
well, since there are 360 degrees in a complete circle, and there are 24 hours in a day, each hour of time shift involves 15 degrees of longitude.

math
what do you mean by "strength" of class?

Science
.0050 * 53.2 = ?

math
geez - impatient much?

maths
where ever did you get those numbers? 4 pi r^2 dr/dt = 4 * pi * 5^2 * 4 = 400 pi cm^3/s

maths
v = 4/3 pi r^3 dv/dt = 4 pi r^2 dr/dt now just plug in your numbers ...

Algebra
say that all 21 are chickens. That would give 42 legs. Each chicken that is replaced with a cow will raise the leg count by 2. we have 20 extra legs, so that means we need 10 cows. Thus, 11 chickens, 10 cows

Algebra2
A sound wave is modeled with the equation y = 1/4 cos 2pi/3 ?. a. Find the period. Explain your method. b. Find the amplitude. Explain your method.

Algebra2
A wave is modeled with the function y = 1/2 sin 3?, where ? is in radius. Describe the graph of this function, including its period, amplitude, and points of intersection with the x-axis. My answers are Amplitude = 1/2 Period = 2pi/3 Intersection= (0,0), (?/3,0) and (2?/3,0)

MATH
see related questions below.

Algebra2
thank you

Algebra2
3tan(?/3) = 8 tan(?/3) = 8/3 Now, tan(1.212) = 8/3, so use that as your reference angle. tan? is positive is QI and QIII, so ?/3 = 1.212 or ?+1.212=4.353 so, ?=3.636 or 13.061 The only solution in [0,2?) is 3.636

Algebra2
3tan 1/3 theta=8 in the interval from 0 to 2pi. Solve the equation.

Algebra2
I think it is 172 ft^2

Algebra2
Since the height is 5tan?, the side length must be 10. Draw a diagram to see this. Now you have the base and height of each triangle, so crank it out.

Algebra2
A pentagon can be divided into 5 congruent triangles. The function y=5 tan theta models the height of each triangle. What is the area of the pentagon if theta = 54 degrees?

maths - ouch!
That pesky zero key! Grrr

maths
300/1500 = 1/5 = 2%

Algebra2
Thank you

Algebra2
Can't tell just what you mean. Ever heard of notation for powers (^) of arguments () ? ? = ?/4 sin(2?) = sin(2*?/4) = sin(?/2) = 1 C is correct if you meant sin^2(?)

Algebra2
Use the graph of y=sin2theta to find the value of sin 2 theta for theta=pi/4. a--1 b-0 c-0.5 d-1 my answer is -1

Algebra
well, 2? radians every minute, so how many minutes have passed?

MAth
(3a+4)/(4a+4) * (a^2-6a-7) = (3a+4)/(4(a+1)) * (a+1)(a-7) The (a+1) factors out of top and bottom, leaving = (3a+4)(a-7)/4 = (3a^2-17a-28)/4

Physics
if the "x" axis is for time, then a negative position means that motion has backed up past where it started.

Maths
If he started with x, then x - x/3 - 12 = x/2

algebra
(4/?50)/?(189x) * ?(189x)/?(189x) = (4?50 ?189x)/(189x) = 4?(50*189x)/(189x) = 4?(25*2*9*21x)/(189x) = 4*5*3?(2*21x)/(189x) = (20?(42x))/63x Somehow I suspect a typo

math
divide one by the other, I guess. Pretty vague question

c/4 - 5 = 4 add 5 to get all the c stuff on one side: c/4 = 9 now multiply by 4 to clear the fraction: c = 4*9 c = 36

discrete math
(a) you have 5 1s and 3 0s so, use the formula for permutations of a set with duplicates: 8!/(5!3!) = 56 That's because for every one of the 8! permutations, the 1s and 0s can be shuffled without altering the string. (b) and (c) are similar.

discrete math
Assuming that k from 1 to n fails to execute if n < 1, when i=1, j fails when i=2, k fails at j=1 when i=3, j=1..2, k=0+1..1=1 when i=4, j=1..3, k=0+1+2=3 when i=5, j=1..4, k=0+1+2+3=6 ... when i=n, j=1..n-1, k=0+1+2+...+n-2 = (n-2)(n-1)/2 so, the total prints executed is 1...

Calculus
I assume you have drawn the region. It's a triangular shape with vertices at (0,1), (1,1) and (1,e). So, using discs (washers) of thickness dx, v = ?[0,1] ?(R^2-r^2) dx where R=y+2 and r=3 v = ?[0,1] ?((e^x+2)^2-3^2) dx = ?/2 (e^2+8e-19) Or, using shells of thickness dy, v...

Math
2.5/1.5 = ?

math
time = distance/speed just use your numbers.

MATHS
In triangle BCF, sides BC and BF are equal, since they are both the length s of one side of the pentagon. angle B is 18° (90°-72°, the exterior angle of the pentagon) So, since BCF is isosceles, angle BCF = (180-18)/2 = 81°

math
3/4 of 24 = 18 dozen so , ...

Algebra 1
that's better

math
so, pick one.

Calculus
the distance is s = ?[0,2] -2t^2 + 4 dt = -2/3 t^3 + 4t [0,2] = -16/3 + 8 = 8/3 you are correct

Calculus
The curves intersect at x = ±0.824 Since the area is symmetric we can just work with one half of it, and double that value: a = 2?[0,0.824] cosx - x^2 dx

Math
which pair of factors of 96 add up to 22? (p+6)(p+16) which pair of factors of 63 differ by 18? (q+21)(q-3)

GEOMETRY
It's certainly possible, but I'm not going to work through all the possible combinations of sides to come up with 650. Why not just show us your work, describe the sides of each figure, and we can check the accuracy.

Maths
1 2 3 0.1 2 2.1 1.9 2 3.9 Just pick any two numbers that differ by 2; one above 2 and one below.

Math algebra
a+15 = 4a a=5 check: in 15 years she will be 20=4*5

Calculus
The graphs intersect at (0,2) and (5,2). So, the area is just the region below the parabola and above the line: a = ?[0,5] y-2 dx = ?[0,5] (-x^2+5x+2-2) dx = 125/6

discrete math
(a) 36^5 (b) 10*36^4 (c) 10*9*9*9 (d) assuming you just mean that the exact sequence of 3 letters does not repeat, then 36P3 * (36P3 - 1) extra credit: what if you mean that the first 3 letters do not all repeat in the 2nd half of the password?

discrete math
huh? I read the problem. It says two circuits are considered the same if they have the same output bit for every possible input string There are only two possible output values for a single bit, so ...

discrete math
Well, since there are only two outputs possible, I'd say that there are only 2 "different" circuits, regardless of the number of bits read in.

Math
what is the shape of the truss?

maths!
Sorry - I've kinda lost track of what you're referring to. I don't recall using any foreign alphabets. Maybe you could refresh my memory here ...

math
I guess that would depend on the size of the box, dontcha think?

maths
Start at -20 and move right to +5 How far have you moved? That's how many years had passed

Math-Trigonometry
A Ferris wheel has a radius of 37.8 feet. so, the amplitude is 37.8, and you can start with f(t) = 37.8 sin(kt) The bottom of the Ferris wheel sits 0.7 feet above the ground. So, the axle is 37.8+0.7 = 38.5 feet off the ground: f(t) = 38.5+37.8 sin(kt) You board the Ferris ...

Calculas
approximate how? There are lots of methods. c-e = 2.74-e = 0.00217 (c-e)/e = 0.00798 ? 0.8%

math-precalculus
A Ferris wheel is 50 meters in diameter amplitude is 25, so y = 25sin(kt)+k The boarding platform is 1 meter from the ground, so the axle is 26 feet up y = 26+25sin(kt) The period is 6 minutes, so 2?/k = 6 ==> k = ?/3 y = 26+25sin(?/3 t) If we assume that at t=0 we are ...

Maths
f-15 = 3(s-15) f-19 = 4(s-19) solve for s and f, and then find x such that f-x = 2(s-x)

algebra
V = k/P, so PV = k you want P such that 180P = 250*35 By the way, pressure is in Pascals = N/m^2, not kg/cm^3 kg/cm^3 is density

Probablity
Since there is replacement, all the events are independent. So, for n draws, P(any specific n colors) = (1/7)^n

math
just do the dot product. You get cosx*cos(a+x) + sinx*sin(a+x) = cosx*cosa*cosx - cosx*sina*sinx + sinx*sina*cosx + sinx*cosa*sinx = cosa(cos^2x+sin^2x) = cosa

Math
Draw the figure. Since AP and BQ are parallel, PABQ is a trapezoid. Draw PR to intersect BQ at R. AP=BR=4 so RQ=5 So, the sides are PA=4 AB=PR=13 BQ=9 QP = ?(5^2+13^2) = ?194

math URGENT HELPPPP!
With a slant height of 12, each triangular face has a base of s and a height of 12, so 3(12s/2) = 198 s = 11

math
no. try it. it's easy to demonstrate.

Math
well, 363 is 2 std below the mean. So, apply your rule.

discrete math
there are 2^n possibilities for n bits.

mathvariation 2(steve,reiny,reed) pls I need help!
E = a+bL 1.4 = a+0.02b 2 = a+0.03b subtract, and you have 0.6 = 0.01b b = 60 so a = 0.2 E = 0.2 + 60L

variation! Steve pls check my solution!!!
there seems to be a typo 3 lines up from the end... But the math looks good, sorta.

GGHSS COTTON HILL Maths
clearly, d = -6 and, a=57 Now you can take it from there ...

maths
Either the 1000 should be 100 or the answer is -951

math
Just start trying factors, up to the square root of the number. 3|953? no clearly 5 is not a divisor 7|953? no trying all the primes up to 30, we see that there are no factors of 953. It is prime. We stop at the square root, because if there is a factor greater than ?n, then ...

Math
sure, but not likely. If the scores were something like 100,100,100,100,100,100,100,100,5,5 sum=810, so mean=81