Wednesday

July 30, 2014

July 30, 2014

Total # Posts: 24,029

**math**

In other words, the two vectors are perpendicular If the two magnitudes are equal, then assuming that |z| >= |w| |z| = √(a^2+b^2) |w| = √(c^2+d^2) z+w = (a+c)+(b+d)i z-w = (a-c)+(b-d)i √((a+c)^2+(b+d)^2) = √((a-c)^2+(b-d)^2) (a+c)^2+(b+d)^2 = (a-c)^2...

**Math - PS**

Well, my most obvious mistake was using 3 as the length, not 300 (cm).

**Math**

when the water has depth y cm, the width of the surface has width 25+(75/50)y cm So, at depth y, the area of the trapezoidal cross-section is 1/2 (25 + (75/50)y)(y) = 3/4 y^2 + 25/2 y cm^2 So, the volume is v = 9/4 y^2 + 75/2 y cm^3 So, we want dy/dt when y=25, and we know tha...

**Math-Exponential Decay**

if the half-life is n days, then the amount remaining after t days can be modeled by 58(1/2)^(t/n) So, to find n, we just have to solve 58(1/2)^(10/n) = 52 (1/2)^(10/n) = 52/58 = 0.8966 10/n = log(52/58)/log(1/2) 10/n = 0.1575 n = 63.5 So, the half-life is about 63.5 days

**math**

I assume the pool is rectangular, with width x and length y. So, if the deck has width w, 2(x+y) = 50 2(x+2w + y+2w) = 74 2(x+y)+2(4w) = 74 50+8w = 74 8w = 24 w = 3

**maths**

to solve algebraically, just solve 3x-6 = x^2-6x+8 x^2-9x+14 = 0 (x-7)(x+2) = 0 The graphical solution is at http://www.wolframalpha.com/input/?i=solve+x^2-6x%2B8+%3D+3x-6

**Math**

thank you

**Math**

Solve the following 2a(a squared+4a)

**algebra**

If you mean h(t) = s - 16t^2 then we need s so that s-16*9 = 0 s = 144 ft

**Algebra**

ummm. The scores. If there are 10 scores, the 80th percentile ends at the 8th score. That is 80% of the scores. Extra credit: what is "context"?

**Algebra**

sort the scores in order. Find the lowest score greater than 80% of them. That is the 80th percentile score.

**math**

(2a) / (2u)(2v) = 2/4 * a/uv = 1/2 a/uv So, #3.

**Math**

The function rule C= 10 n + 26 where n = number of people and c = cost of party. Show a table if 27,39 , & 43 people go. My answer is the following n 27 39 43 c 296 416 456

**Math**

Write a function rule for the following table. x 2 4 6 y 1 0 -1

**Math**

Is y= -3 x squared +x a quadratic function?

**Math**

thank you

**Math**

If you have the following points for X and Y what is the linear function rule? x = 4, 1 y = 2, -4 I think it is 1/2 x but I'm not sure if it is +6 or - 6

**Math**

Now way it can be y=8x+8. adding two even numbers always produces another even, and most of your y values are odd. Also, if a relation is linear, then equal changes in x will produce equal changes in y. Here, we have x changing by 1 between steps, yet y changes by 8,7,9,8 So, ...

**Math**

Using the table below is it a linear function? x -2, -1, 0, 1, 2 y -7, 1, 8, 17, 25 my answer is that it is a linear function rule: x = -1 y = -8,-9,-7, -8 I think the rule is y= 8 X+8

**Math**

It was what I was doing. Thank you

**Math**

Solve for 5 X 3 to the nth,. my answer is 15, 45, 135, 405

**Math**

Is the following sequence a arithmetic,geometric or neither? 1.6, .8, .4, .2 my answer is geometric

**grammer**

Have you seen my sister Karla around here today? Harriet couldn't study for her comma quiz, because she asked to open the door for the neighbor, whom the dog wouldn't leave alone in the backyard.

**algebra**

I assume you mean to let x represent the "second" angle. So, we have x+23 + x + 6x = 180 Now just solve for x. After that, I assume you are supposed to indicate the measure of each of the angles...

**Aths**

throw a tool away from the ship. Conservation of momentum will cause you to drift slowly toward the ship.

**Math**

the surface was 4 pi r^2 = 36pi Now, replace r with (3/2) r and the new surface area is 4pi(3/2 r)^2 = 4pi * 9/4 r^2 = 4pi r^2 (9/4) = 36pi(9/4) = 81pi Or, you could just solve for r and get that r increased from 3 to 9/2, so the area increased from 36pi to 81pi.

**Math**

for each year, just add 4.5 t

**Calc**

y' = -.15y dy/y = -.15 dt lny = -.15t+c y = ce^-.15t with y(0) = 3, c=3 with y(0) = 4, c=4 with c=3, 3e^-.15t = 1 e^-.15t = 1/3 -.15t = ln(1/3) t = ln(1/3)/-.15 t = 7.32 with c=4, t = 9.24 So, the patient gets the 3rd dose after 7.32+9.24 = 16.60 hours.

**Calculus**

Ok. The information for S allows us to determine p, since the distance SF equals the distance from S to the line x = -p. So, 2p+5 = 10 p = 5/2 The equation of the parabola is y^2 = 4(5/2)x = 10x y = √(10x) Now we have to look at T. The slope of the tangent to the curve a...

**math**

If Ann not buy pink, Tom not buy red.

**Algebra**

sort the values, then divide them into four equal parts. Pick the 1st and 3rd portions.

**ALGEBRA**

√b^4 = b^2 √25 = 5 so, you have √(b^4/25) = b^2/5 = 4 b^2 = 20 so, b = ±√20 Those are the only two real answers. If you want the other two answers, you have to consider that b^2/5 = -4 b^2 = -20 b = ±√20 i

**Algebra**

you are correct. An odd formula, as most such calculations are based on degrees Kelvin.

**pre algebra**

well, geez. You have the formula. Pick any two (x,y) pairs and plug them in: (3-0)/(2+1) = 1 You can see just by looking at the table that when x increases by 1, so does y.

**pre algebra**

What is the slope for the following data? X -1 0 1 2 Y 0 1 2 3 y2 - y1 ---------- x2 - x1 rise / run

**Alegbra**

just solve for t in (1/2)^(t/5730) = 0.75

**alegbra**

so, what's the formula relating distance to amplitude?

**Math**

correct

**Calculus**

well, for f(x) to be differentiable, f'(x) must be defined. Surely you can see that 9x / 2√(3x^2+2) is defined for all real x...

**calculus**

yes, sorry I only gave the volume of the paraboloid, and forgot to subtract the cylinder inside. Better go with MathMate's answer.

**Algebra**

total points scored: 22*88 = 1936 Now we add 5 scores, increasing the total by 3*92 + 2*89 = 454 So, the new average for 27 students is (1936+454)/(22+5) = 88.52

**ALGEBRA**

The sides are in the ratio 1:√3:2, so with the hypotenuse=20, we have 10:10√3:20, with the longer leg opposite the larger angle. Looks like 17.3 to me.

**algebra**

2+4i

**algebra**

2+√-16

**math**

When contesting an answer, it'd be nice if you showed your own steps. I assert that (6x - 3 + 2x/y) * 2xy = (6x)(2xy)-(3)(2xy)+(2x/y)(2xy) = 12x^2y - 6xy + 4x^2 Now, if you just want a single fraction, Only the 2x cancels in all terms in the numerator, and you have 6xy - 3...

**math**

6x - 3 + 2x/y

**ALGEBRA**

why not just say "x+1" instead of "x+4-3"? And if x>=45 works, why not x>=48? or x>=53? I still suspect a typo.

**Math7 Am I right?**

Looks ok to me.

**Science/Math**

I'd say either. If the object is a turkey, chances are it'll be obliterated. If it's a flying block of titanium, it's more likely to have its course altered.

**math**

totals are Px and Ny so, the average we want is (Px+Ny)/(P+N)

**maths**

(a) the -x^2 means it opens downward (b) set x=0 to get y-intercept Since y = (1-x)(x-3) the x-intercepts are easy to see. (c) as usual, the vertex is at x = -b/2a = 1. Find y(1).

**calculus**

The cylinder intersects the paraboloid at z=5. The volume inside the paraboloid is v = ∫[0,2π] ∫[0,2] ∫[0,9-r^2] r dz dr dθ = ∫[0,2π] ∫[0,2] r(9-r^2) dr dθ = ∫[0,2π] 14 dθ = 28π

**Math - eh?**

which two stacks?

**Math (Calculus)**

we've done several of these for you. Got any ideas on this one?

**Algebra**

2h16' = 34/15 hours 4h32' = 68/15 hours Suppose it takes t hours to do the job working together. If the apprentice takes x hours, then it takes Sumi 3/4 x hours. So, we know that 1/t = 1/x + 1/(3/4 x) Also, we are told that (34/15)(1/t) + (68/15)(1/(3/4 x)) = 1 solving...

**math**

yes: (3x+1)(9) = 27x+9

**calculus-answer check**

The chain rule gives 2[(3x^2+1)^3+1] * 3(3x^2+1)^2 * (6x) This is an 11th-degree polynomial, so I suspect your answer is wrong.

**Math**

s = rθ = 13(65 * pi/180) = 169/36 pi

**Math**

r = (a+b-c)/2 5 = (a+b-19)/2 a+b = 29 p = a+b+c = 19+29 = 48

**Math**

If there are x reserved seats, receipts were 1.50x + .05*25x = 2.75x Now, we want y reserved $1 seats to fetch the same money: 1.00y + .05(26x-y) = 2.75x y + 1.3x - .05y = 2.75x .95y = 1.45x y/x = 1.45/.95 = .29/.19 = 29/19 So, now we want y/26x = 29/494 The ratio of reserved ...

**Physics**

well, you have dx/dt = 10cos53.1° = 6 dy/dt = 10sin53.1° - 9.8t = 8-9.8t y = 23.5+8t-4.9t^2 y=0 when t=3.15 At t=3.15, dx/dt = 6 dy/dt = -22.87 so, the speed is √(6^2+22.87^2) = 23.64 m/s Given that, I expect you can do part (b).

**Math**

it appears to be a repeating decimal 0.676767... rounded after 8 decimal places.

**calculus-answer check**

that's the proper method. Using the product rule, y' = (2x+3)(x^2-2) + (x^2+3x)(2x) at x=-1, that's (-2+3)(1-2)+(1-3)(-2) = 3

**Algebra**

1/R = 1/12 - 1/30 1/R = 1/20 R = 20

**Algebra**

just plug it into the formula: 1/12 = 1/R1 + 1/R2 Unless you know R1, you can't figure R2. If the lamps are identical, then R1=R2=24

**Math ~ Check Answers ~**

answers don't tell us much without the questions. #5: slope = 1 y = x-4 #6: slope = 3 y = 3x-1

**Algebra**

It wasn't the root symbol (which you can copy and paste fro my posting), but the "x+4-3" expression. Why not just say "x+1"? I suspect that is not what you had in mind. Was it √(x+4)-3 or something else?

**Algebra - typo?**

we want √(x+4-3) >= 4 I suspect a typo due to the odd nature of the expression.

**Algebra 1**

#1 correct because 256-320 < 0 #2 ok #3 what? you have the answer: ±√(12/5) as a decimal, that's ±1.55 12/5 = 2.4 and √2.4 = 1.55 You got no calculator?

**math**

just plug in the numbers: 2#a = 2*2+a a#3 = 2a+3 so, now we have 4+a = 2a+3 a = 1

**math**

given the area, the radius is 2. So, the diameter is 4. Two glasses side by side have width 8. So, the box is 8x8x8. The area of a face is 64.

**Calculus**

y dy = e^x dx 1/2 y^2 = e^x + c if (0,4) is on the graph, then 8 = 1+c c = 7 1/2 y^2 = e^x + 7 Looks like D to me dP/dt = k(10-t)/∛t Looks like E to me If you must use 3 to indicate the root, why say sqrt? The sq clearly implies square root. Try 3root of cbrt.

**math**

I will assume that you know how to find the area of a circle. In this case, that will be π ft^2 I must also assume you haven't studied packing density of circles, so we'll say the centers of the circles lie on a square grid. That said, since each circle has diamet...

**Math**

Well, think about it. Suppose their budget was 50% of the available property value. They'd have to tax it at 50% Instead, their budget is 27000 out of an available 1173913. So, what % is that? 27000/1173913 = 0.023 or, 2.3%

**math**

OK. I have an idea, if you know the Pythagorean Theorem. Draw ABC with the base BC, and point A at the top. Now, the line AB is length 2√2 and angle B is 45°. Draw the altitude AD to the base BC. Now you have a right triangle BDA with hypotenuse 2√2. Its legs A...

**math**

Hmm. So, you haven't had calculus, trig, or much algebra. What have you studied to enable you to find the area of a triangle, given two sides and the included angle? What chapter of the text presents this problem? I'd love to help you solve it, but some context would b...

**math**

Use the law of cosines to find AC: 8+64-2*2√2*8/√2 72 - 32 AC = 2√10 Now you can use Heron's formula to get the area = 8

**geometry**

You may not have seen it like this, but A = C/π

**algebra**

-3° is 18° less than 15° At 3°/hr that will take 6 hours, and happen at 6 pm. midnight is 12 hours after noon, so the temperature then will be 15-3*12 = -21°C Note that since 6pm is halfway between noon and midnight, since the temperature dropped 18° by...

**science - not brilliant**

The greater minus the lesser is -39 - (-98) = -39+98 = 59°C

**math - typo?**

since the diagonals are equal, 2(5a+1) = 2(a+1) 10a+2 = 2a+2 a=0 I don't think so...

**maths - oops**

oops - heh heh 3w = 12 w = 4

**maths**

length+width=9, so w + 2w-3 = 9 3w = 6 w = 2

**math**

r = 6w+1, so since r+w=50, 6w+1 + w=50 7w = 49 w = 7 r = 43

**Math**

the circumference is 20pi meters. So, the linear velocity is 60pi m/min. angular velocity is 2pi radians per revolution, so 6pi radians/min you know the circumference. Divide that by 8 to get the distance between seats.

**new neutrich high school**

depends -- do you want to know how many calories are burned as time passes, or do you want to know how long it takes to burn a calorie?

**algebra**

(f*g)(x) = f(x)*g(x) = (2x^2+7)(x-6) So, now just plug in x=1

**Algebra**

assuming you want to find the value(s) of s that make the equation true, place everything over the common denominator of (s^2-1) and clear fractions. Note that s=±1 are excluded, because that would involve division by zero. 3(s+1) + (s^2-1) = 12 s^2+3s-10 = 0 and I gues...

**math**

every time she works one more hour, how much more money does she get? That is the slope of the line.

**Algebra**

$2/item is the slope

**Algebra**

15000(1+r)^2 = 16099.44 (1+r)^2 = 1.0733 1+r = 1.036 r = 0.036

**Math (Calculus)**

The volume of a shell of radius r, height h and thickness dy (because revolving around the y-axis) is 2πrh dx Now, our plane region is symmetric about the y-axis, so revolving all of it it is the same as revolving only the part for x>=0. o, we'll take the volume to...

**Math (Calculus)**

v = ∫[0,4] 2πrh dx where r=5-x and h=y = 2π∫[0,4] (5-x)(4x-x^2) dx = 2π(x^4 - 3x^3 + 10x^2) [0,4] = 64π check using discs: v = ∫[0,4] π(R^2-r^2) dy where R=5-(2-√(4-y)) and r=5-(2+√(4-y)) = π∫[0,4] (3+√(4-...

**Grade 12 Math**

(2a-5b)•(3a+b) 2a•3a - 13a•b - 5b•b 6 - 13a•b - 5 1 - 13a•b Now |a+b| = √3, so using the law of cosines to get the angle θ between a and b, we have 1+1-2cosθ = √3 cosθ = 1-√3/2 Now, we know that since a and b are u...

**math**

divide the volume by the base area to get (40*pi*3.5^2)/(28*22) = 35/44 pi or 2.5

**Calculus**

#1 ok #2 dy/y = dx/x^2 lny = -1/x + c y = e^(-1/x + c) = ce^(-1/x) so, (B)

**Algebra**

They all look fine to me, though it took me a while to separate the problems from your answers. If they were marked wrong, then the key is in error. As you have presented them, your answers are all correct.

**Math - Pleeeease**

once you start tossing in angles, you'd better have some trig. Either that or know some basic facts about certain right triangles. I assume you have heard of the Pythagorean Theorem. For this problem, draw a right triangle with the hypotenuse going from the starting point ...

**Math - Pleeeease**

well, since plane #1 is rising at 45°, its ground distance is equal to its altitude, or 5600. The 2nd plane coves less ground than its altitude. It is 8200 cos 60° = 4100

**Math**

1 = (x+6)/(x+6) so, the right hand side becomes ((2x-6)+(x+6))/(x+6) = 3x/(x+6)

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