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Posts by Reiny

Total # Posts: 38,773

Find the equation of the perpendicular line
steps: - find the midpoint for the given points - find the slope of the line passing through those points - the slope of the line you want is the negative reciprocal of that slope - find the equation using the method you learned.

Standard Form
steps: - find the slope of the line passing through the given points - find the equation using the method you learned.

Specify a Period on the graph
for y = cos(kx), the period is 2?/k apply this to your question

Trig
the way you typed it: 2+1/3tan(theta)=2 1/3tanØ = 0 tanØ = 0 then Ø = 0, 180°, 360°, ... since the period of tanØ = 180°, you can obtain a new answer by simply adding or subtracting multiples of 180° to any answer. did you mean 2 + 1...

math geometry
What method have you learned. There are multiple ways to answer the question, e.g. Heron's formula etc

Geometric Progression.
ar^4 - ar^3 = 13.5 ar^3(r - 1) = 13.5 ** ar^3 - ar^2 = 9 ar^2(r-1) = 9 *** divide ** by *** r = 13.5/9 = 1.5 sub into *** a(1.5)^2 (1.5-1) = 9 a(1.125) = 9 a = 9/1.125 = 8 first term is 8, common ratio = 1.5 or 3/2 check: the terms are: 8, 12, 18, 27, 40.5, ... term5 - term4...

Geometry
Not clear if we want only the lateral surface area or the area including the base. Including the base does not make a not of sense in a storage container for grain, but ... LSA = ?rl, where l is the slant height l^2 = 24^2 + 8^2 l = ?640 LSA = ?(8)?640 = appr 635.81 ---> ...

Math
We have a GS with a = 3600 and r = 1.01 , n = 12 sum(12) = a(r^12 - 1)/(r-1) = 3600(1.01^12 - 1)/.01 = 45,657.01

Geometry
What sphere ?

maths
I am sure you meant: 16x^2- 4x^(x-1) -12 = 0 Wow, what a nasty equation. We have no standard way to handle that one. 16x^2 -12 = 4x^(x-1) by inspection, x = 1 is an obvious solution Let's see what Wolfram can do with it .... http://www.wolframalpha.com/input/?i=solve+16x%...

Math
divide (x^3+7x^2+11x+2) by (x+2) using either long division or synthetic division. or factor (x^3+7x^2+11x+2) , it does

Math
number for George --- x Deb has ----- .4x Tom has 5(.4x) or 2x x + .4x + 2x = 204 solve for x

math
not complete, see your previous post of this

Math
Poor presentation. Each new line should have an equal sign in front. You lost the square root operation in the second line. Secondly, where did the 2 go? Ahhh, it came back in the third line. Hope you see my point. 2?72 + ?32 = 2?36 ?2 + ?16 ?2 = 12?2 + 4?2 = 16?2

Math
number of 2-pointers ---- x number of 3-pointers ---- 74-x 2x + 3(74-x) = 160 solve for x

Math
(-x^2-94x+600)/(x+100) = -(x^2 + 94x - 600)/(x+100) = -(x+100)(x - 6)/(x+100) yup, the divisor is a factor of the dividend. You claim that you know how to do long division. Then your result should have yielded the same conclusion. Mine did.

Math
Yup, there is an error! However, it is a poor question which asks to explain somebody's error Correct way: (x^3-8) = (x-2)(x^2 + 2x+ 4) so ... (x^3-8)(x-2) = (x-2)(x^2 + 2x+ 4)/(x-2) = x^2 + 2x + 4 , x ? 2

Math
Volume of tub = 1.7(1)(.46) = .782 m^3 5075 L per minute for a shower???? A quick google gave me about 8 L per minute for an average shower volume of shower for 16 minutes = 5075(16) litres. ??? (fix that) 1 m^3 = 100^3 cm^3 = 1000 L so .782 m^3 = 782 L Once you have the ...

Calculus
step 1: interchange the x's and y's x = 3 e^(y-1)^5 take ln of both sides ln x = ln3 + (y-1)^5 (y-1)^5 = lnx - ln3 = ln(x/3) y - 1 = (ln(x/3) )^(1/5) y = (ln(x/3) )^(1/5) + 1 check: let x = 2.2 y = 3e^2.48832 = appr 36.123 plug that into second function y = 2.2 My ...

Precalculus
according to your correction we simply have x^6 = (x+1)^6 take 6th root of both sides, since we are taking an even root, x = ±(x+1) x = x+1 or x = -x-1 x = x+1 ---> no solution or x = -x-1 2x = -1 x = -1/2 check: LS = (-1/2)^6 = 1/64 RS = (-1/2+ 1)^6 = (1/2)^6 = 1/64...

Math
you are choosing 2 of the 13 hears and 3 of the 13 spades number = C(13,2) x C(13,3) = 78(286) = 22308 in factorial form: 13!/(2!11!) x 13!/(3!10!) = 13x12/2 x 13x12x11/6 = 22308

Math
sum of 2 : 1 --(1,1) sum of 3 : 2 -- (1,2) (2,1) sum of 4 : 3 -- (1,3) (3,1) (2,2) So sum of 4 or less : 6 of them Then the number of tosses with a sum greater than 4 is 30 (there are 36 possible cases) prob(of your event) = 30/36 = 5/6

college algebra
smaller --- x larger ---- 34-x 2(34-x) - x = 26 easy to solve for x

Trigonometry
or 2x is a 2nd quadrant angle : --> 90° < 2x < 180° 22.5° < x/2 < 45° , which is in quadrant I

calculus
base of box: x by x inches height of box : y inches V = x^2 y 1600 = x^2 y y = 1600/x^2 cost = 3(2x^2) + 5(4xy) = 6x^2 + 20x(1600/x^2) = 6x^2 + 32000/x d(cost)/dx = 12x - 32000/x^2 = 0 for a min of cost 12x = 32000/x^2 x^3 = 8000/3 x = 20/3^(1/3) = appr 13.867 sub that into y...

math
correct A = 25000 e^(.084t) dA/dt = Pr e^(rt) we know r = .084 dA/dt = .084(25000) e^(.084t) = 2100 e^(.084t) when A = 30,000 30,000 = 25,000 e^(.084t) 1.2 = e^(.084t) ln 1.2 = .084t ---> I assume you know log rules t = ln 1.2 / .084 = appr 2.17 Plug that into 2100 e^(.084t)

Math
V = (4/3)? r^3 dV/dt = 4? r^2 dr/dt when r = 6, dV/dt = 5 5 = 4? (25) dr/dt dr/dt = 5/(100?) = 1/(20?) cm/s A = 4? r^2 dA/dt = 8? r dr/dt = 8?(5)(1/100? ) = 2/5 cm^2 /s

math
d = 2p+2 - p = p+2 or d = 5p+3 - (2p+2) = 3p + 1 but those d's must be equal, so 3p+1 = p+2 2p = 1 p = 1/2 which makes d = 1/2 + 2 = 5/2 the terms are: 1/2 , 3, 11/2 , 8 , 21/2 , 13

Maths
By the midpoint theorem, DE = (1/2)AB and DE || AB so we have similar triangles EDC and ABC let the altitude from C to DE be h then by similar triangles the altitude from C to AB = 2h and AB = 2DE area of triangle DEC = (1/2)(DE)h area of triangle ABC = (1/2)(AB)(2h) = (1/2)(...

math
Draw perpendiculars to create a rectangle and 2 congruent right-angled triangles. Look at one of those right-angled triangles. let the missing side be x x^2 + 4^2 = 8^2 x^2 = 48 x = ?48 = 4?3 Let the acute angle of the parallelogram be Ø In the triangle, sinØ = 4...

Algebra2
(fog)(4) = f( g(4) ) , g(4) = -2(4)-6 = -14 = f(-14) = 3(-14) - 7 = -49 or f( g(x) ) = f(-2x-6) = 3(-2x-6) - 7 = -6x - 25 f( g(4) ) = -6(4) - 25 = -49

Algebra2
what is (-2x+4) - (-6x-7) ?

Math
?(x-3) - ?x = 3 ?(x-3) = ?x + 3 square both sides: x-3 = x + 6?x + 9 -12 = 6?x ?x = -2 by definition of ? , this has no solution. proceeding anyway ... square both sides again: x = 4 since we squared, all answers must be verified: if x = 4, LS = ?1 - ?4 = 1 - 2 = -1 ? RS There...

Maths
What is (3/7)(5/9) ?

math
looks like the hyperbola is vertical, so (x-4)^2 /a^2 - (y-2)^2/b^2 = -1 we know b = 3 , (the distance between (4,2) and (4,5) ) 4y-3x=-4 3x - 4y = 4 slope of asymptote = 3/4 that is b/a = 3/4, but b = 3, so a = 4 (x-4)^2 / 16 - (y-2)^2 /9 = -1 confirmation: http://www....

Physics
The three legs of the trip are 70 km , 15 km , and 30 km for a total time of 1 hour average velocity = (70 + 15 - 30)/1 = 55 km/h average speed = (70+15+30)/1 = 115 km/h velocity involves both magnitude and direction. Since the direction was reversed for the last part, I used -30

maths
let log3 x = a and log3 y = b then: 3^a = x and 3^b = y 3^a (3^b) = xy 3^(a+b) = xy (9^(1/2))(a+b) = xy 9^(a+b)/2 = xy log9>/sub> xy = (a+b)/2 can you do anything with that? btw, what does log 9 mean? is 9 the base, as I assumed ? But then the logarithm had no argument. ...

Mathe
Just plug it in. 2(-1) + 5(2) = a evaluate

math
One rotation = 30? inches, you had that 65 miles per hour = 65(63360) inches per 60 minutes = 68640 inches/min number of rotations = 68640/(30?) = 728.3 rotations correct!!!

trig
I will use a sine curve amplitude = 25 so let's start with y = 25 sin t , where t is in seconds period = 16 seconds 2?/k = 16 16k = 2? k = ?/8 so far y = 25 sin ?/8 t we want the lowest point to be +8, so we have to raise the sine curve 33 units so far: y = 25 sin ?/8 t + ...

MATH
Why not just say, x^2 + 2x = 80 ? x^2 + 2x - 80 = 0 (x+10)(x-8) = 0 your number was either 8 or -10 both work

math
Don't "guess" in mathematics, it is a precise language, be sure. x/(45-5x)=1/[5(x-1)] x/(5(9-x)) = 1/(5(x-1)) multiply by 5 x/(9-x) = 1/(x-1) multiply both sides by (x-1)(9-x) x^2 - x = 9 - x x^2 = 9 x = ± 3 so the product of the solutions is -9

Math (Algebra 2)
correct, see my reply to your previous post of this

math
Lisa's present age --- x Richard's present age --- x+6 5 years from now: Lisa ---- x+5 Richard -- x+11 4 years ago: Lisa --- x-4 Richard --- x+2 x+5 + x+11 = 2(x-4 + x+2) 2x + 16 = 4x - 4 20 = 2x x = 10 Lisa is 10 and Richard is 16

Math
The nickel will have two branches. For each of those the die will have 6 branches and for each of those the quarter will have two branches, thus 2x6x2 = 24

Math (Please help!!)
To do these kind of questions, you MUST know how to find the midpoint between two given points. That is what I did to find (7,-5) You must also know that the equation of a line in point slope form for a given slope m and a given point (a,b) is y - b = m(x - a). that is what I ...

Math (Please help!!)
The first thing you would have done of course is to make a sketch, it does not have to be perfect. Secondly, watch your sloppy typing, I will read point B as (4,4) and point C as (18,-8) In the first part, you want the equation of the line BD, where D is on AC, and BD is ...

math
1 km/5 minutes = 1000 m / 300 seconds = 10/3 m/s

Maths
What is 7000(.9)^2 ?

MATH
solve for p, 3p = 15

Álgebra
Easy to translate from English to Math. Let the 2nd number be x and the first one y "The first number is three times the second" y = 3x "The second number is five less than two times the first" x = 2(3x) - 5 -5x = 5 x = 1 then y = 3 The first number is 3 ...

math
I will assume that your question will ask "How many shirts does he have ? " number of shirts ---- x , where x is a whole number (1/2)(x - 4) = (3/10)x times 10 5(x-4) = 3x 5x - 20 = 3x 2x = 20 x = 10

Pre-cal
your graph should look like this http://www.wolframalpha.com/input/?i=plot+y%3D+-2-4sin(%CF%80%2F2(x-1%2F3))

MATH
GOOD GRIEF, Just realized I did this same question a week ago. At least I ended up with the same answer. http://www.jiskha.com/display.cgi?id=1484278204

MATH
Let the perpendicular distance from C to AB meet AB at D vector AB = [9,8,12] equation of plane through C and D having AB as a normal: 9x + 8y + 12z = c but (6,2,3) lies on it , so the plane is 9(6)+8(2)+12(3) = c = 106 plane equation: 9x+8y+12z = 106 equation of line AB: x = ...

Math
LS = sec? - tan?sin? = 1/cosØ - (sinØ/cosØ)sinØ = 1/cosØ - sin^2Ø/cosØ = (1 - sin^2 Ø)/cosØ ---> you had it up to there = cos^2 Ø/cosØ ---> since sin^2 Ø + cos^2 Ø = 1 = cosØ...

math
Should be in your textbook. projection of vector u onto vector v = (u dot v)/|v|

math
use the dot product. [4,4,2] dot [4,3,12] = |[4,4,2]| |[4,3,12]| cosØ 16 + 12 + 24 = ?36 ?169 cosØ 52 = (6)(13) cosØ cosØ = 2/3 Ø = appr 48.19° or .841 radians let u be the projection vector of [4,3,12] onto [4,4,2): cosØ = |u|/|[4...

Math
nope! Area of circle with radius r = ?r^2 so combined area of two of those circles = 2?r^2 twice the circumference = 2(2?r) = 4?r e.g. suppose the radius = 5 cm area of 2 such circles = 2(?(25)) = 50? twice the circumference = 2(2?(5)) = 20? clearly different!

Math
Repeat without typos and with correct grammar.

math
Repeat without typos and with correct grammar. Are we talking about arithmetic or geometric sequences or what?

math - word problem
red apples ---- x green apples ---- x+35 (x+35)/x = 8/3 8x = 3x + 105 .. x =

math
4th term is 3 ---> ar^3 = 3 7th term is 8/9 --> ar^6 = 8/9 divide them: r^3 = 8/27 r = 2/3 in ar^3 = 3 a(8/27) = 3 a = 81/8 GP is 81/8 , 27/4 , 9/2 , 3 , .....

maths calculus also
Two parabolas, one opening up the other down Intersection: x^2 - 2x = 4x - x^2 2x^2 - 6x = 0 2x(x - 3) = 0 x = 0 or x = 3 effective height of region = 4x-x^2 - (x^2 - 2x) = 6x - 2x^2 area = ? (6x - 2x^2) dx from 0 to 3 = [3x^2 - (2/3)x^3] from 0 to 3 = 27 - (2/3)(27) - 0 = 9 ...

MATHS
(x^4 +2x^3 + 3x + 4) by (x^2 +x) , those brackets are essential = (x+1)(x^3 + x^2 - x + 4)/( x(x+1)) = (x^3 + x^2 - x + 4)/x = x^2 + x - 1 + 4/x x^2 + 2x + 8 is an irreducible polynomial because it cannot be factored over the rationals. that is, we cannot find two numbers that...

maths help calculus
A = ? r^2 dA/dt = 2? r dr/dt given: dA/dt = 3 , find dr/dt when r = 2 3 = 2? (2) dr/dt dr/dt = 3/(4?) cm/s

mathss
2 + 3x + 4x^2 + 5x^3 = ?(i+1) x^(i-1) for i= 1 to 4

Maths
(1+x)(1-x) = 1 - x^2 (1+x+x^2)(1-x) = 1 - x^3 (1+x+x^2+x^3)(1-x) = 1 - x^4 mmmhhh??? (1 + x + x^2 + . . . + x^16)(1 - x) = ......

geometry
let the point be (x,y) (?(x^2 + y^2) = 2?(x-3)^2 + y^2) = 0 square both sides x^2 + y^2 = 4(x^2 - 6x + 9) + y^2) x^2 + y^2 = 4x^2 - 24x + 36 + 4y^2 3x^2 + 3y^2 - 24x + 36 = 0 x^2 + y^2 - 8x + 12 = 0 complete the square x^2 - 8x + 16 + y^2 = -12 + 16 (x - 4)^2 + y^2 = 4 indeed ...

math
follow the order of operation (5-2*.5)(4-2*.5)(63) = (5-1)(4-1)(63) = 4(3)(63) = ..

Algebra
smaller number --- x larger number ---- x+4 3(x+4)/x = 4 + 5/x times x 3(x+4) = 4x + 5 3x + 12 = 4x + 5 7 = x the smaller is 7 , the larger is 11 check: 33/7 = 4 with remainder 5 OK, all is good

Pre calc
cos a = 4/5, and a is in quad I Make your sketch and use Pythagoras: x^2 + y^2 = r^2 16 + y^2 = 25 y^2 = 9 y = 3 in quad I so sin a = 3/5 do the same for sin b = -15/17 , b in quad IV x^2 + 225 = 289 x = +8 in quad IV evaluate WHAT expression ? but you now have both sines and ...

Pre-Cal
the centre of this one is (0,0) and the major axis lies horizontally, so x^2/a^2 + y^2/b^2 = 1 ** for such an ellipse: a^2 = b^2 + c^2, but c = 4 a^2 = b^2 + 16 sub back into ** x^2/(b^2+16) + y^2/b^2 = 1 but (4,1) lies on it, so 16/(b^2+16) + 1/b^2 = 1 16b^2 + b^2+16 = b^2(b^...

Math
from x=7t-2 t = (x+2)/7 from y=-4+3t t = (y+4)/3 (x+2)/7 = (y+4)/3 3x + 6 = 7y + 28 3x - 7y = 22 ---> slope = 3/7

math
think of it as y = 0x - 4 and compare it with your famous y = mx + b what do you think?

Math
Did you make your sketch? On mine, I have a triangle with sides 100 and 400 and the contained angle of 135° Using the cosine law: x^2 = 100^2 + 400^2 -2(100)(400)cos135° x = 475.992.. To get the angle opposite the side of 400: sinØ/400 = sin135/475.992.. sin&...

Calculus algebra review
I think you have a typo and you meant: ((1/(2+h)) -(1/2)) / h if so: = ( (2 - 2 - h)/(2(h+2)) / h = -h/(2(h+2))/h = -1/(2h+4)

Math
from the last: 2X+2z= 4 x+z=4 z = 4-x from the first: -X-y-z= -8 z = 8-x-y so 4-x = 8-x-y y = 4 from the 2nd: -4+4y+5z =7 -4 + 16 + 5z = 7 5z = -5 z = -1 then in z = 4-x -1 = 4-x x = 5 x=5, y=4, z=-1

Math
3/6 ? why not just say half of the 24 students are boys? So ....

math
number bought --- n cost price = 50n selling price = 1.2(50)n = 60n 60n = 600 n = 10

Math
Explain what an "over" is.

math
amount of pure acid added ---- x litres .1(2) + x = .2(x+2) 2 + 10x = 2(x+2) 2+10x = 2x + 4 8x = 2 x = 1/4 L

math
I assume you made the simple sketch and translated the angles of depression given to be the base angles of the two right-angled triangle. Let the distance of the hut with the 60° angle be x, let the other distance be y case1: tan60 = 150/x x = 150/tan60 case 2: ..... y = ...

Math
area of smaller = 16 perimeter of smaller = 16 area of larger = 36 perimeter of larger = 24 area of smaller : larger = 16:36 = 4 : 9 perimeter of smaller:larger = 16:24 = 2:3

Algebra
width --- x length ---x+9 2x + 2(x+9) = 62 2x + 2x + 18 = 62 4x = 44 x = 11 the width is 11 and the length is 20 check: 2(11) + 2(20) = 62 , as needed

math
The question seems too simple. Since there are 16 books, you could pick any of them. So 16 different ways to pick a book. Are you sure that that was all it said?

DPS ( Math)
If I understand your question .... 1+2+3+4+...+n = 300 you have an AS with a=1, d=1 sum(n) = (n/2)(2a + (n-1)d) = 300 n(2 + n-1) = 600 n^2 + n - 600 = 0 (n+25)(n-24) = 0 n = 24, since n > 0 term(24) = a + 23d = 1 + 23 = 24

math
let the two numbers be 4x and 7x 4x = 36 x = 9 So what is the larger of the numbers ?

math
So 2/9 of the full tank remain, (2/9)x = 14 x = 14(9/2) = 63 L

AP Calculus
When you say, "I don't understand any of this", I am troubled. This question is as fundamental in beginning Calculus as it gets. Are you taking this course in a traditional classroom setting? What is your background in math that enables you to take Calculus? ...

math
open http://davidmlane.com/normal.html enter 70 into SD click on <above> and enter 850 adjust Mean until you get .16 in the area (probability) window I had 780.39 days as the mean.

Algebra 2
number of dimes ---- x number of quarters --- x-4 equation based on value: 10x + 25(x-4) = 320 etc

Math
How about just using the cosine law? let the distance be x x^2 = 500^2 + 1050^2 - 2(500)(1050)cos 86°

Math
Of course you made a diagram. let the distance to the first connection be x let the distance to the second connection by y x < y from the smaller right-angled triangle: sin55 = x/15 x = 15sin55 from the larger triangle: sin 63 = y/22 y = 22sin63 distance between the two ...

Algebra 2
correct, it is a) another way would be to look at the regions that each defines and see if the point lies in that region. since you only have two boundaries to worry about, that would be quite easy. So sketch y = 3x -1 , (y-intercept of -1 and slope of 3) and y = -x+1 , (y-...

Algebra 2
test your point in each of the cases. I will try c) is 1 > 12-1 and 1 < -4+1 is 1 > 11 and is 1 < -3 I guess not! , so not c) remember , since they use the logical operator "and", both parts must be true

Math
6x +12 + 2cosx = 0 or 2cosx = -6x - 12 No straight-forward or easy way to get a reasonably accurate number. Let's start by looking at the graphs of y = 2cosx and y = -6x-12 http://www.wolframalpha.com/input/?i=plot+y+%3D+2cosx+,+y+%3D+-6x-12 looks like there is a solution ...

help in "logic" needed - Math
I have seen your post several times. Have not answered it since I am not familiar with the topic. The last time I would have seen something like that must be about 55 years ago and it has long since gone into my "delete" part of my memory.

MATH
simply use the "length of line between 2 points" formula. I will do PQ, you do the other two PQ = ?( (7+3)^2 + (3-5)^2 ) = ?(100 + 4) = ?104 = ?4 ?26 = 2?26

math
assuming you mean: 225 ÷ 15[60 ÷ 3|10+18 ÷ (9-7)-14|+11] and the | .. | means absolute value = 225 ÷ 15[60 ÷ 3|10+18 ÷ (2)-14|+11] = 225 ÷ 15[60 ÷ 3|10+9-14|+11] = 225 ÷ 15[60 ÷ 3|5|+11] = 15[20|5|+11] = 15...

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