Sunday
April 20, 2014

Posts by Reiny


Total # Posts: 26,034

Algebra
change in record sales = 4683 - 14000 = -9317 change in time = 11 years rate of change = -9317/12 = -776 records/year I included the years 1987 and 1998 .

math
I count 7 months, so rate of change per month = (800 - 1050)/7 = - $35.71 balance is declining at a rate of appr $36 per month

trig
let AP be the vector of magnitude 23 lbs and direction 18° and BP be the vector of magnitude 27 lbs and direction -15° Complete the parallogram APBQ , with AP=2 BP=27 angle P = 33° then angle B = 180-33 = 147° So PQ is the force pulling by the puppy to hold the...

Precalculus
sure, After sketching in all the angles, and doing some arithmetic, I have a triangle with sides 30 and 40 and the angle between them as 10° let the resultant be R R^2 = 30^2 + 40^2 - 2(30)(40)cos10° = 900+1600-2400cos10° = 136.46.. R = √136.46 = 11.68 , whic...

Quick math help
use the first 2 points to find the slope How is the slope of your new line related to this slope ? follow the method I just used in the previous reply to your other question. Let me know what you get.

Quick math help
Slope of given line = 2/8 = 1/4 so the slope of the new line = -4 y = -4x + b , but (4,5) is on it, so ... 5 = -4(4) + b b = 21 y = -4x + 21

Math
profit = 25x - 10x, where x is the number they sell = 15x They want to make a profit of 1000 15x = 1000 x = 1000/15 = 66 2/3 So they must sell 67 cups check: for 67 cups: revenue = 25(67) = 1675 expenses = 10(67) = 670 profit = 1675 - 670= 1005 cents or $10.05 for 66 cups prof...

Quick math help
When the slope of the line changes its sign, that would be a reflection in the y-axis There are many different kinds of reflections, the above is just one of them so y = 3x - 2 ----> y = -3x - 2 , a reflection in the y-axis now down 3 y = -3x-2 - 3 or y = -3x - 5

Quick math help
what kind of reflection ?

Quick math help
f(x) = -6x -10 + 6 = -6x - 4

math
Solving implies that you have an equation. You don't have one. If you mean simplify .... (x^3 y)^2 /(8x^(1/3)) , notice I put brackets in so it makes sense = x^6 y^2 / 2x^(1/3) = (1/2) x^(17/3) y^2 (certainly does not "look" any more simplified)

Precalculus
resultant = 30(cos200, sin200) + 40(cos10, sin10) = (-28.19-10.26) + (39.39 , 6.946 = (11.20 , -3.315) magnitude = √(11.20^2 + (-3.315)^2) = 11.68 miles bearing: tanØ = -3.315/11.2 = ... Ø = 343.5°

Algebra
number of units sold --- x profit = 5x - 1.7x = 3.3x 3.3x = 33000 x = 33000/3.3 = 10000

Math - Oh my gosh please help!
Since this is supposed to be an approximation, I see three days with 4 km each and two days with 2 km each total = appr 16 km so appr 16 km in 5 days or about 3 km/day 32 km in 10 days 96 km in 30 days 100 km in about 31 days

algerbra
Since the + and = signs are on the same key, I suspect you meant 3x-2y = 8 2x+2y = 22 ---->x+y=11 --->y = 11-x sub into the 1st 3x - 2(11-x) = 8 3x - 22+2x = 8 5x = 30 x = 6 then y = 11-6 = 5

calculus
Not sure how your "sign chart" method works, I will solve it the traditional way. x^2 - 2x +6 < 0 Just looking at the graph of y = x^2 - 2x + 6 we can tell that there is no solution. http://www.wolframalpha.com/input/?i=Plot+y+%3D+x%5E2+-+2x+%2B+6

math
I will assume the left side is supposed to be absolute value ... |3x+12| ≥ 21 3x+12 ≥ 21 OR -3x-12 ≥ 21 3x ≥ 9 or -3x ≥ 33 x≥ 3 or x ≤ -11

Algebra
And I also came up with the same answers.

math - trig
The angle of elevation is 350 ??? I suspect a typo. Did you mean 35° ? Correct your typo, then set it up like I showed you in the previous post.

math - trig
Always make a sketch. draw a horizontal showing 250 ft below the water line mark it as 1500 draw a vertical at the end of the horizontal to show the depth of the dive, label it x label the angle of the dive as 15° Now, in relation to the Ø, isn't the horizontal ...

math - trig
tanØ = 2059/5280 = ... Ø = 21.3°

mathematics
The way you typed it, I would let f(x) = 3x - (1/2)x f(x) = (5/2)x , and there would be only that one term I suspect you have a typo, Please clarify before I do it.

algebra
Since the = and the + signs are on the same key , I will assume you meant: 4x + 5y = 7 as the given line. Since the new line must be parallel to the given one, it will differ only in the constant new line: 4x + 5y = c but (3,2) lies on it, so 12 + 10 = c = 22 4x + 5y = 22 or y...

math
1/2 mile jogged : 3/4 mile walked = 1 mile jogged : 3/2 miles walked = 2 miles jogged : 3 miles walked or .5 : 75 = 50 : 75 = 2 : 3

alegbra
P(1.03)^30 = 50000 P = 50000/1.03^30 = 20599.34 the same as yours. No idea why they wont' take it

College Algebra
Minding my p's and q's, I would say: if p = 3q in p = q+4 3q = q+4 2q = 4 q = 2 then p = 6

College Algebra
look at the top two "related Questions" below

math
Don't know about the screaming, but here it is when it made sense to me http://www.jiskha.com/display.cgi?id=1358210190

6th grade math
1,2, and 3 are ok #4 has the right answer, but I don't like the way you stated your solution First of all, don't put equal signs in front of each new line when solving. Youre 2nd last line has no relation to the problem, what happened to the 5 ? here is how I would wri...

math
let the 3 pieces have length: 3x, 5x, and 7x 3x + 5x + 7x = 33 3/4 inches = 135/4 15x = 135/4 x = 9/4 I will let you finish the rest, just 3 multiplications.

business math
c ' (x) = -.001 - 2000/x^2 = 0 for max/mins -.001 = 2000/x^2 x^2 = 2000/.001 = a negative. that is not possible, so there are no max or min points Here is a picture of your problem http://www.wolframalpha.com/input/?i=plot+y+%3D-0.001x%2B2%2B2000%2Fx

Mathematics
25th term = 7 1/2 a + 24 d = 15/2 sum of first 23 terms = 98 1/2 (23/2)(2a + 22d) = 197/2 23(2a+22d) = 197 2a+22d = 197/23 a+11d = 197/46 subtract the two equations 13d = 15/2 - 197/46 = 74/23 d = 74/299 sub back into first equation a + 24(74/299) = 15/2 a = 933/598 so sum of ...

Calculus
as you can see from the graph, they do not intersect, so we simple take the integral from 1 to 2 area = ∫ e^x - x dx from 1 to 2 = [e^x - x^2/2] from 1 to 2 = e^2 - 2 - (e^1 - 1/2) = e^2 - e - 3/2

Calculus
Here is a sketch http://www.wolframalpha.com/input/?i=plot+y+%3D+x%5E2+−+4x+%2B+1+and+y+%3D+−x%5E2+%2B+4x+−+5 Easy to find their intersection points: (1, -2) and (3, -2) effective height between x = 1 and x = 3 = (-x^2 + 4x - 5) - (x^2 - 4x + 1) = -2x^2 +8x -...

College Algebra
prob(2 i's, no replacement) = (2/11)(1/10) = 1/55

College Algebra
I counted 11 letters in the given word, of which two of them were b's so Prob(b) = 2/11

math
slope = (difference in the y values)/(difference in the x values), make sure you subract in the "same direction" slope = (-2 - 7/3)/(3/2 - (-3) = (-6/3 - 7/3)/(3/2 + 6/2) =(-13/3) / (9/2) = (-13/3)(2/9) = -26/27 by subtracting in the same direction .... we could have...

go with Steve -Trigonometry
I made an error in multiplying the two i terms go with Steve's solution

Trigonometry
Your question makes little sense. I see no equation. Are you attempting to use De Moivre's theorem? (0.9644+1.0342 i)(0.0349+2 i) = .03366 + 1.9649 + .0361 i^2 = -.00244 + 1.9649 = 1.9649( cossØ + i sinØ) where tan Ø = 1.9649/-.00244 Ø = appr 90...

GEOMETRY CIRCLES
#2 Notice the centre of the inscribed circle must lie on the bisectors of the angles. We have an isosceles triangle, with sides 10,10 and 12 If we place the triangle on the x-y grid, we can have the base from (-6,0) to (6,0) and the third vertex on the y-axis. The y-axis becom...

GEOMETRY CIRCLES
1. Make a reasonable sketch. draw radii to A and B Triangle ABO is isosceles with sides 52 , 52 , and 96 By the cosine law we can find cosA 52^2 = 52^2 + 96^2 - 2(96)(52)cosA cosA = 96^2/(2*52*96) = 12/13 In triangle AMO MO^2 = 33^2 + 52^2 - 2(33)(52)cosA = 1089 + 2704 - 3432(...

Parametric equations/Trigonometry - Lattice points
x = 30 - 40cost ---> cost = (30 - x)/40 y = -50 + 30cost --- cost = (y+50)/30 (y+50)/30 = (30-x)/40 40y + 200 = 900 - 30x 30x + 40y = 700 3x + 4y = 70 So your graph is simply a straight line with x -intercept of 70/4 or 17.5 and y-inercept of 70/3 or 23 1/3 draw the line fo...

Trigonometry
http://www.wolframalpha.com/input/?i=plot+r+%3D+%3D+4%281-cos%28theta%2Bpi%2F4%29%29

Math
And what have you got so far? BTW, the ellipse should be an equation of the type (x+3)^2/12 + (y-2)^2/16 = 1

Math
let the 4 consecutive intergers be x-1, x , x+1 and x+2 (x-1)(x) -2 = 3(x+1)(x+2) x^2 - x - 2 = 3x^2 + 9x + 6 2x^2 + 10x + 8 = 0 x^2 + 5x + 4 = 0 (x+1)(x+4) = 0 x = -1 or x = -4 case 1: the numbers are -2, -1, 0, and 1 or case 2: the numbers are -5, -4, -3, and -2

Math
y = 5(x^2 + (1/25)x + 1/2500 - 1/2500) - 10 = 5( (x + 1/50)^2 - 1/2500) - 10 = 5(x + 1/50 )^2 - 1/500 - 10 = 5( x + 1/50 )^2 - 5001/500 vertex i (-1/50 , - 5001/500)

math
g(2) = 3(2) - 5 = 1 since g(2) = 1 f(g(2)) = f(1) = 2(1) + 1 = 3

math
You can't get an answer. Division by zero is undefined. Here is a little experiment. Take your calculator and divide 5 by .001 then by .0001 then by .00000001 notice you are dividing by a number which is getting close to zero, but is still NOT zero What do you think should...

Calculus
2x = -2y dy/dx dy/dx = -x/y at (3,4) dy/dx = -3/4 differentiate again, 2 = -2y (d^2 y/dx^2) + (dy/dx)(-2dy/dx) 2 = -2y (d^2 y/dx^2) - 2(dy/dx)^2 2 = -2(4)(d^2 y/dx^2) - 2(9/16) (d^2 y/dx^2) = (2 + 9/8)/-8 = -25/64 or y^2 = 25-x^2 y = (25-x^2)^(1/2) dy/dx = (1/2)(25-x^2)^(-1/2)...

calculus
dy/dx = 2x at (a,a^2) , dy/dx = 2a equation of tangent: y - a^2 = 2a(x-a) at 2,1) 1 - a^2 = 2a(2-a) 1 - a^2 = 4a - 2a^2 a^2 - 4a + 1 = 0 let's complete the square: a^2 - 4a + 4 = -1 + 4 (a-2)^2 = 3 a-2 = ± √3 a = 2 ± √3 or let point of contact be ...

Math-Precalculus-Parametric Equations - Ellipses
(x-h)^2 /a^2 + (y-k)^2 /b^2 = 1 we know that sin^2 t + cos^2 t = 1 so let cos^2 t = (x-h)^2/a^2 cos t = (x-h)/a and let sin^2 t = (y-k)^2 / b^2 sin t = (y-k)/b from (x-h)/a = cos t x-h = acos t x = h + a cos t from (y-k)/b = sin t y-k = b sin t y = k + b sint thus: x=h + acost...

Algebra 1 (Reiny or Kuai)
I usually pick values of x near the origin of the x-y grid e.g. x = 0 , ± 1, ± 2 , ±3 since you know it is a straight line, you really only need 2 points. But, I usually take a third point as a check: x=0 , y1 - 0 , y2 = 6 x = 1 y1 = 1 , y2 = -1+6 = 5 x = ...

Help me pls geometry
Since perimeter is a linear function of the sides and the two triangles are similar, the ratio of sides = the ratio of perimeters so P/168 = 25/60 P = 168(25/60) = 70

CALCULUS!!!!!
done, check your earlier post

Differential Calculus
place ship B 65 miles east of ship A and mark them that way. Let the time passed be t hrs Draw a line BP , so that P is between A and B showing the distance traveled in those t hours. Draw a line downwards AQ showing the distance traveled by ship A. Join PQ to get the right-an...

Trigonometry
8 cis 240° = 8(cos 240° , i sin240° = 8(-1/2 , -√3/2) = (-4 , -4√3)

math
bobpursley and anne both gave you a solution to this question You even thanked them both. http://www.jiskha.com/display.cgi?id=1386205975

Trigonometry
They must be imaginary, I don't see them

Trigonometry
They must be imaginary, I don't see them

typo - Statistics
near the end it should say: So now we have 4 cases hobbits believing in neither one = .65 hobbits believing in both = .09 hobbits believing in only elves = .19 hobbits believing in only ents = .07 add them up to get 1

Statistics
conditional probability: prob (ents given elves) = prob(endts | elves) = prob(elves AND ents)/prob (elves) prob(ents | elves) = .09/.28 = .3214 prob (2hobbits believing in elves) = (.28)(.28) = .0794 They do add up to 1 if you add up ALL possible cases, you added up only 3 A g...

Math
incomplete Where did they start, which way did they go ?

Algebra 2
y = (x-1)(x-2)(x-3)(x+3) = (x-1)(x-2)(x^2 - 9) =(x^2 -3x+2)(x^2-9) = x^4 - 3x^3 - 7x^2 + 27x - 18

math
let there be x ducks at the start x - 28 + 7 = 43 x = 43 - 7 + 28 = 64

Pre calculus
I promise you that no physical harm will come to you when you use either one of these harmless procedures.

Trigonometry
The tangent has a period of 180°, the others listed have periods of 360° (2π)

Algebra
Annuities imply that there are periodic payments. Do you want the present value of an annuity of $8000? I will assume that. PV = 8000( 1 - 1.06^-10)/.06 = $58,880.07

Math - Linear Algebra
1st one times 2 2x - 8y - 6z = -36 2nd -2x + 8y + 7z= 41 add them z = 5 sub into 1st x - 4y - 15 = -18 x - 4y = -3 x = 4y - 3 let y = 0 , x = -3, z = 5 ---> point (0,-3,5) let y = 2 , x = 5, z = 5 ---> point (2,5,5) so direction of line of intersection is (2, 8, 0) using...

Math
the x value for the vertex of f(x) = -3x^2 + 5x + 8 is -5/-6 = 5/6

GEOMETRY CIRCLES PLEASE
1. Make a sketch by placing the triangle on the x-y gird so that the altitude falls along the y-axis with (0,12) the top of the triangle and (0,) the middle of the base. Look at the righ-angled triangle in the first quadrant. You know the hypotenuse is 13 and the height is 12,...

Math
oops , typo 6 x 60cents = $3.60

Math
volume = π(1.5)^2 (4) = 9π cubic inches volume of new jar π(3^2)(6) = 54π cubic inches which is 6 times the original So the new one should cost 6(.60) or $3.00

Trigonometry
vector v is [ √3/2 , -√3] parallel to [ 1 , -2] vector w = [4√3 , 4] parallel to [ √3 , 1 ] using dot product definition √3 - 2 = (√5)(√4)cosØ cosØ = (√3-2)/(2√5) Ø = 93.4° or doing it as is: cos&Os...

math
Step 1 ---- graph both relations let me know what you get

Math
let the medians intersect at F, so we have 90° angles at F Remember that the medians intersect at the centroid and the centroid divides each median in the ratio of 2 : 1, the longer side towards the vertex So let FE = x, then AF = 2x let FD = y, then FB = 2y In triangle AF...

Math
C must be the right angle. You have 3 similar triangle, the original and 2 smaller ones let the altitude be h 2/h = h/16 h^2 = 32 h = √32 in the smaller right-angled triangle h^2 + 2^2 = BC^2 BC^2 = 32 + 4 = 36 BC = 6 In the other right-angled triangle: AC^2 = h^2 + 16^2...

math
amount = 20000( 1.05^20 - 1)/.05 = .. I will let you do the button-pushing on your calculator

Math
Did you mean 2x - 5y = -8 for the first one ? I will assume that is what you meant: Personally I would not use substitution, but .... from the 2nd 26-3x = 2y (26-3x)/2 = y into the 1st: 2x - 5(26-3x)/2 = -8 times 2 to get rid of that fraction ... 4x - 5(26-3x) = -16 4x - 130 +...

calculus
The function crosses the origin so I see it as A = ∫ x(x^2+16)^(1/2) dx from 0 to 3 = [ (1/3)(x^2+16)^(3/2) ] from 0 to 3 = (1/3)(25)^(3/2) - 0 = (1/3)(125) = 125/3

Easy Statistics
prob(Joe not at work) = .51 prob(Joe not at home) = .75 prob(joe not at work and not at home) = (.51)(.75) = .3825 = 38% Don't know how they got 39%

algebra
36x - 3y = 3 reduce to 12x - y = 3 or y = 12x -3 There are an infinite number of solutions pick any x you feel like, then evaluate the corresponding y e.g. x = 1 y = 12(1)-3 = 12-3 = 9 x = -3.56 y = 12(-3.56) -3 = -45.72 etc. To have the instruction: "Determine X and Y&qu...

Math :)
The probabilities are correct your total should be the total of the probabilities. 5/10 + 3/10+2/10 = 10/10 = 1 If the total is supposed to be the total of prob's don't say 10 , it is 10/10 or 1

math
" ... as shown " ????

Math
Ok, Xian, I will answer no more until you show me some work of your own, or give some indication where your problems lie.

Math
find the circumference of the wheel. Find the circumference of the circuit, multiply it by 12 , then divide by the circumference of the wheel change everything to metres. Since you are in the metric system, this is very easy to do.

Math
D1/D2 = 5/9 D1 = √(5^2 + 8^2) = √89 so √89/D2 = 5/9 5D2 = 9√89 D2 = 9√89/5 notice that the diagonal increased by a factor of 9/5 or the same as the increase in the sides.

Math
the three circles can cut each other in 6 different points (think of a typical Venn diagram) A line can cut a circle in 2 point so each line can cut all the circles in 6 points so total = 6 + 6 + 6 = 18 BUT, let's not forget that the two lines can also intersect so the tot...

asking for a teacher's opinion
I would never want to presume that I could accurately evaluate a student totally objectively even in a subject like Mathematics. We conducted a workshop in our Math Department once, where we each marked the same paper each marker given the same "marking scheme" . Mar...

Math
call them b , for "big" and s for "small" so you have 6 b's and 2 s's prob = (6/8)(5/7)(4/6) = 120/336 = 5/14

Math
prob all three defective = (.04)^3 = .000064 My question to you: What would it be if he had not returned the clocks after checking them?

Advanced Functions/Precalculus
1. since cscØ = 1/sinØ if sin Ø = 0 , the cscØ = 1/0 since we cannot divide by zero, and 1/0 is undefined csc 0 is undefined Here is a graph of y = csc x for about 4 periods the vertical lines are asymptotes, and shows where the cscx is undefined. t...

Trigonometry - Geometry - side lengths
joint BD, and use the cosine law twice, once for each triangle we know AB = DC = 180 let angle A be Ø let AD = a and BC = b BD^2 = a^2 + 180^2 - 2(180)a cosØ BD^2 = b^2 + 180^2 - 2(180)bcosØ a^2 + 180^2 - 360a cosØ = b^2 + 180^2 - 360b cosØ a...

Algebra 2
the way you typed it, multiply each term by 2 x^2 + 4x + 6 = 0 complete the square ... x^2 + 4x + 4 = -6+4 (x+2)^2 = -2 x+2 = ± √-2 x = -2 ± i√2

For Sam - math
Even if tossing around a few numbers often yields the "correct answer", the statements must be mathematically correct and logically sound look at your statement: 3/5 = 2+4 , now that is news to me, I always thought 2+4 is 6 and not 3/5 Do you see what I mean ? .........

math
tan E = y/x = (4/5) / (3/5) = 4/3

Algebra
in standard form we usually lead with the x term with a positive coefficient, so I wanted a +x as my first term, it was -x . to change a standard form to slope- yintercept form usually takes 2 steps: 1. move all terms except the y term to the right e.g. 4x - 5y = 8 ---≥ ...

Algebra
your slope is correct as +1 your equation of y+1 = 1(x+2) is also correct then y+1 = x+2 y = x+1 ---> slope-yintercept form y-x = 1 x - y = -1 ----> standard form ( I multiplied each term by -1)

math
first round: x --> 3x --- >3x-2 2nd round: 3x-2 ---> 9x-6 ---> 9x-8 3rd round: 9x-8 ---> 27x - 24 ---> 27x - 26 27x - 26 = 271 27x = 297 x = 11

math question grade 8!!
Wow, those rooms are pretty small even for a doll-house.

Math - Calculus I
Draw a side view of the situation (The cone will look like an isosceles triangle with a rectangle (the cylinder) sitting on its base and touching the sides) let the radius of the cylinder be r and let the height of the cylinder be h Look at the small right-angled triangle at t...

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