Answers by visitors named: oobleck
Huh
6 years ago
this might be a good place to start. google is your friend. https://web2.0calc.com/questions/find-all-integers-x-for-which-there-exists-an-integer-y-such-that-1-x-1-y-1-7-in-other-words-find-all-ordered-pairs-of-integers-x-y-that
6 years ago
x += 1 x *= 2 x -= 1 and lots of others
6 years ago
aa
6 years ago
aaa
6 years ago
First, check for any local maxima within the interval. f'(x) = 2x, which is zero at x=0. But x=0 is not in the domain. So, except for the hole there, f(x) = x^2-3, so the limit as x->0 is -3 f(-4) = 16-3 = 13 f(3) = 9-3 = 6 So, the absolute maximum of f(x...
6 years ago
they still had to sell at least 175 glasses, at 25 per hr, meaning they needed at least another 175/25 = 7 hours to make their goal.
6 years ago
since they double every month, that means you multiply by 2 for each month. So, after m months, the population will be p(m) = 4*2^m Since a year has 12 months, in 2 years there will be 4*2^24 = 67,108,864 I hope you have (a) a huge yard (b) lots of lettuc...
6 years ago
For s" I get (3t(t^3+4)) / (4(t^3+1)^(3/2)) so, s"(2) = 2/3
6 years ago
I don't think so. Consider the numbers 36 and 37
6 years ago
I'd say go with the highest yield. Was there something in particular you wanted to ascertain?
6 years ago
??? My google search resulted in many such sample tests. Maybe not all are suited to young teens, but it's a start: https://www.google.com/search?client=firefox-b-1&q=free+sample+Cognitive+Abilities+and+Achievements+Tests.
6 years ago
hmmm. hard to say what you want, but (4.5,60°) translates to 4.5cis60° = 4.5*√3/2 + 4.5*1/2 i = 3.90+2.25i
6 years ago
since volume = basearea * height, V = 750m^2 * 1.5m = 1125 m^3
6 years ago
since T = 2π√(L/g), g = (4π^2L)/T^2 the ratio of g1/g2 = (4π^2L1)/(T1^2) / (4π^2L2)/T2^2 = (4L)/(6T)^2 / (3L)/(2T)^2 = (4/36) / (3/4) = 1/9 * 4/3 = 4/27
6 years ago
well, 196 = 14^2 and 4 = 2^2 so, √(196*4) = √196 * √4 = 14*2 = 28
6 years ago
so, log 2x = 4/3 2x = 10^(4/3) x = 1/2 * 10^(4/3) = 5∛10
6 years ago
42 = 7*6 so, 7:9 = 7*6 : 9*6 = 42:54
6 years ago
Note that if you have sin(kx-b) that gives you little information about the phase shift. You will need to plot a bunch of points to see the graph. But, if you write that as sin( k(x-b/k) ) you can see immediately that the shift is (b/k) to the right. You...
6 years ago
If so, then you know that x + (1 3/5)x + (1 2/3)x = 24 Now, 1 3/5 + 1 2/3 = 8/5 + 5/3 = 24/15 + 25/15 = 49/15 so, now you know that x + 49/15 x = 24 64/15 x = 24 x = 24 * 15/64 = 45/8 = 5 5/8 hours
6 years ago
The constant difference is obviously 6. So, you expect something close to f(n) = 6n. 6*1 = 6, but f(1) = -2, which is 6-8 So, f(n) = 6n-8
6 years ago
Okay, for x pkgs of low-grade nuts, he needs 8x lbs of peanuts and 4x lbs of cashews. For y pkgs of high-grade nuts, he needs 6x lbs of peanuts and 6x lbs of cashews. That means that we need 8x+6y <= 100 4x+6y <= 80 Assume we use all the available nuts. T...
6 years ago
Huh? They give you the value of x. I read this as meaning when x=0 you want the average rate of change of f(x) between x=0 and x=2 f(x) = 0.4^x so f(0) = 0.4^0 = 1 f(2) = 0.4^2 = 0.16 so the average rate of change is (0.16-1)/(2-0) = -0.42 That is the slo...
6 years ago
Or you can just plot both lines, and any lattice points (with positive integer coordinates) in the shaded region will be solutions. https://www.wolframalpha.com/input/?i=solve+8x%2B6y+%3C%3D+100,+4x%2B6y+%3C%3D+80+over+the+positive+integers
6 years ago
If both nc5 and nc5 are in the sequence, then d=0. I shall assume a typo, and that you meant nc6. So, now you have nc5 - nc4 = nc6 - nc5 Expanding this out gives you a 5th-degree polynomial equation (n-14)(n-7)(n-3)(n-2)(n-1) = 0 Since n has to be at leas...
6 years ago
PE = mgh I assume you want the KE at the end of the fall. It will, of course, be equal to the PE at the start. Otherwise, not sure what (2) means.
6 years ago
that depends on how long it accelerates. Just note that v = at
6 years ago
suppose you have two points on a graph. The average rate of change between those two points is the slope of the line joining them. So, for example, if f(x) = x^2, then the average rate of change of f(x) on the interval [1,3] is ∆y/∆x = [f(3)-f(1)]/(3-1) =...
6 years ago
The final is 11%, so the rest make up 89% Without knowing how many grades you have so far, it's hard to say how the 56 will affect the total points available. So, let's say you have an average of 68 on 5 quizzes. That means your score of 56 will change th...
6 years ago
check out the reflexive property of congruence
6 years ago
note that you can rewrite the 1st line as 5x+6y = 24 how does that relate to the 2nd equation?
6 years ago
You surely know that the graph of y=|x| is a V shape with the point of the V at (0,0) So, what do you have to do to it to get to your rule?
6 years ago
If you add x, then you need 3/16 + x > 1/2 3/16 + x > 8/16 x > 5/16 Note that the question should have specified "at least" 1/2, rather than "greater than" 45 is between 36 and 49, so √45 is between √36 and √49
6 years ago
well, your posting is rather confusing. If he bought them at 9 for 9.60 and sold them at 11 for 12.00 then his unit cost is 9.60/9 = 1.0667 his unit revenue is 12/11 = 1.0909 1.0909/1.0667 = 1.0226 = 2.26% profit If I read the facts wrong, fix things and...
6 years ago
#1 ok #2 If they are proportional, then you need 80/96 = 77/84 Thus, you need 80*84 = 77*96, clearly false or, since 80/96 = 5/6 = 0.833 and 77/84 = 11/12 = 0.916 they are not equal #3 increased by a factor of 1 1/2 means you multiply by 1 1/2 3 1/4 * 1 1...
6 years ago
Assuming the $10/day rate holds even for a half-day trip, (10 + 15*10)/10 = $16/person if there are 10 people in the family If n people ride for the flat rate, then 100/n < 16 6.25 < n So, it's cheaper for 7 or more to pay the flat rate
6 years ago
well, one is 5(2a-5+b)
6 years ago
actually, you mean the circumference is divided into n equal parts. The triangles are isosceles, with the equal sides being r, and the vertex angle 2π/n Thus, b = 2r*sin(π/n) and h = r*cos(π/n) The area of each triangle is thus r^2/2 sin(2π/n) So, the app...
6 years ago
sigh you want the limit of nr^2/2 sin(2π/n) Now, you know that sinx/x -> 1, so you need to massage your expression so it looks like that nr^2 sin(2π/n) / 2 = r^2 sin(2π/n) / (2/n) = πr^2 sin(2π/n)/(2π/n) Now, if you let x = 2π/n, you have πr^2 sinx/x as n...
6 years ago
nothing hard here. As with all y=ax^2+bx+c, the vertex (max height) is at (-b/2a, c - b^2/4a) and you can use the quadratic formula to solve for the roots (when the height is zero)
6 years ago
the carrier's speed is 3/2 that of the container ship. So, if the container ship's speed is x, then 3/2 x = x + 5 x = 10 As for your attempt, since time = distance/speed, you should have said 450/(x+5) = 300/x again, x=10 Dividing by v both times was wron...
6 years ago
or, if that's too opaque, (1/2)^(10/2) = 1/32
6 years ago
Your use of upper- and lower-case X and weird symbols, combined with the lack of parentheses makes things very confusing and ambiguous. Now, even though the formatting is garbled, you seem to be doing things right, till the last line, where you had 2x/5+3...
6 years ago
(x,y) -> (x+1,y+3)
6 years ago
4/3 log125 = log625
6 years ago
If the two squares are x and y, then xy = 45 x^2 + y^2 = 106 so, x^2 + (45/x)^2 = 106 x^2 + 2025/x^2 = 106 x^4 - 106x^2 + 2025 = 0 (x^2-25)(x^2-81) = 0 x^2 = 25 or 81 x = 5 or 9 yep, 5*9 = 45
6 years ago
If the high power pump can fill it in x hours, then the slower pump takes x+5 hours. So, we have 1/x + 1/(x+5) = (1/2)/3 x = 10
6 years ago
An "equilateral" trapezoid is a square. So, I assume you mean an isosceles trapezoid. Using the 30° angle, we know that since point A is (-1,0) and D is (5,0), point B is (-1+2√3,2) point C is (5-2√3,2) But that cannot be, since the axis of symmetry is at...
6 years ago
recall how to change base of logs. 8 ^((ln 10) / (ln 2) ) = 8^log<sub><sub>2</sub></sub>10 = (2^3)^<sub><sub>2</sub></sub>10 = 2^(<sub><sub>2</sub></sub>10)^3 But, 2^<sub><sub>2</sub></sub>10 = 10 so, it's still 10^3
6 years ago
E' is everything in U that is not in E. So, which odd numbers in U are you missing?
6 years ago
hmmm. do you know what determines the atomic number? then, protons+neutrons=55, so if you have the protons, getting the neutrons is easy ... right?
6 years ago
you know that y = a(x-3)^2 - 12 so, now just find a by solving a(0-3)^2 - 12 = 6
6 years ago
suppose y = ax^3+bx^2+cx+d so, y" = 6ax+2b you know that y"(0) = 0 so, b=0 y" = 6ax since y(2) is a maximum, y"(2) < 0, so a<0 y' = m(x-2)(x+2) = m(x^2-4) = 3ax^2+c y'(2)=y'(-2)=0, so 12a+c = 0 c = -12a so, y = ax^3-12ax+d so, let's try some value for a,...
6 years ago
using your numbers, we have b = 6400+800 = 7200 a = 6400+5400 = 11800 So, just plug that into the standard equation for an ellipse, with center at (0,0)
6 years ago
For the ellipse, you can see that a = 50/2 = 25 b = 20 So, put that into standard form, then find 2x when y=10
6 years ago
so, you just gonna sit on your hands, or try to see where I went wrong, and use some ideas of your own?
6 years ago
staying with parametric functions makes it hard. So, let r^2 = x^2+y^2 tanθ = y/x z = r^2 tan^2θ = (x^2+y^2)(y^2/x^2) = y^2 + y^4/x^2 ∂z/∂x = -2y^4/x^3 ∂z/∂y = 2y + 4y^3/x^2 ∂^2z/∂x∂y = ∂^2z/∂y∂x = -8y^3/x^3 = -8tan^3θ
6 years ago
note that angle ZXY is a right angle. (a) |YZ| = 100 (b) from Y, ∆y/∆x = (-20/√2)/(-140/√2) = 1/7 the reference angle is 8.13° So, referring to your diagram, the bearing of Z from Y is 270-8.13 = 261.87°
6 years ago
sure looks to me like y=7x so, which choice would that be?
6 years ago
Not quite. You want (x,y) -> (x,-y) A’(1, -4) B’(3, 2) C’(4, -2) you did (mostly) a reflection over the y-axis.
6 years ago
Since y' = 1 for x <= 0 y' = 2 for x>0 y' is not continuous at x=9. So, y is not differentiable there. Whenever you have a cusp or point on a graph, the function is not differentiable there. Better reread the definition of differentiable.
6 years ago
for which fractions is the bottom less than 2x the top?
6 years ago
change all to % and then it will be easy to compare them
6 years ago
you want a line with slope -1/5 so, using the point-slope form, y-2 = -1/5 (x-10)
6 years ago
Seems to me that k(x) = (5x^4 + 2)(3sin x) k' = (20x^3)(3sinx) + (5x^4+2)(3cosx) = 15x^3(4sinx + xcosx) + 6cosx
6 years ago
It appears you cannot tell the difference between one(1) and L(l). I assume you meant ln 2 + ln x = 5 recall that lna+lnb = ln(ab). So, ln(2x) = 5 2x = e^5 x = e^5 / 2
6 years ago
Just FYI, which may come in handy, the y-coordinate of the vertex is (4ac-b^2)/(4a) or c - b^2/(4a)
6 years ago
Looks good to me.
6 years ago
KG = KH ..... HL-KL = GJ-KJ (subtraction of equals) m∠GKL = m∠HKJ ......... vertical angles ∆GKL ≅ ∆HKJ .......... SAS m∠GLJ = m∠HJL ............. CPCTC
6 years ago
Not unless it was there to start with.
6 years ago
7 days/week means 56/7 = 8 lbs bananas each day So, they use 10-8 = 2 lbs more apples than bananas each day. So, what do you think?
6 years ago
.96 Vi = 60 Vi = 62.5 so, the loss was 2.5 hp
6 years ago
(1) SinB+Sin²B sinB(1+sinB) = 0 so, sinB = 0 or -1 which angles fit that? (2) (2CosA+1)(1-CosA)=0 cosA = 1 or -1/2 (3) 2Sin²A-SinA-1=0 (2sinA+1)(sinA-1) 0 see #2 (4) 4Cos²A+2CosA=1 (2cosA+1)^2 = 0 cosA = -1/2 ... (5) 1+CosB/2-CosB=1 1+cosB = 2-cosB 2cosB...
6 years ago
well, just divide 560 into 7 equal parts. hint: "divide" is the key word here, right?
6 years ago
9 4/5 = 9 8/10 = 98/10 8 1/2 = 8 5/10 = 85/10 Now you can add them easily, right?
6 years ago
if any two pairs have the same 1st element, it is not a function domain is the set of 1st elements, range, of the 2nd continuous if defined over an interval, otherwise discrete. so, whaddaya think?
6 years ago
y-intercept is the initial account balance (time=0) x-intercept is how long it takes to empty the account (money=0)
6 years ago
No. two pairs start with zero. f(0) cannot be both 1 and 6. stop guessing.
6 years ago
All your are belong to us...
6 years ago
have you looked up any of the words? In these days of google translate, it's very easy to check on the meaning of a word. If you'll spend about 1 minute with google, you will be able to answer this question easily. Hint: la cocina is the kitchen.
6 years ago
so, she stocks 9 bags per hour. So, a good first guess would be f(x) = 9x But she started with 7 bags, so how do you think that changes the function?
6 years ago
your answer is correct, but I'm not sure about your logic. "wouldn't subtract from the equation" ? It's f(x) = 9x+7 because if it were just f(x) = 9x then f(0) would be 9*0 = 0 But, there were 7 bags to start with (x=0), so that means f(x) = 9x+7
6 years ago
the product with the lowest unit rate is presumably the best buy. So, just compare 1.10/810 1.38/12 0.84/6 I suspect a typo for the 810-oz product ... Probably just 10, right?
6 years ago
unit rate is mi/hr. You have miles and hours, so just divide 1269mi/3hr = ? mi/hr
6 years ago
It is an equation. To find its solution, 1+5*99-10+a=100000 1+495-10+a = 100000 496-10+a = 100000 486+a = 100000 a = 99514
6 years ago
Let x = # large mugs sold y = # small mugs sold so, what have they told you? Total income: 2.50x + 5.75y = 56.00 mugs sold = 200-188 = 12. So, x+y = 12 Now just solve for x and y
6 years ago
The symmetric one looks a bit off. You need an equation for z, but there's nothing to compare it to. Maybe in this case (only one nonzero deb=nominator) there is no symmetric form. See what google has to say.
6 years ago
half as many men, so twice as much time
6 years ago
clearly not a function, since f(0) cannot be both 0 and -4 thanks for waiting, though.
6 years ago
this just a line, with slope=20 so, if x grows by 6, c(x) must grow by 20*6=120
6 years ago
sorry we don't sit around waiting for your next question... a) The most commonly used graphs are linear, power, quadratic, polynomial, rational, exponential, logarithmic, and sinusoidal. Yours is none of these types. b) whenever you see a function describ...
6 years ago
remember to use the product rule and the chain rule y = 5e^(5x^2) y' = 5(e^(5x^2)*10x) = 50xe^(5x^2) now using the product rule, and recalling that x'=1 y" = 50[e^(5x^2) + xe^(5x^2)*10x] = 50((1+10x^2)e^(5x^2)) is the same as your answer
6 years ago
s(t)=cost-16t^2 v(t) = s'(t) = -sint-32t a(t) = v'(t) = -cost-32 now plug in t=0
6 years ago
a(t) = v'(t) If v has a max or min, its derivative is zero, right?
6 years ago
so, yesterday he walked 15 minutes 30 is 100% more than 15 So none of the choices is correct. His total walking time for the two days: 45 minutes is 50% more than today's time (30 min), making it 150% as much I suspect a typo somewhere in the question.
6 years ago
neither, since 1/-3 (- 1/3) ≠ -1/-3 (+ 1/3) and (1/-3)(-1/-3) = -1/9 ≠ -1 Nice try. two lines can clearly NOT be both perpendicular and parallel!
6 years ago
parallel lines have the same slopes Two slopes m1 and m2 belong to perpendicular lines only if m1 * m2 = -1 So, if you calculated your slopes correctly, the two lines are neither parallel nor perpendicular. That means the two lines intersect at exactly on...
6 years ago
surely you can evaluate the functions at t=0: 1a)y=250(1+0.2)^t at t=0: 250(1.02)^0 = 250 2b) y=9.8(1.35)^t at t=0: 9.8(1.35)^0 = 9.8 For the special triangles, consult your text. These come up very often, so learn them and love them! Just do it. It will...
6 years ago
Well, if the notebooks cost x, then you know that 3x + 45.87 = 60.54 right? so, solve for x.
6 years ago
I disagree vehemently. The programming interprets the binary data.
6 years ago