# oobleck

Newest questions and responses by oobleck-
## Mathematics

The exterior angle at B (CBD) is the sum of the other two interior angles at A and C. The two angles at B (CBD and CBA) form a linear pair. Looks like you need to review the section on triangles.

*posted on March 23, 2019* -
## Mathematics

that is correct. The external angle is the sum of the other two interior angles. The two angles at B form a linear pair.

*posted on March 23, 2019* -
## Math

do you read what I write? 2 inches of sand is 1/6 foot!

*posted on March 23, 2019* -
## Math

if all dimensions are in feet, the height of sand is 1/6 foot So the volume is 36*20/6 = 120 ft^3

*posted on March 23, 2019* -
## Calculus

[3,13] has a span of 10 with 4 rectangles, each has width 2.5 So the distance is 2.5(f(5.5)+f(8)+f(10.5)+f(13)) You don't give the table, so if the given data points are unevenly spaced, that will have to be changed some.

*posted on March 23, 2019* -
## Calculus

just put everything over a common denominator: A/x + B/(x-2)+ C/(x+2) = (A(x^2-4) + B(x^2+2x) + C(x^2-2x))/(x(x-2)(x+2)) Now you want that to be identical to (x^2+12x+12)/(x(x-2)(x+2)) That means that A(x^2-4) + B(x^2+2x) + C(x^2-2x) = x^2+12x+12

*posted on March 22, 2019* -
## Calculus

for large x, √(x+1) ≈ √x √(10x+1) ≈ √10 √x so, what do you think?

*posted on March 22, 2019* -
## Calculus

I think D Unless it's just logx/x or something where the denominator is the derivative of the numerator (so it is just p(u) du with p a polynomial) it will not succumb using elementary functions.

*posted on March 22, 2019* -
## math

the vertex form y = a(x-h)^2 + k The vertex (max or min) is at (h,k)

*posted on March 22, 2019* -
## Maths

that would be the same as -cos45 + sin15 = -1/√2 + (√3-1)/2√2 = (-2+√3-1)/(2√2) = 1/2 (√3-3)/√2 = 1/4 (√6-3√2)

*posted on March 22, 2019* -
## math

why do you have two x terms?

*posted on March 22, 2019* -
## algebra

If the length is x, then x^2 + 15^2 = 27^2 right?

*posted on March 22, 2019* -
## Maths

I think you're stuck using some kind of numeric or series method. If a is anything other than pi/2 (so the integrand is just x/(1+sinx)) it does not have a solution in elementary functions. Mosey on over to

*posted on March 22, 2019* -
## Math

The characteristic polynomial is just x^5-5x^3+5x^2+5x-6 So, solve that to get the exponentials. There are 3 real roots and 2 complex roots, so there will be 3 terms involving e^kx and two with sin kx and cos kx Review your section on homogeneous DEs and

*posted on March 22, 2019* -
## math

the prism has two triangular faces and three rectangular sides. Since you do not provide any information on which dimensions are for the triangle, I can't say what the area is. However, I assume you know how to find the area of triangles and rectangles, so

*posted on March 22, 2019* -
## Math

please describe figures!!

*posted on March 22, 2019* -
## physics

as usual, vx = 18 cos37 vy = 18sin37

*posted on March 22, 2019* -
## math

Let's say that p(x) = (x-3)(x+1)q(x) + (ax+b) That is, it has some linear remainder when divided by x^2-2x-3 We know from the Remainder Theorem that p(3) = 5 p(-1) = -7 That means that 3a+b = 5 -a+b = -7 So, a=3, b=-4 The desired remainder is 3x-4

*posted on March 22, 2019* -
## Computers

control panel -> system & security -> system

*posted on March 21, 2019* -
## Physics

I checked using the equations of motion. The height h(t) = 27.5 + 9.629t - 4.9t^2 The ball hits after 2.237 seconds The vertical velocity v(t) = 9.629 - 9.8*2.237 = -12.294 m/s The horizontal speed is 16cos37° = 12.778 m/s So the final speed s^2 =

*posted on March 21, 2019* -
## Math

looks good to me

*posted on March 21, 2019* -
## Math

(a,a)

*posted on March 21, 2019* -
## Math

much better.

*posted on March 21, 2019* -
## Math

so, is 2-6 = -6? is 4-6 = -12? Don't just guess.

*posted on March 21, 2019* -
## Chemistry

well, you'll use up 2.5 moles of Ca, right? So add up the molar mass of 2.5Ca + 5Cl

*posted on March 21, 2019* -
## Math

all you have to do is solve y = at^2+bt+c given three points: Let's use t=1,2,3 a+b+c = 103.45 4a+2b+c = 74.2 9a+3b+c = 18.25 h(t) = -13.35t^2 + 10.8t + 106 Now you can answer the questions. It hits the ground when h=0 max height at the vertex: t = -b/2a

*posted on March 21, 2019* -
## Math

the faster vehicle travels 3/2 as fast as the slower vehicle. So, if x is the slower vehicle's speed, 3/2 x = x+30 x = 60 check: 200/60 = 300/90

*posted on March 21, 2019* -
## Math

If y is the larger number x+y = 12 1/x - 1/y = 2/9 1/x- 1/(12-x) = 2/9 Now it ends much nicer

*posted on March 21, 2019* -
## Math

possibly 5,7,2

*posted on March 20, 2019* -
## Math

is that supposed to be multiplication? If so, -1/2 * 3/4 = -3/8

*posted on March 20, 2019* -
## Maths

-(x-1)^2

*posted on March 20, 2019* -
## math

.40x = 240

*posted on March 20, 2019* -
## Math

you seem to recall that x = r cosθ y = r sinθ How could you forget that r^2 = x^2+y^2 ? Just use the distance formula. Or, if you insist on trig, recall that x^2+y^2 = r^2 sin^2θ + r^2 cos^2θ = r^2 (sin^2θ + cos^2θ) = r^2 or, heck - read your math

*posted on March 20, 2019* -
## Math

when you say 1/4 the size, do you mean for each dimension? If so, then just divide length and width by 4 If you mean 1/4 the area, then you will have 1/4 * length * area = (1/2 length)(1/2 width) so divide each dimension by 2.

*posted on March 20, 2019* -
## Math

well, 52 = 50+2, right?

*posted on March 20, 2019* -
## Math

no, r = cosθ is a circle with radius 1/2 and center at (1/2,0) y = x Is just a line with a slope of 1, right? r sinθ = r cosθ sinθ = cosθ tanθ = 1 don't forget your algebra 1.

*posted on March 20, 2019* -
## Math

huh? It's just a circle of radius 5! r=5 r^2 = 25 x^2+y^2 = 25

*posted on March 20, 2019* -
## Math

looks good to me

*posted on March 20, 2019* -
## English

asleep

*posted on March 20, 2019* -
## maths

It grew by 0.7 as a percentage, that's 0.7/1.5 = 0.466 = 46.7%

*posted on March 20, 2019* -
## math

If ticket sales were x dollars, then 500 + .10x = 1200

*posted on March 20, 2019* -
## Math

well, they sold 480/20 = 24 shirts, so 24*4 = $96 or, they make 4/20 = 1/5 of the sales as profit 1/5 * 480 = $96

*posted on March 20, 2019* -
## Science

looks like 58.5/(58.5+50) = 53.9%

*posted on March 20, 2019* -
## self teach calculus

∫[0, π/2] 4e^(sinx) cosx dx = 4(e-1) divide that by π/2 and you are correct

*posted on March 20, 2019* -
## Math

well, if A is at (0,0) then D = (0.94,-5.57) That should get you started.

*posted on March 20, 2019* -
## Math

x=0

*posted on March 20, 2019* -
## history

long expensive trip, right? Gotta pay the bills.

*posted on March 19, 2019* -
## Math

Use what they told you: 41c+28a = 222 14c+21a = 133 Now just solve for c and a

*posted on March 19, 2019* -
## Math

I'm sure you have the formula. Use it to figure the values.

*posted on March 19, 2019* -
## Algebra

by noon, A has gone .75*87 = 65.25 miles That leaves 412.75 miles when V takes off. Their combined speed is 186 mi/hr So, it will take 412.75/186 = 2.219 hours They crash at 2:13:08.4 pm You can surely figure out where that puts the trains.

*posted on March 19, 2019* -
## math, log, interest, precalc

5% per month compounded continuously means A = Pe^(.05m) To double, you need e^(.05m) = 2 .05m = ln2 m = ln2/.05 = 13.8 months so, slightly less than that to reach 1800 = 1000 * 1.8 In 10 years (120 months), 1000e^(.05*120) = 1000e^6 = 1000*403.4287935

*posted on March 19, 2019* -
## Math

pardon my skepticism. Any introduction to complex numbers explains how to find their magnitude.

*posted on March 19, 2019* -
## Math

By general form I assume you mean some variation of y = ax^2+bx+c (x+10)^2+(y+5)=16 y+5 = 16 - (x+10)^2 y = -(x+10)^2 - 11 y = -(x^2+20x+100)-11 y = -x^2 - 20x - 111 But I suspect a typo, since there's no reason for both (y+5) and 16

*posted on March 19, 2019* -
## Math

Clearly you have not read the section on complex numbers |3-2i| = √(3^2+2^2) = √13 |5-i| = √(5^2+1^2) = √26

*posted on March 19, 2019* -
## Calculus

((te^7t)/7)-((e^7t)/49) = e^(7t) (7t-1)/49 What is the limit on t? t->0 : no problem t->∞ : ∞ t->-∞ : 0 t -> 1/7 : 0 you need something like 0/0 or 0*∞ of ∞/∞ for l'Hospital's Rule

*posted on March 19, 2019* -
## Calculus

2C The boundary for the discs is a single curve, so there is no extra volume to include. I only included the shells to show that the two methods produce the same answer. 5. Since the graph is sometimes negative, simple integration subtracts the area below

*posted on March 19, 2019* -
## Physics

how long does it take to fall 10000 ft? 16t^2 = 10000 t = 25 How far will the plane travel in 25 seconds?

*posted on March 19, 2019* -
## Linear Algebra

It should be no problem to demonstrate that the sum of two 2x2 matrices is another 2x2 matrix. The definition of matrix addition guarantees it. Just review the properties of a vector space and it should be clear that M quialifies.

*posted on March 19, 2019* -
## math

hmmm 3 vowels, 6 letters. so ...

*posted on March 19, 2019* -
## math

1/(2+2) = 1/4

*posted on March 19, 2019* -
## Calculus

Sorry - I didn't see your final answers. Everything looks good except as noted below 1st set 1D. Hmmm. Maybe I'm off. Better check your text for those definitions. 2C. Things are easy for discs. Using shells, the boundary changes at y = 1/27 Below there,

*posted on March 19, 2019* -
## Calculus

I'd have to say they all look good to me... Mainly because I wrote those posts!

*posted on March 19, 2019* -
## calculusII

since e^(7z) shrinks much faster than z grows, the integral converges. In fact, you can evaluate it and see that the limit is -1/49

*posted on March 19, 2019* -
## java programming

ever hear of google? But, just as a note, if you're listing numbers, print the first (easy to know when that happens) and then prefix all the rest with a comma. That way, at the end of the list, there is no trailing comma.

*posted on March 19, 2019* -
## Math

no, the answer is E I told you the line is horizontal! geez! If you can't work it out, at least read what I write!

*posted on March 18, 2019* -
## math

4.5% = 4.5/100 = .045 That means you add .045 times the amount present every year. That is, for the first year, you get 700 + 700 * .045 = 700(1+.045) = 700*1.045 and you multiply by that every year.

*posted on March 18, 2019* -
## @ oobleck

np people seem to think we live our live at the computer. I did help nebula, though I did not just give her the answer. Sorry I had to go live my life a little during the interim...

*posted on March 18, 2019* -
## calculus

Hmmm. Some context would be nice. if t=0 then ((te^9t)/81) = 0 But (9e^(9t)/81) = (9*1)/81 = 1/9

*posted on March 18, 2019* -
## Recordkeeping?

ok. Now what?

*posted on March 18, 2019* -
## Physics

power = work/time = force*distance/time = (40*9.8N)*(30*0.150m)/6s = 1764/6 N-m/s = 294W

*posted on March 18, 2019* -
## Math

if the slope is zero, the line is horizontal, and all points on it have a y-coordinate of 18

*posted on March 18, 2019* -
## statistics

P(no defective in 4 draws is) = 26/41 * 25/40 * 24/39 * 23/38 = 115/779 So, P(at least 1) = 1 - P(none) = 664/779

*posted on March 18, 2019* -
## Math

That's just rubbish, if all you want is the degree. It is just an integer. If all you are doing is finding a polynomial, you don't need an equation. I have no idea what that 2^0 is supposed to do. The degree of 5a^2+12ab-7b^2 is 2. Just 2. 2^0 = 1

*posted on March 18, 2019* -
## math

After t years, the amount in the account will be 700*1.045^t So just plug in t=10 and subtract the original 700 to find the interest earned 700(1.045^10 - 1) = 387.08

*posted on March 18, 2019* -
## Math

no. you want x all alone x+5 = 12 means x=7 since 7+5 = 12

*posted on March 18, 2019* -
## Math

2x is the same as 2x^1 So the implied power is 1. It's just usually not written out. 2x+3 therefore is of degree 1. it is the degree only if here are no other higher powers in the expression.

*posted on March 18, 2019* -
## math

if x=2, -4x^2 = -4*2^2 = -4*4 = -16 Not sure why you guessed instead of doing the math

*posted on March 18, 2019* -
## math

since the top of the tree is 100m down, and tan30° = 1/√3, the tree is 100√3 meters from the building. So if the angle to the foot of the tree is x, then tanx = 300 / 100√3 = 3/√3 = √3 x = 60°

*posted on March 18, 2019* -
## Math

no. 6 is 4 less than 10, right? 10-4 so, you want 3x-5

*posted on March 18, 2019* -
## Math

5 is the degree -- the highest sum of powers x^5: 5 x^2y^3: 2+3=5 time to review degree of polynomials ...

*posted on March 18, 2019* -
## math

no. -4(0^2) = 0 just try the other pairs. And note that -4x^2 = (-4)x^2

*posted on March 18, 2019* -
## algebra

then that is what I did in my 2nd half above. ∞ Σ -4(1/3)^(n-1) = -4 (1 + 1/3 + 1/9 + 1/27) ... = -6 n=1 I see I did make a typo: S∞ = a/(1-r) not 1/(1-r) Looks like it's time for a review of your textbook.

*posted on March 18, 2019* -
## algebra

Do you mean a_n = 1 - 4(1/3)^(n-1) ? If so, then the sequence is 1 - 4*1, 1 - 4/3, 1 - 4/9, 1 - 4/27 ... = -3, -1/3, 5/9, 23/27, ... But that's not a geometric sequence. I suspect you meant a = -4 r = 1/3 If so, then that sequence is -4, -4/3, -4/9, -4/27,

*posted on March 18, 2019* -
## Math

3r^7 whatever r is

*posted on March 18, 2019* -
## math

"Thrice divided by y" is gibberish. However, Three divided by y = 3/y Now you get murky. The result could be either (3/y - 12)*m or 3/y - 12*m or even 3/(y-12) * m or 3/((y-12)*m) I suspect it is supposed to be 3/y - 12m

*posted on March 18, 2019* -
## Calculus

#1. The curves intersect at (0,0) and (3,3) so the area is ∫[0,3] 3x - x^2 dx #2. using discs of thickness dy, v = ∫[0,4] πr^2 dy where r = 2-x = 2-√y v = ∫[0,4] π(2-√y)^2 dy Using shells of thickness dx, v = ∫[0,2] 2πrh dx where r=2-x and

*posted on March 18, 2019* -
## Calculus

#1. the average value is just the area divided by the width. It's just the height of a rectangle with the same area as under the graph. A. So, assuming you know how to find the area of a trapezoid, the first one has area 10(17+20)/2 = 175 figure the

*posted on March 18, 2019* -
## Physics help

what do you mean by "average time?"

*posted on March 18, 2019* -
## Math

not until you give us the dimensions. then just multiply them all together. I could make up a set of sizes to fit any of the choices.

*posted on March 18, 2019* -
## Math

uh, noooooo the first 4.5 feet already are full of water They just need to raise the water level the last 0.5 feet till it starts to overflow.

*posted on March 18, 2019* -
## Math

since m=0, all the points have y = -2 trick question.

*posted on March 18, 2019* -
## Math

so, you need .5 ft of height to be filled with people v = pi * 9^2 * .5 ft^3 divide that by 2.5 to get the number of people

*posted on March 17, 2019* -
## Science

the diagram omits the disgronificator.

*posted on March 17, 2019* -
## Math - repost

Since you didn't like my other formula, let's try this: If the plane is at height h, then h = 5/(cotθ-cotϕ) d = h/sinϕ = 5/(sinϕ(cotθ-cotϕ)) Equivalent trig expressions can be massaged to appear very different

*posted on March 17, 2019* -
## Math

pi r^2 h * 62.43

*posted on March 17, 2019* -
## Math

for (b) note that if the plane is x miles east of B at an altitude h, h/x = tanφ h/(x+5) = tanθ eliminating h, xtanφ = (x+5)tanθ x = 5tanθ/(tanφ-tanθ) Now note that x/d = cosφ d = x/cosφ = (5tanθ/(tanφ-tanθ))/cosφ = 5tanθ/(cosφ(tanφ-tanθ))

*posted on March 17, 2019* -
## Calculus

c'mon - this is one of the standard forms -- arctan(x)

*posted on March 17, 2019* -
## Business Math

just as a hint, adding 8% every year means multiplying by 1.08 for each year, not adding 8% of the original 8000.

*posted on March 17, 2019* -
## Math

I showed you how to get the long diagonal. I also explained how to find the short diagonal and the altitude. Surely you can't want anything else!

*posted on March 17, 2019*