Posts by steve
Total # Posts: 56,000

Algebra
12! ways 
math
all look good to me 
math
Clearly false. 
Math
34sin^2a = (3sec^2a4tan^2a)*cos^2a = (3(tan^2a+1)4tan^2a)*cos^2a = (3tan^2a)*cos^2a 13tan^2a = 13(sec^2a1) = 43sec^2a = (4cos^2a3)/cos^2a now just multiply and the cos^2a factors cancel 
Math
For Q7, I disagree. Vertical angles share only the intersection. I don't have the diagram, but I can't see how CED and BED can be vertical angles, since D is on both of them. Q9 looks like a better possibility. 
math
1/2 * 3/6 = 1/4 
Physics
step1: v=0+2a=1, so a = 1/2 km/min^2 s=0+1/4*2^2=1 step2: s=1*10 step3: a = 1/3 km/min^2 s = 1*3  1/6 * 3^2 = 3/2 PQ = 1 + 10 + 3/2 = 25/2 avg speed = (25/2)/(2+10+3) = 5/6 km/min there are two different accelerations, shown above. I assume you can convert to m/s^2 
Algebra
looks like y=5x so, what is that? 
Math
No. how did you get that? Just a guess? (8+11+12+16+n)/5=12 
Math
the average of 5 numbers is their sum/5 So, now you know that (sum)/5 = 12 
Math
two ends at pi*2.1^2 each is 27.71 cm^2 the curved side is 2 pi*2.1*8.8 = 116.11 cm^2 I agree with your answer, but it does not seem like quite enough. 
Trigonometry
just use the parametric formulas... r = 2/(1+sin?) r+rsin? = 2 r+y=2 r = 2y r^2 = (2y)^2 x^2+y^2 = y^24y+4 x^2 = 44y y=1x^2/4 check the polar form for conics and you will see that the curve is a parabola, since e=1 y=3 rsin? = 3 r = 3csc? 3x^2+3y^26x=0 3r^2 = 6rcos? r=2cos? 
math
assuming you mean to cover the entire board, then since GCD(50,70)=10 The largest square which will work has side 10 
science/math
work = force * distance 140N * 7.0 m/s * 40s = 39200J 
math
the given line has slope 5/2 so, our new line will have slope 2/5 Now, we have a point and a slope, so using the pointslopr form, our new line is y8 = 2/5 (x+7) 
Math
?(3974^2492^2) ? 3943 ft love your creative spelling ... not! 
calculus
I guess you could use the law of cosines. Draw a diagram and you will see that 3a5b^2 = 3^2+5^22*3*5*cos120° do the same for the other 
Physics
You might start here: http://www.dummies.com/education/science/physics/howtocalculaterotationalkineticenergy/ 
Math
total points so far is 196 so, the mean for those 4 games is 196/4=49 They need 49 in the next game to keep the same mean. 
math
add up the total points and divide by 4. 
trig
in QIV, y = 2 r = 3 x = ?5 cos? = x/r = ?5/3 
calculus
Let a=<1,0> Then b=<1/2,?3/2> Now you just add the components. For example, 2a+3b = <2,0>+<3/2,3?3/2> and 2a+3b=?((2+3/2)^2+(0+3?3/2)^2) = ?(49/4 + 27/4) = ?76/2 = ?19 
Math
(76)/0.65 = 1.538 std so, look that up in your Z table to see how much lies in the right tail. 
MATH
you're kidding, right? Why not show your work, so we can see whether you did it right... 41*41 = 1681 ... 
Math
ln(3x)ln(x) = ln(3x/x) = ln3 is constant 
Math
The revenue must be positive, so if there are x price increases, the revenue is (400040x)(2.00+0.15x) So, they need 6x^2+520x+8000 >= 10450 5 <= x <= 81.67 So, the fare must be between $2.75 and $14.25 The maximum revenue of $19270 will be achieved at a price of $8.50 
trigonometry
cosine is not a quadrant. With x positive and y negative, that is QIV cosine = x/r 
math
ooops  my bad. So, divide the circumference by the plant's diameter. If you knew enough to catch my mistake, you should know enough to figure the correct answer. What did you get? 
math
the obvious answer, though probably not technically correct, is gotten by dividing the total area by the area required by each plant. That would be ?*140^2 / ?*0.5^2 = (140/0.5)^2 = 78,400 
C++ Programming
so, what have you done so far? I assume you know how to declare the (main) function, and define a structure... Presumably you have covered these topics, and many code samples can be found online. 
Math
I assume by "one with the smallest ratio" you mean the one who received the smallest amount. In that case, multiply everything by 25/2 and the ratios become 125/2 : 75/2 : 25 But that requires some split mangoes. The total is 125 mangoes. 
math
sinB/6 = sin50/6.188 2.82^2 = g^2+7^22*6*7 cos(CAD) area of ACD = 6*(7*sin(CAD))/2 
Maths
draw a diagram. Clearly the distance x is found using 86/x = sin 36° 
Algebra
y=x y=x^2 
Maths
I think you have left out some important parts of the description. 
Pre Calculus
Looks like (c) to me. Just set u=2t and you have x(t)=2cos2u y(t)=sin3u The names have been changed to protect the innocent parameters. 
12th math
c'mon, guy  you're not in Algebra I any more. Just plug in t=(x+1)/4 and you have y = 2((x+1)/4)^2+3(x+1)/44 Now just expand that out 
Math
Ummm. Did you ever think of describing the designs? I don't mind working on an answer, but I refuse to provide the question as well! 
PreCalculus Help?
looks like B to me 
Science
it's one mole So, add up the atomic weights of all the atoms, and that's how many grams of CaCO3 there are. 
PreCalculus Help?
work = force * distance so, how far between the points? 
Math
42 
Trig
got to know how high the pulley axles are. Also, where on the circumference of B is the drop of paint at time t=0? Then it's just a matter of knowing that A rotates twice as fast as B. 
Chemistry
PV=kT If P is constant, then V/T is constant (k/P) So, you want V such that V/(72+273.15) = 62/(15+273.15) 
Chemistry
°K 
geometry
The altitude of the large yellow area is 12, the side of the square. So, if you folded the small triangular area which includes the blue, the area outlined by the large yellow triangle would be 12*12/2 = 72 subtract the blue twice (once in its present location, and again after... 
geometry
v = ?r^2h, so h = v/(?r^2) a larger r means a smaller h, so 315/(?*7^2) <= h <= 315/(?*6.5^2) 2.05 <= h <= 2.37 
Math
1st step: subtract two from each side to get 5x = 60 Now what, do you think? 
math;)
u = ?(9+4) = ?13 So, divide u by its length to get a unit vector (length=1) so, (a) If you've advanced to the point where you're studying vectors, your teacher should stop insisting on rational denominators. I much prefer 1/?13 to the cumbersome ?13/13 just sayin'... 
Math
yes 
Geometry
the areas scale as the square of the ratio the volumes scale as the cube of the ratio so, volumes scale as the 3/2 power of the area ratio So thar larger pyramid's volume is 8*(40/25)^(3/2) = 8 * (9/4)^(3/2) = 8 * 27/8 = 27 
Math
you need a compass to do it right. Pick a point A on the circle. Set the compass to reach to the center, then use that radius to mark where the arc intersects the circle at B. Since all 3 sides of the triangle are the same, the angle is pi/3. The arc s = pi/3 * r 
Calculus
F' = (1/(3x))*3  (1/x)*1 = 11 = 0 so, F is constant 
Geometry
the center of the circle is the midpoint of the diameter: (3,2) The length of the diameter is ?(14^2+8^2) = ?260 = 2?65 so, the radius is ?65 That means the equation is (x+3)^2 + (y2)^2 = 65 
Calculus
using shells, v = ?[0,2] 2?rh dx where r = 5x and h=x0.5x^2 or, using discs, v = ?[0,2] ?(R^2r^2) dy where R=5y and r=5?(2y) 
Calculus
time to post your answer. Remember the 2nd FTC. If F(x) = integral[a,u(x)] f(t) dt then F'(x) = f(u(x))*du/dx 
Calculus
for each trapezoid number i the area is (f(x_i)+f(x_i+1))/2 * (x_i+1  x_i) 
Calculus
By the 2nd FTC, F' = cos((x^3)^4)(3x^2) = 3x^2cos(c^12) why minus? 
Trig
the curve is an ellipse with semiaxes a and b. If a=b it is a circle. 
maths
The volume of a thin slice of water is the area of the slice times its thickness, dy At a depth of d, with d<r, we have the radius of the surface of the water is x = ?(r^2y^2) v = ?[r,dr] ?(r^2y^2) dy Now you can answer the last part by subtracting the volume from the ... 
math
infinitely many try it  pick any value you want for x, and the equation will balance. 
calculus
actually, F' = 2tan((2x)^2) = 2tan(4x^2) F' = 2sec^2(4x^2)(8x) = 16x sec^2(4x^2) 
English
odd. I gave the phrase to google and the very first link explained it. Maybe you can start here: https://blog.udemy.com/imageryinliterature/ 
Trigonometry
since the height h is the same on both ends, and the extra length of the long base is 143.47, then h = x tan 68°39.2' = (143.47x) tan 72°6.0' solve for x. Now, one diagonal d is seen to be d^2 = (x+254.15)^2 + h^2 and the side s nearest that vertex is s^2 = h^... 
Math
since the ratio of weights is constant, x/7 = 18/15 
Calculus
A. The volume of a spherical cap of height h of a sphere of radius r is V = ?/3 h^2(rh) This is a known formula, but you can always verify it by finding the volume made by rotating a circular segment. For example, V = ?[h,r] ?(r^2y^2) dy B. The mass of any small disc of ... 
math
well, how much has he saved so far? 3*.50 + 4*.20 + 1*.10 = 1.50+0.80+0.10 = 2.40 so, what do you think? 
Math
all correct 
analytic geometry
you have b=6 c=8 so, a=10 and e=4/5 
calculus
yes. the height of each rectangle is the distance between the curves: xx^3 or, you can consider finding the area below y=x and then subtracting from that the area below y=x^3 
maths
the average of n numbers is the total divided by n. 
Math
f(6) = f(3*2) = 3f(2) so, 12 = 3f(2) f(2) = 4 you are correct 
maths
yes, I can do it. 
Math
just plug your numbers into the annuity future value formula, which you must have. 
Math
even integers differ by 2, right? So, if the width is w, then the length is w+2 Now just figure the perimeter and find w: 2(w + w+2) = 196 
algebra
Nope. You divided the coefficients, but you also have to subtract 3 from each power. (c) 
math
geez  impatient much? 
math
The slope of the line is (5+23)/(6+8) = 2 So, using the pointslope form of a line, y5 = 2(x6) y5 = 2x12 y = 2x7 Or, you could go through the hassle of solving 6a+b = 5 8a+b = 23 subtract to get 14a = 28 a=2 so b = 7 
algebra
1/x  6/x^2 = 12 multiply by x^2 and you have x6 = 12x^2 12x^2+x6 = 0 (3x2)(4x+3) = 0 x = 2/3 or 3/4 
Physics
The initial 25 m/s is upward The acceleration is downward: 3.7 m/s^2 The final impact speed is also downward. 25  3.7t = 75 3.7t = 100 t = 27.03 seconds 
Algebra
let x be the amount invested at 2½% Then the rest (23456.78x) was invested at 1¾% So now, just add up the interest to find x. 0.025x + 0.175(23456.78x) = 368.50 once you have x, you know the two amounts. 
maths
as always draw the diagram. If you review your basic trig functions, you will see that h (in feet) can be found using h cot43°  h cot68° = 70 
math
this is just an arithmetic sequence with a=2 d=3 So, S15 = 15/2 (2*2+14*3) If you really wanted a geometric sequence, the I assume you meant ?3^(n1) In that case, a=1 r=3 so S15 = 1*(3^151)/(31) 
math
S6 = 200(1.09^5  1)/(1.091) 
maths
impatient much? reposting after 3 minutes? 
math
#1 is indeed 30% for #2, just substitute values 1,2,3,4 for n. The terms are seen to be 2*1+3=5 2*2+3=7 2*3+3=9 2*4+3=11 
multimedian
so, what have you done so far? 
Science
The ISU provides handy names for various combinations of units. For example 1N = 1kgm/s^2 You could just as easily have used slugchains/yearweeks (a) most people would not have the slightest feel for what that means (b) you'd have to carry around that cumbersome ... 
Calc
so, assuming that you have the linear function 1+x/5 root(0.95) = root(1.05) ? 1+(.05)/5 = 1.01 = 0.99 root(1.1) = root(1+0.1) ? 1+0.1/5 = 1.02 
Calc
since ln(sqrt(u)) = 1/2 ln u y = 1/2 ln(4+t^2) dy = 1/2 * 1/(4+t^2) * 2t dt = t/(4+t^2) dt 
Calculus
Note that x=4siny and you want the area "above" the curve a = ?[0,pi/2] 44siny dy = 4y+4cosy [0,pi/2] = 2pi4 
Maths
ok. now what? 
Calculus
f(0)=0 f(9)=0 So, that satisfies the theorem f is continuous and differentiable. So, we just have to find c such that f'(c)=0 f'(x) = 1/(2?x)  1/9 1/(2?c)  1/9 = 0 1/(2?c) = 1/9 2?c = 9 c = 81/4 which is in [0,81] 
Science
could be the same, if the mug is the same metal. Otherwise, they will probably be different. 
math
come on  just add them up. S1 = 9 S2 = 9+12 = 21 ... 
Calculus
clearly you must have meant C(t)=15t/(80+t) which > 15 I am troubled by the fact that the equation for C(t) does not reflect the data given in the words. Also, at some point the tank will overflow, so having t unbounded is not realistic. 
Calculus
come on  this is Algebra II How far do you get? 
Calculus
clearly, after 1 hour, the population has increased by 6000 
Calculus
geometrically the argument makes sense. But algebraically, ?[a,b] f(x) dx = ?[b,a] f(x) dx 
Math
you know that log_3(3)=1 so, log_3(x)+c = 1+c when x=3