Saturday
February 28, 2015

Posts by STEVE


Total # Posts: 29,289

calculus
(If the base has side x and the box has height h, the area 2x^2 + 4xh = 600, h = (300-x^2)/2x So, the volume v = x^2 h = 150x - x^3/2 dv/dx = 150 - 3/2 x^2 So, dv/dx=0 when x^2 = 100 I think you can take it from there, ok?
January 19, 2015

math
just start writing down the facts as math. n = 2d+2 eight fewer quarters than twice the number of nickels q = 2n-8 value of the quarters was $1.60 more than four times the value of the nickels and dimes together 25q = 4(10d+5n)+160 Putting all that together, we have n = 2d+2 q...
January 19, 2015

AP Calc
well, it's clear that f(x) = x^2-3x+c and you know that f(2) = 5, so just find c.
January 19, 2015

Geometery
you just have to remember that the angles of a triangle add up to 180 degrees. So, with angles M+P+N = 180 x + 2x-1 + 2x+1 = 180 Now it's easy to find x, the evaluate the actual angle measures.
January 19, 2015

Calculus
dv/dt = pi r^2 dh/dt just plug in your numbers to find dh/dt
January 19, 2015

grade 7 math
by 3:00, the tug has traveled upstream 3*15 = 45 km, so it is now 20 km upstream from B. The boats' relative speed is 35 km/hr, so how long does it take the foil to make up the 20 km head start of the tug? Add that time to 3:00.
January 19, 2015

grade 7 math
Melvin travels 30 km/hr faster than Jessie. So, how long does it take to cover extra 15 km?
January 19, 2015

Calculus
first, it's "bacteria are" growing. You are told that the for a population p of these bacteria, dp/dt = kp so, that means that dp/p = k dt ln p = kt + c p(t) = c e^(kt) p(0) = c = 50 So, p(t) = 50e^(kt) p(1) = 200, so 50e^k = 200 k = ln 4 p(t) = 50e^(ln4 t) Or, ...
January 19, 2015

math
just plug the coordinates into your rotation matrix Rx: 1 0 0 0 cosθ -sinθ 0 sinθ cosθ A' = Rx * AT and so on
January 19, 2015

math
as usual, just recall that distance = speed * time Now just plug in your numbers...
January 19, 2015

Math
(2+5i)+(-2-4i) 2+5i-2-4i 2-2 + (5-4)i 0+i You can omit the 0+ and write is as just i, but if you want to make it clear that you are in fact working with a complex number, the standard form a+bi is used. Although, just the presence of "i" itself makes it evident that ...
January 18, 2015

math
You want 40/2 (2a+39d) where 12/2 (2a+11d) = 186 a+19d = 83 Just solve those last two for a and d, then plug them into the first formula.
January 18, 2015

Algebra
If y = x^3-2 y+2 = x^3 x = ∛(y+2) That means that ∛(x+2) is the inverse of x^3-2 To check, you know that f(f-1(x)) = x and f-1(f(x)) = x So, if g(x) = f-1(x), f(g) = g^3-2 = (∛(x+2))^3 - 2 = x+2-2 = x and the same for g(f).
January 18, 2015

Math
all look correct to me.
January 18, 2015

Calc
the distance d is found using d^2 = x^2 + (y+3)^2 Since x = -y^2, that means d^2 = y^4 + (y+3)^2 Now all you do is find dd/dy = 0 and that is where the distance is minimum. Then evaluate x = -y^2 and you have your point.
January 18, 2015

maths
2/5 * 1/2 = 1/5 1/3 * 3/4 = 1/4 1/4 is 25% more than 1/5
January 18, 2015

Physical Science
good question. Find the chemical formula for the sweetener, divide the mass of the package by the molecular mass of the formula, and multiply by Avogadro's Number. If that's all gobbledegook to you, then clearly you haven't been presented with the means to do the ...
January 18, 2015

physics
since v = at, clearly it is 1.1i + 0.56*4.8j
January 18, 2015

Math
No idea what a pattern of 1,3,5 means. You do know that y = a(x+4)^2 + 5 It opens up, so a > 0. Use that with the weird pattern data to finish it off.
January 18, 2015

Math
4+5+6+7+9 = 31 So, the new sum will be between 34 and 41 Divide both of those by 6 and match it up with the choices.
January 18, 2015

Math
I think you can easily fill in the first two. Simple multiplication and division, right? (g◦(h◦f))(-4) = g(h(f(-4))) = g(h(-2)) = g(9) = -33 Note that h(x) = (x-1)^2. So, f(h(a+4)) = f((a+4-1)^2)) = f((a+3)^2) = (a+3)^2+2 You can expand that if you want.
January 18, 2015

Physics
just plug your numbers into y = tanθ x - g/(2(v cosθ)^2) x^2 and solve for x when y = -125
January 18, 2015

algebra
64+35-14 = 86 So, two buses can hold the lot. Even chaperones! (A ∪ B) = {6,7,8,9,10,11} So, (A ∪ B) ∩ C = {8,10}
January 18, 2015

algebra
just recall the rule that total = one + other - both. So, counting just the ones taking something, you have 20+32-6 = 46 So, the other 4 took nothing.
January 18, 2015

Mathematics arithmetic sequence
a+d + a+5d = 4 a+2d = a+10d + 24 Collect terms and solve for a and d. Then write a,a+d,a+2d
January 18, 2015

Algebra 1a
just add the exponents. x^2 = xx x^3 = xxx x^4 = xxxx So, adding the exponents just means counting how many times you have x multiplied together.
January 18, 2015

Algebra 1a
(xy)^-3 = 1/(x^3y^3) (x^-5y)^3 = x^-15y^3 = y^3/x^15 So, you have 1/(x^3y^3) / (y^3/x^15) = 1/(x^3y^3) * x^15/y^3 = x^15/(x^3y^3y^3) = x^15/(x^3y^6) = x^12/y^6
January 18, 2015

Physics
#1 is correct
January 18, 2015

Algebra
√(48a^2b^7) recall that √x^2 = x, so factor out all the perfect squares: √(16*3*a^2*b^6*b) √(16a^2b^6)√(3b) 4ab^3 √3b
January 18, 2015

Math Homework Help
I think that's just sec^2 y - 1, which is tan^2 y cot^2 y * tan^2 y = 1
January 18, 2015

geometry
since angles E and F are congruent, the sides opposite them (DF and DE) are congruent. That means that 4x-6 = 2x+8 x = 7 Now you can figure the perimeter.
January 18, 2015

chemistry
Lothium Iodide?
January 18, 2015

geometry
you know how to find the area of a square, right? So, consider that the sides of the entire area are 12 feet longer than those of the playground. Subtract the area of the playground from the entire area.
January 18, 2015

physics
1/√2i - 1/√2j
January 18, 2015

physics
v = dy/dt = b - 2ct now just solve for t when v=0
January 18, 2015

math
x(1-2/5)(1-1/3) = 56 x = 140 check spent 2/5 of 140 = 56, leaving 84 spent 1/3 of 84 = 28, leaving 56
January 18, 2015

addmath A.P.
clearly the lengths of the sides are sequential integers, starting with x. The sum of the perimeters is thus 4(10x + 9*10/2) = 40x+180 = 380 ...
January 18, 2015

Algebra
(f o g)(x) = f(g(x)) g(-6) = 1 f(-1) does not exist (fog)(-18) nope (fog)(-14) nope (fog)(-2) nope For no value does fog exist (gof)(-4) = 9 (gof)(0) = 1 (gof)(-6) = 13 (gof)(2) = -3 So, the domain of gof is the domain of f.
January 17, 2015

calculus
we have x^2+y^2 = 225 2x dx/dt + 2y dy/dt = 0 Now plug in x=9, y=12, dy/dt=-1/3
January 17, 2015

calculus
oh, well, you really want it all, eh? The very first one (calculus honor) has slightly different numbers, but it is exactly the same problem. Follow the solution, using your numbers.
January 17, 2015

calculus
Damon did this. Look at the related questions below.
January 17, 2015

algebra - obfuscation
pretty confusing, especially where it says mary was six years before the time when . . . Not sure what that is intended to mean.
January 17, 2015

Composite Functions
Hmmm. (g*f)(x) = g(x)*f(x) = √(x-15)(x^2-2x) The composite function (g◦f)(x) = g(f(x)) = √(f-15) = √(x^2-2x-15) Your factoring is correct, but I see no advantage to it. It ought also to be written as √((x-5)(x+3)) to avoid confusion with √(x...
January 17, 2015

AP Calc (Limits on Piecewise Functions) #2
well, geez, these are common enough angles . . . the left limit is sin π/3 = √3/2 the right limit is (π√3)/(2π) = √3/2 Looks like f(x) is continuous
January 17, 2015

Algebra 2 - typo
Go with Reiny on #3. I made a typo in my (x-3) factor.
January 17, 2015

Algebra 2
In general, it is very difficult to find zeros of polynomials higher than degree 2. So, you have to look for some low-hanging fruit using synthetic division, or try grouping. Graphical methods may also be useful, if it's obvious that the roots are easy ones. I usually ...
January 17, 2015

Physical science
when they are acting in the same direction.
January 17, 2015

geometry
ok. now what?
January 17, 2015

math
everything appears ok down to the last part. 4"/mo for 9 months is 36". Since the average annual amount is 43.2", those 9 months did not exceed the annual average. This is to be expected, since the monthly amount was only a little bit more than the usual monthly...
January 17, 2015

AP Calc (Limits on Piecewise Functions)
left limit is 1/2 f(pi/6) = 1/√3 right limit is √3/2 So, not only are the left and right limits different, but even if they were the same, f(x) is defined to be something else at x=pi/6!
January 17, 2015

Algebra 1
Write a scientific notation for .0042 My answer is 4.2 10^-3
January 17, 2015

7th grade math
You are correct. The total cost is $22.68
January 16, 2015

A big thank you to Ms.Sue☺
I assume this is relevant to the above topic because we might want to buy stock in such companies? . . .
January 16, 2015

speed
you want t where 9000t = 10000(t-0.25) Then plug that value for t into either side of the equation. Just recall that distance = speed * time
January 16, 2015

Algebra 1
Simplify mn^-4/p^0 q^-2 My answer is mq^2/n^4
January 16, 2015

Geometry
Take a look here: http://www.algebra.com/algebra/homework/Geometry-proofs/Geometry_proofs.faq.question.392003.html
January 16, 2015

Algebra 1
correct
January 16, 2015

Algebra 1
Simplify 5^-1(3^-2) My answer is 1/45
January 16, 2015

meeting and chasing problem
it takes Amy 1/3 hr to get to the store. Another hour passes. During that time, Beth has walked 1+3 = 4 miles. So, the two must cover 26 miles at a combined rate of 30+3=33 mi/hr. That takes 26/33 hours. During that time, Beth has walked another 26/33*3 = 26/11 miles. So, they...
January 16, 2015

Math
it took Sally 2 hours to go 180 km. That's 90 km/hr. If Kelley traveled at 80 km/hr, it would take her 2.25 hr. So, she would arrive at 10:45 am
January 16, 2015

Math
No. The temperature really makes no difference. What you want is 1088 = 0.2204 x where x is the speed of sound in cold water.
January 16, 2015

math
1-digit: none 2-digit: 1 (21) 3-digit: 10 (201 ,,, 291) 4-digit: 1 (2001) So, 12 in all.
January 16, 2015

Math
cylinder: πr^2h = 1200 cone: 1/3 πr^2h = 1/3 (1200) = 400
January 16, 2015

math - I'm outta here.
Ignore that post. It added the window and door, rather than subtracting them. Also, you started out by saying the walls were 8' high. What's the 5x7 foot stuff? And we STILL don't know how wide the walls are!!!!
January 16, 2015

math
Boy, you're not willing to put anything into this, are you? so, the painted area is (converting the door and window to feet, rather than inches): 4(5*7) + 7*3 + 2*3 = 167 ft^2 So, how many cans will it take, at 100 ft^2 per can?
January 16, 2015

math - still incomplete
so, the walls are 8' high. How wide are they? Are they all 4 the same width? If not, can we assume the room is rectangular? At any rate, you surely know that for a rectangle, the area is height x width. So, add up the areas for all the walls, then subtract the areas of the...
January 16, 2015

Math
each large tile covers 3x3 = 9 small tiles. So, what do you think?
January 16, 2015

algebra2
any value of y which makes the denominator zero is excluded. So, what is y when y+4 = 0?
January 16, 2015

calculus
one
January 16, 2015

algebra
since you cannot divide by zero, any value of b which makes b-2 = 0 is excluded.
January 16, 2015

calculus
s = 4π r^2 ds/dr = 4π(2r) = 8πr
January 16, 2015

trigonometry
review your basic trig function definitions. Draw a diagram, and you will see that the line-of-sight distance x is given by 800/x = sin 12° The distance along the ground is given by 800/x = tan 12° Pick your case, and just solve for x.
January 16, 2015

trigo
If the angle is x, then tan x = 50/60
January 16, 2015

Coeakwanga
well, just plug in the numbers in your formula: An = 2+2n
January 16, 2015

Math, Quadratic Functions
2(x+y)=80, so y = 40-x area = xy = x(40-x) = 40x-x^2 That's just a parabola. Find the vertex and you will have the maximum area. A little investigation that the rectangular shape of maximum area for a given perimeter is always a square.
January 16, 2015

calculus
y = 8/x y' = -8/x^2 now plug in x = -3 the avg rate of change is change in y ------------------ change in x So, that would be (y(4)-y(-3))/(4-(-3)) Now just plug in the numbers
January 16, 2015

calculus
study any proof of the MVT or Rolle's Theorem for the first one. For the 2nd one, since f satisfies the conditions of the MVT, and is concave down over the whole interval, there is but one number c in the interval.
January 16, 2015

MATH
h(t) = 149 - 59cos(2pi t) all your answers are correct
January 16, 2015

Pre-Calc
s = rθ, so 1*θ = 10 θ = 10 radians
January 16, 2015

science
work = force * distance no distance, no work.
January 16, 2015

Circles
w00t!
January 15, 2015

Math
F=ma So, since a on earth is 9.8, on earth he weighs 60*9.8 N on the moon, he weighs 60*1.6 N
January 15, 2015

Math
A to B: Since the scale does not change, 60/(3/4) = x/(4 5/8) 60*4/3 = x * 37/8 x = 60 * 4/3 * 8/37 Do the other parts the same way. Remember that the scale does not change! If a distance is twice a big on the map, it is twice as big in the world.
January 15, 2015

math
$7 is 1/6 of 3/7 of Bella's money, so she had $98 to start with. 4/7 of 98 is $56, as you figured. The dictionary and the books cost 56 d+3b = 56 3/8 d = 1/2 * 3b so, 3d = 12b 4b + 3b = 56 b = 8 check: 3 books cost 24 dictionary cost 32 3/8(32) = 1/2(24) 12=12
January 15, 2015

Math
have you no calculator? If not, just type 1221/3 into google's entry box, and it will do the calculation for you. The answer is 407. If you go to http://www.webmath.com/divide.html and enter you numbers, it will show how the division is done.
January 15, 2015

math
180 = 5/8 x
January 15, 2015

math
could be any of those. What haven't you told us?
January 15, 2015

Math
.70 * 185 = ?
January 15, 2015

Math
right. x+y=7 that counts the coins. Now you have to count the value. If you have x nickels and y quarters, then 5x+25y = 95 Now, you can insert your first equation into this one as follows: 5x+5y+20y = 95 5(x+y)+20y = 95 5(7)+20y = 95 35+20y = 95 20y = 60 y=3 so, x=4 That is ...
January 15, 2015

geometry - bogus?
I don't see how you can say that LM ≅ TU, and then say that LM=15 and TU=10. Also, when you say LMN ~ TUV that implies that the vertices are listed in the same respective order. That is, LM ~ TU MN ~ UV NL ~ VT But that's not the case here.
January 15, 2015

Math
32+56 = 8(4+7)
January 15, 2015

math
what you really need is to think about the problem. By 12:30, car A had been traveling 1/2 hr at 50 mph. SO, it had gone 25 miles. At 3:PM, both cars had been traveling an additional 2.5 hours, so Carter had gone another 2.5*50 = 125 miles. Carter's total distance is thus ...
January 15, 2015

Math
7*9+7 = 63+7 = 70
January 15, 2015

Math
that is correct, but to follow the advice given, you should have taken the following step: 43+9 = j-9+9 That gets rid of the 9 from one side and leaves j all alone: 52 = j That is the result you wanted, not just rewriting it with the solution inserted. When it says to solve ...
January 15, 2015

Math
8000(1+0.11/2)^(2*8) = ?
January 15, 2015

math
a = (5-2x)(3-2x) a = 12
January 15, 2015

Math
just set 4x = 2x^2 4 = 2x x = 2
January 15, 2015

Math - oops
y(-1) = -2
January 15, 2015

Math
you ever gonna show any of your work? you want the slope of the line (-2) to be the same as the slope of the parabola. The slope of the parabola at any point (x,y) is 6x+4 So, if 6x+4 = -2, x = -1 y(-1) = 6, so the line y = -2x+b must pass through (-1,-2) I think now you can ...
January 15, 2015

Math
downstream speed: 10/(1/2) = 20 mi/hr upstream speed : 10/(5/6) = 12 mi/hr So, if te boat's speed is b and the current's speed is c, b+c=20 b-c=12 now go figure c
January 15, 2015

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