# Posts by Steve

Total # Posts: 49,668

**Precalculus**

I think I can read this as z^7 = 1/?2 - 1/?2 i so, that means z^7 = cis 315° z = cis(315/7)° = cis45° + k*360/7 for k=1..6

*January 27, 2017*

**Maths**

If they work 3/2 as fast, it will take 2/3 the time.

*January 27, 2017*

**algebra**

clearly, when -16t^2 + 156t + 105 = 0

*January 26, 2017*

**Math**

h * h/2 * 1/2 = 100 h = 20

*January 26, 2017*

**Math**

well, 8 pts = 1 gal, so ...

*January 26, 2017*

**trig**

sin? = y/r cos? = x/r tan? = y/x tan? is the slope, so you have tan? = 5 r^2 = x^2+y^2 = 26

*January 26, 2017*

**Math**

it appears so.

*January 26, 2017*

**Trig**

csc^2 ? = 1+cot^2 ? so, ...

*January 26, 2017*

**Algebra**

a = 7 d = 3 Now you can answer the questions: T8 = a+7d Sn = n/2 (2*7 + (n-1)*3) > 425

*January 26, 2017*

**formal language**

ok. and ... ?

*January 26, 2017*

**8th grade math**

hmmm. I don' see no steenking triangles!

*January 26, 2017*

**math**

t = 2s k = t-3 t+s+k = 37

*January 26, 2017*

**Math**

so, we have (1,9) -> (3,-3) (3,12) -> (5,-6) (4,4) -> (6,2) x -> x+2 y -> 6-y = 3-(y-3) So, shift right 2 reflect across the line y=3.

*January 26, 2017*

**Math**

time = distance/speed, so time for sound to return: d/c time to fall: t = T-d/c d/c + gt^2/2 * d/t = T now just solve for d

*January 26, 2017*

**algerbra**

Looks like A to me. The prices are in the ratio 1:3:5:7, just like the times.

*January 26, 2017*

**Math**

450/(600+450+270) = 15/44

*January 26, 2017*

**math**

12^2 + L^2 = 20^2 L = 16 It's just a 3-4-5 triangle scaled up by a factor of 4.

*January 25, 2017*

**Trigonometry**

sin? = 1.2/4.4

*January 25, 2017*

**Calculus**

#1 correct ?[1,4] ?(1 + 1/4x) dx ?[1,2] ?(1+4y^2) dy where did you come up with [16,1]? The curve goes from (1,1) to (4,2) Note that ?(1+4y^2) is NOT (1 + 2y) ?(a^2+b^2) is not a+b !! #2. looks ok. For C, the radius is just x+2 For D, the radius is just 3-y

*January 25, 2017*

**Math**

use your standard conversion factors for gal/L and mi/km

*January 25, 2017*

**Measurement**

u = 10^-6 p = 10^-12 you surely have a list of prefixes - use them.

*January 25, 2017*

**Algebra**

you know that x = 3y-6 So, use that in the other equation: 20y + 35(3y-6) = 3795 20y + 105y - 210 = 3795 125y = 4005 y = 32.04 Now use that to find x. Odd, I expected an integer answer. Check for typos.

*January 25, 2017*

**Algebra 1**

just evaluate at x=5

*January 25, 2017*

**Trigonometry with right triangles**

you can always get a book on geometry and study it. I learned calculus on my own from my teacher's textbook. But I suggest you finish Algebra I before trying geometry or trig. It will give you a good foundation to work with.

*January 25, 2017*

**Trigonometry with right triangles**

what, you can't figure 90-25 ?

*January 25, 2017*

**Trigonometry with right triangles**

cos(x) = sin(90-x) That's what the co- in cosine means: sine of the complement.

*January 25, 2017*

**Algebra 2**

I get B. What did you do? Maybe we can figure what went wrong.

*January 25, 2017*

**Calculus**

sin = y/r cos = x/r sinx = 1/5 cosx = -?24/5 = -2?6/5 cosy = 1/8 siny = ?63/8 = 3?7/8 I'll do sin(x+y) and you can apply the formulas for the rest. sin(x+y) = sinx cosy + cosx siny = (1/5)(1/8)+(-2?6/5)(3?7/8) = 1/40 - 6?42/40 = (1-6?42)/40 makes sense, since x+y is in QIII

*January 25, 2017*

**Algebra**

If the walkway has width w, then 2(6+2w + 10+2w) = 60.8

*January 25, 2017*

**maths**

a = 31 1/4 = 125/4 ar^(n-1) = 2 r^(n-1) = 8/125 Now, 8/125 = (2/5)^3 Looks to me like r = 2/5 and n=4 and the sequence is thus 125/4, 25/2, 5, 2 I think you'll find it adds up to 203/4

*January 25, 2017*

**Algebra**

Draw a diagram. Set the center of the ellipse at (0,0). Then we have semi-axes a = 74 b = 48 x^2/74^2 + y^2/48^2 = 1 Now plug in y=10 and find x. The distance d is then d^2 = x^2 + 10^2

*January 25, 2017*

**calculus**

3xy^3+4xy=63 3y^3 + 9xy^2 y' + 4y + 4xy' = 0 y'(9xy^2+4x) = -(3y^3+4y) y' = -(3y^3+4y)/(9xy^2+4x) So, at (9,1) y' = -7/117 Now you have a point and a slope, so the line is y-1 = -7/117 (x-9) Refer to http://www.wolframalpha.com/input/?i=plot+3xy%5E3%2B4xy%...

*January 25, 2017*

**Math 114**

so, did you check? 3+9=12 so, ok.

*January 25, 2017*

**MATH**

well, 4 for each kg, so ...

*January 25, 2017*

**math**

72/4 = 18 So, multiply all the lengths by 18 to get 54+72+36 = 162

*January 25, 2017*

**Math**

-8+3 = -5

*January 25, 2017*

**math**

1/5 boys absent means 4/5 present 4/5 boys = 160 = 4*40 So, there are 5*40 = 200 boys 2/5 of the students are boys 200 = 2/5 * 500 So, there are 500 students in all. Now you can see how many are girls.

*January 25, 2017*

**Trigonometry with right triangles**

Since <DEF is 60° and DE = ?2, EF=?6. So, the area is (?2*?6)/2 = ?3 Rather than all this *line in between answer D* stuff, you could have just written ?3/?2

*January 25, 2017*

**trigonometry**

If the pedestrian is x meters from the short building, 10/x = tan20°10' the distance to the tall building is 40-x You don't seem to care how tall the other building is, but if the tall building has height h, then (h-10)/40 = tan15°20'

*January 25, 2017*

**complex number help**

?-16 = ?(16 cis ?) = ?16 cis ?/4 = 2(1/?2 + 1/?2 i) = ?2 + ?2 i That is the 1st root. There is an equivalent root in each quadrant. See http://www.wolframalpha.com/input/?i=x%5E4+%3D+-16 Work the 5th root the same way, using de Moivre's theorem.

*January 25, 2017*

**maths**

assuming that the wood purchased will be used efficiently, the volume of wood is the outside volume less the inside volume. Since there are parallel sides, the inner dimensions are 5 cm less than the outer. Thus, the volume of wood is (200-5)(120-5)(75-5) = 1569750 cm^3 = 1....

*January 25, 2017*

**MATH**

x^2 * x^2 = (x*x)*(x*x) = x*x*x*x = x^4 or, x^2 * x^2 = x^(2+2) = x^4 or, x^2 * x^2 = (x^2)^2 = x^(2*2) = x^4

*January 25, 2017*

**Math**

f(5/2) is the remainder when f(x) is divided by (x - 5/2) This site can help: http://calc101.com/webMathematica/long-divide.jsp

*January 24, 2017*

**Math**

see http://calc101.com/webMathematica/long-divide.jsp

*January 24, 2017*

**Math**

well, (8-5)^2 = 3^2 = 9 I assume you can take it from there ...

*January 24, 2017*

**Calculus**

a little synthetic division will show that f(x) has roots in (-2,-1) and (0,1).

*January 24, 2017*

**Calculus**

F'(-4) = lim(h->0) [((-4+h)^3 + (-4+h)^2) - ((-4)^3+(-4)^2)]/h = lim(h->0) [(h^3-11h^2+40h-48)-(-48)]/h = lim(h->0) (h^3-11h^2+40h)/h = lim(h->0) (h^2-11h+40) = 40

*January 24, 2017*

**Calculus**

secx = 2 or -2 or, cosx = 1/2 or -1/2 One root in each quadrant.

*January 24, 2017*

**Calculus**

The slope of the line is (30000-280000)/10 = -25000 So, V(t) = 280,000 - 25,000t

*January 24, 2017*

**Math**

A - 1/2a = P

*January 24, 2017*

**Physics (9th)**

sorry. 26.39/4 = 6.59 don't know how I got so far off. So, fix t and redo the calculation...

*January 24, 2017*

**Physics (9th)**

recall that the equation for distance is s = vt + a/2 t^2 95 km/hr = 26.39 m/s So, it will take 26.39/4 = 6 seconds of braking to stop. s = 95*7 - 2*6^2 = 593 meters to stop I guess she had good eyes, seeing an antelope at half a km away! Or, maybe she just hit it, or swerved ...

*January 24, 2017*

**Algebra**

p = 3b-6 20b+35p = 3790 Now just solve for b and p to see how many of each there are.

*January 24, 2017*

**Math**

correct

*January 24, 2017*

**Math**

oops 47+30 = 77 > 70

*January 24, 2017*

**Math**

well, 70-47 = 23 so, any number bigger than 23 will make the statement true 47+30 = 73 > 70 I have no idea what outlandish method they taught to solve the problem.

*January 24, 2017*

**chem**

impatient much? see your other post...

*January 24, 2017*

**chem**

29 moles of O2 --> 58 moles of H2O So, how many grams is that?

*January 24, 2017*

**find the equation**

review the point-slope form.

*January 24, 2017*

**Standard Form**

slope=0 so, the line is of the form y=k for some k.

*January 24, 2017*

**trig**

forget you algebra I?? subtract 2 from both sides ...

*January 24, 2017*

**math**

initial amount of $57 expense = 57 materials cost $7 for each necklace expense = 57 + 7x sales = 26x ...

*January 24, 2017*

**math geometry**

This might help. google can provide more help.

*January 24, 2017*

**maths - Typo?**

a = ar^3 + 13.5 ar^3 = ar^2 + 9 a(1-r^3) = 13.5 ar^2(r-1) = 9 Now divide both sides to get (1-r^3)/(r^3-r^2) = 13.5/9 2-2r^3 = 3r^3-3r^2 5r^3-3r^2-2 = 0 Hmmm. No real solutions.

*January 24, 2017*

**Algebra**

No, the solutions are the values of x which make x = 0 x+5 = 0 x+2 = 0 x = 0, -5, -2 x = 0 5x-1 = 0 x+4 = 0 x = 0, 1/5, -4

*January 24, 2017*

**Calculus**

Your pieces overlap. That is not the way to define a piecewise function. Looks like your inverse function will also be piecewise, no? Just take the inverse on each piece.

*January 24, 2017*

**Anonyms**

c = 2?r = 4? so, r=2 a = ?r^2 = 4? A square with area 4? has side ?(4?) = 2?? So, its perimeter is 4*2?? = 8?? Note that 8?? > 4?. A circle has minimum perimeter for a given area. Or, a circle has maximum area for a given perimeter.

*January 24, 2017*

**math**

Odd that you know it's a Bernoulli equation, yet seem to have no technique for solving such a well-known form. y = ±1/?(cx^2-6x^3) If you have not studied them, try here: http://tutorial.math.lamar.edu/Classes/DE/Bernoulli.aspx

*January 24, 2017*

**Math geometry**

x = 20+3(180-x)

*January 24, 2017*

**Trig**

you're welcome.

*January 24, 2017*

**math**

)&( ? !

*January 24, 2017*

**Math - Algebra 1**

16 cows * 4.5 cups/cow/day * 7days * 1bucket/250cups * $26.75/bucket = $53.93

*January 24, 2017*

**Math - Algebra 1**

for a given perimeter, a square has the largest area.

*January 24, 2017*

**math**

a square with diagonal d has side length s = d/?2 And the question should have been worded: The walkway is 24 meters long. To the nearest tenth of a meter, how long is the side of the playground?

*January 24, 2017*

**Geometry probability**

There are 5 blue out of 12 marbles. So, there is a 5/12 chance of drawing a blue marble. That means that in 4 draws, the chance of drawing a blue on the 1st draw only is 5/12 * 7/11 * 6/10 * 5/9 = 35/396 Now, add that to the chance of drawing a blue only on the 2nd, 3rd, of ...

*January 24, 2017*

**Trig**

3 - 1/5 tanx = 16/5 -1/5 tanx = 1/5 tanx = -1 Now recall that tanx is negative in QII and QIV

*January 24, 2017*

**Maths**

well, one revolution is ?d = 14? cm, so ...

*January 24, 2017*

**help with trigonometry??**

draw a diagram. review your basic trig functions. It should be clear that if the height is h, h/112 = tan62°

*January 24, 2017*

**math**

?2.8x+5.6 < 8.4 -2.8x < 2.8 x > -1

*January 24, 2017*

**algebre**

using the law of cosines, 12^2 = 10^2 + 8^2 + 2*10*8 cos? = 164+160cos? BD^2 = 10^2 + 8^2 - 2*8*10 cos? = 164 - 160(-20/160) = 184 BD = 13.56

*January 24, 2017*

**Math grade 6, ratio**

a = 3/7 b = 2/3 a = 2/3 * 3/7 = 2/7 c = 1 - 3/7 - 2/7 = 2/7 b/c = (2/7) / (2/7) = 1 c = 2/3 a = a-49 1/3 a = 49 a = 147 c = 2/3 a = 98

*January 24, 2017*

**Grade 6, ratio**

if there were x 50-cent coins and y dollar coins, then if 6 dollars were replaced with 12 halves, x/y = 3/4 (x-6)/(y+12) = 1/3 clearing the fractions, we have 4x = 3y 3(x-6) = y+12 4x-3y = 0 3x-y = 30 now we see that y=3x-30, so 4x-3(3x-30) = 0 4x-9x+90 = 0 5x = 90 x = 18 So, ...

*January 24, 2017*

**Math**

that is correct.

*January 24, 2017*

**Math**

they add to 90 degrees, so 4x+5x = 90 find x, and then the angles are 4x and 5x

*January 24, 2017*

**Algebra**

1 3/5 and 2 1/2 are both bigger than 1. how can each person eat more than the whole pizza? In any case, 1 3/5 + 2 1/2 = 1 6/10 + 2 5/10 = 3 11/10 = 4 1/10

*January 24, 2017*

**Math**

This just the sum of the first 12 terms of a geometric sequence with a = 3600 r = 1.01 So, 3600 * (1.01^12 - 1)/(1.01-1) = 45,657 Not quite sure how to get your answer.

*January 24, 2017*

**Algebra**

you know that x^a * x^b = x^(a+b) x^(1/2) * x^(1/2) = x^(1/2 + 1/2) = x^1 = x ?x * ?x = x (?x)^2 = (x^(1/2))^2 = x^(2 * 1/2) = x^1 = x

*January 24, 2017*

**Math**

they are equal due to the associative property of multiplication: (a*b)*c = a*(b*c)

*January 24, 2017*

**Calc 2**

Hmmm. Kind of murky. In any case, it's just the chain and product rules. y = ?x e^(x^2) (x^2+1)^10 Recall that if y=uvw then y' = u'vw + uv'w + uvw' So, that would give us y' = 1/(2?x) * e^(x^2) * (x^2+1)^10 + ?x * 2x e^x^2 * (x^2+1)^10 + ?x * e^x^2 * ...

*January 24, 2017*

**Math**

correct. It is shown.

*January 23, 2017*

**Math**

if you mean that the 2nd was sold for 20% more than the first, then if the first sold for x, we have x + 1.2x = 3000 If not, then I'm not sure what each gaining 20% on the other means...

*January 23, 2017*

**Algebra**

half as many workers, so twice as long.

*January 23, 2017*

**Math**

215lb * 1kg/2.2lb = 97.727kg 97.727kg * (4.8mg/day)/kg = 445.091 mg/day 445.091 mg/day * 11ml/16mg = 306ml/24hr = 76.5 ml/(6hr)

*January 23, 2017*

**math**

square roots that end with a decimal?? square roots are called radicals, but so are cube roots, etc. 3?2 = ?18 = ?18.000 not sure where you're going with this.

*January 23, 2017*

**Precalulus**

I am assuming the usual carelessness with parentheses, and getting -2/(-3x-7) - 3/(2x-1) = 3/2 -2*2(2x-1) - 3*2(-3x-7) = 3(-3x-7)(2x-1) 4-8x + 18x+42 = -18x^2-33x+21 18x^2+43x+25 = 0 (x+1)(18x+25) = 0 x = -1 or -25/18 Assuming a little less sloppiness, I'd read (-2/-3)x - ...

*January 23, 2017*

**11th Grade Algebra 2**

just review the techniques of long division. You can see all the details if you play around here: http://calc101.com/webMathematica/long-divide.jsp It's just like regular numeric long division, as long as you line up the powers of x the way you do columns of digits in big ...

*January 23, 2017*

**Math**

you can play around with these things here, and see all the details. http://calc101.com/webMathematica/long-divide.jsp

*January 23, 2017*

**Math**

96/6 = 16 All we know is that the base has an area of 16 ft^2. I'm sure you can some up with two factors of 16 which could be the length and width.

*January 23, 2017*

**MATH @Damon @ms. Sue**

f(x) = 2*3^x on [0,1] the average rate is (f(1)-f(0)))/(1-0) = (2*3^1 - 2*3^0)/1 = 6-2 = 4 on [2,3] the average rate is (f(3)-f(2))/(3-2) = (2*3^3 - 2*3^2)/1 = 54-18 = 36 the ratio of the rates is 36/4 = 9. The reason the rate increases is that exponentials grow ever faster. ...

*January 23, 2017*