Wednesday
May 27, 2015

Posts by Reiny


Total # Posts: 30,069

algebra
any horizontal line has equation y = c , where c is the y element of your given point so y = -3 or, the long way: slope of a horizontal line is 0 , then y = 0x + b plug in the given point(5,-3) -3 = 0(5) + b b = -3 y = 0x - 3 y = -3
May 12, 2015

Algebra
f(x) = 3x - 1 f(0) = 3(0) - 1 = -1 f(3) = 3(3) - 1 = 8 f(z) = 3z - 1
May 12, 2015

Math
2(x+2)+4x-10x use distribution for the first part = 2x + 4 + 4x - 10x now combine like terms = -4x + 4
May 12, 2015

math
(2^2)(2^8) = 2^10 so B is the correct answer
May 12, 2015

No - math help please
It asked for the coefficient of x, which is -7 What you gave is the coefficient of x^2 the correct answer is D
May 12, 2015

Math
btw, I have a typo, the equation should have said: ax + by + c = 0
May 11, 2015

Math
Little tricks that can come in handy ... For a linear equation ax^2 + bx + c = 0 the slope is -a/b so the slope of the given line is -3/-2 = 3/2 thus the slope of the new line must be -2/3 But your choice of D has a slope of 3/2, so it can't be D so write the given choices...
May 11, 2015

math
C) So in effect, the radius of one revolution is 42 cm, and one rotation is 84pi. Multiply 84pi by the number of rotations
May 11, 2015

math
use the property: ln(e^x) = x 2 = 1 e^(kt) ln 2 = kt t = ln2/k , replace k with the given value
May 11, 2015

maths
a = 1 , r = -4 you are showing 6 terms, so sum(6) = a(r^6 - 1)/(r-1) = 1((-4)^6 - 1)/(-4-1) = 4095/-5 = -819
May 11, 2015

Pre-calculus ( Absolute value)
you might plug in x = 5, but x=5 does not satisfy the equation, so it is not a solution. So what if both sides are positive. We know by definition that x-1 > 0 or x>= 1 7+3x = x-1 or -7-3x = x-1 2x = -8 or -4x = 6 x = -4 or x = -3/2 subbing either one of these does not ...
May 10, 2015

math
... at a rate of 5 inches/hr sounds like a linear rate of change. I will assume that the radius is changing at that rate V = (4/3)pi r^3 dV/dt = 4pi r^2 dr/dt dV/dt = 4pi(100)(5) = 2000pi cubic inches/hr
May 10, 2015

maths
= 2sqrt(5) - sqrt(5) + 3sqrt(5) = 4sqrt(5)
May 10, 2015

Trigonometry
RS = (1/2)(cosacosb + sinasinb - (cosacosb - sinasinb) = (1/2)(2sinasinb) = sinasinb = LS
May 10, 2015

Probability
the second differences are a constant so the relationship is quadratic. the the equation be y = ax^2 + bx + c when x = 1 a+b+c = 20 when x=2 4a+2b+c = 17 when x = 3 9a+3b+c = 13 subtract 1str from 2nd 3a+b=-3 subtract 2nd from 3rd 5a + b = -4 now subtract those last two: 2a...
May 10, 2015

Maths
the angle between the two directions is 162-25 or 137 Use the cosine law, let the distance between them be d d^2 = 10^2 + 6^2 - 2(10)(6)cos137 = ...
May 10, 2015

Linear Functions
sketch somethink like y = 2x + 3 (m>0, b>0 ) and see what you get
May 9, 2015

Linear Functions
e = .04s + 200 see which of your choices match that
May 9, 2015

Math
(I don't have my calculator with me, so I will describe the method) - find the length of the diagonal of the base using Pythagoras - take half of that length (the midpoint of the base) - use tan^-1 (147/half-length of diagonal)
May 9, 2015

college precalculus I still dont get it
To be an arithmetic sequence, the difference between any term and its previous term is a constant. e.g. 3, 5, 7, 9 , ... the common difference is 2 To be geometric, if you divide any term by its previous term you will get a common ratio, e.g. 3, 12, 48, ... 12/3 = 4, 48/12 = 4...
May 9, 2015

math
a) exclude the case where none are cracked Prob(none are cracked) = C(30,0)(.05)^0 (.95)^30 = .... b) follow the above pattern to get Prob(none) + prob(one broken) + prob(two broken) = ..... + C(30,1) (.05)^1 (.95)^29 + .... = ....
May 9, 2015

algebra
go with Steve, I messed up, right side is .60(20)
May 9, 2015

algebra
amount of 40% stuff --- x L amount of 85% stuff --- 20-x L .4x + .85(20-x) = .60x
May 9, 2015

Calculus(URGENT PLS!!!)
how about -e^cosx + c (differentiate it to test my answer)
May 8, 2015

Calculus - Derivative
2x + r(y)^(-1/2) dy/dx = x dy/dx + y dy/dx (r(y)^(-1/2) - x) = y - 2x dy/dx = (y - 2x)/(r(y)^(-1/2) )
May 8, 2015

Math - Polynomials
1. The way you typed it should give us 15g + 10k 2. D 3. B Hope you weren't just guessing
May 8, 2015

maths
the difference between 17^2 and 13^2 is 120. the next perfect square is 121 So we have to add 1
May 8, 2015

7th grade math (probability)
1-3 are correct #4. you should have divided 4 by 1/6 to get 24 "3" was the event, it happened 4 times, so 4 is the important number last one , I did not check the actual entries, but there are 24 of them
May 8, 2015

Calculus
here is a picture of what we are doing http://www.wolframalpha.com/input/?i=plot+y%3D+x%5E%281%2F3%29+%2C+y+%3D+x%2C+y+%3D+1 clearly y = x and y = x^(1/3) intersect at (0,0) and (1,1) so outer radius = R = x-1 -->R^2 = x^2-2x+1 inner radius = r = x^(1/3) - 1) --> r^2 = x...
May 7, 2015

Calculus
V = π∫(y^2) dx from a to b = π∫x^4 dx from 0 to 3 = π[x^5/5] from 0 to 3 = π(243/5 - 0) = 243π/5 cubic units
May 7, 2015

maths
I see a common factor of 10^7 (5x10^7)+(2.3x10^7) = 10^7(5 + 2.3) = 7.3 x 10^7 your answer should have said 73 x 10^6 In general a number in scientific notation should be a number between 1 and 9 multiplied by a power of 10 so 73 x 10^6, although correct in its value, is not ...
May 7, 2015

Math Please Check My Answer
From you data it looks like you made 69 choices, thus prob(pink) = 36/69 = 12/23 prob(brown) = 33/69 = 11/23 comparing: theoretical prob(pink) = .5125.. experimental prob(pink) = .5217 not bad
May 7, 2015

Math
let the base be x by x cm let the height be y xm Volume = (1/3) r^2 h = 216 r^2 h = 648 h = 648/r^2 pick any r, let's say r = 10, then h = 648/100 = 6.48 cm pick x = 12 cm, then h = 648/144 = 4.5 cm As you can see, there is not enough information. as it stands the ...
May 7, 2015

XD
Suppose it took Alice 4 hrs, when she finished Alice went at 6 km/h Becky went 16 km at 4 km/h Caitlin went 12 km at 3 km/h So for Becky to finish her remaining 8 km would take an extra 2 hrs, but in 2 hrs Caitlin only went 6 more km of her remaining 12 km, so she still has 6 ...
May 6, 2015

XD
So the total water they have is 2 + 1 3/4 gallons = 15/4 gallons or 3.75 gallons So in effect 3.75 gallons cost $2.00 1 gallon would cost 2/3.75 = .53... so James should receive 2(.5333...) or $1.07
May 6, 2015

Calculus
did you find their points of intersection? x^2 - 2x = x+4 x^2 - 3x - 4= 0 (x-4)(x+1) = 0 x = -1 or x = 4 effective height of region = x+4 - (x^2 - 2x)= 3x + 4 - x^2 area = [integral] (3x + 4 - x^2) dx from -1 to 4 = [(3/2)x^2 + 4x - (1/3)x^3] from -1 to 4 I will leave the ...
May 6, 2015

Pre-Calculus
1-|200+||-2|(-5)^3|| 1-|200+||-2|-125|| = 1-|200+||-2(125)| = 1-|200+||-250| = 1 - |200 + 250| = 1 - 450 = -449 I think your |'s are confusing
May 6, 2015

algebra--1 question
This is called the factor theorem. If the division by some binomial leaves a remainder of zero, then that binomial is a factor the same is true for numbers. e.g. 12÷3 = 4 with Remainder of 0 so 3 is a factor of 12 12÷5 = 2 with remainder of 2, so 5 is NOT a ...
May 6, 2015

Calc
How do you expect us to know what "table of integrals" you are using ? It is up to you to find the pattern of the given question in your tables.
May 6, 2015

Math
for the mean, add them up and divide by 5 for the sd: take the difference between each of the data values and the mean and square that result repeat for all 5 of them add them up, divide by either 5 or 4 depending on the definition of sd you are using, take the square root. ...
May 6, 2015

Algebra
term4 = a+3d = 15 term10= a+9d = 39 subtract them 6d = 24 d = 4 in a+3d = 15 a + 12 = 15 a = 3 term40 = a+39d = ... sum40 = (40/2)(2a + 39d) = ...
May 6, 2015

Trig
if sinA = 12/13, and since the since is + A must be in II using our standard 5-12-13 triangle, cosA = -5/13 if sinB = -7/25, to state -90 ≤ B ≤ 90 is ambiguous, since you could be on the right or the left of the y-axis I will assume B is in III , (could be in IV) ...
May 6, 2015

math
cost of 6 vans at the end of 4 yrs = 148800 i = .03 n = 4(4) = 16 P(1.03)^16 = 148800 solve for P
May 6, 2015

Math Help
the parabola is vertical, and opens downwards standard form x^2 = 4py but vertex is (-1,2) (x+1)^2 = 4p(y-2) but p = -2 (x+1)^2 = -8(y-2) (x+1)^2 = -8y + 16 8y = -(x+1)^2 + 16 y = (-1/8)(x+1)^2 - 2 for the 2nd , use y^2 = 4px and follow the above steps
May 6, 2015

Calculus
y ' = sec^2 ((1 - x)^(1/2) ) (1/2)(1-x)^(-1/2) (-1) clean it up to whatever level you need it simplified.
May 6, 2015

Calc 1
f ''(x) = 6+cosx f '(x) = 6x + sinx + c f (x) = 3x^2 - cosx + cx + k f(0) = 1 0 - cos 0 + 0 + k = 1 -1 +k= 1 k = 2 so f(x) = 3x^2 - cosx + cx + 2 f(7π/2) = 0 3(7π/2)^2 - cos(7π/2) + (7π/2)c +2 = 0 solve for c, plug into the f(x) equation and you...
May 6, 2015

Math/algebra
ok, then you know f + t = 70 or t = 70-f recall that the equation said: 5f + 10t = 595, which we reduced to f + 2t = 119 replace t with 70-f f + 2(70-f) = 119 f + 140 - 2f = 119 -f = -21 f = 21 so she has 21 fives. Can you take it from there ?
May 5, 2015

Math
several ways: if x = (2 ± √5)/3 then the factors are (x - (2 +√5)/3) and (x - (2 - √5)/3) then (x - (2 +√5)/3)(x - (2 - √5)/3) = 0 ( x - 2/3 - √5/3)(x - 2/3 + √5/3) = 0 x^2 - 2x/3 + x(√5/3) - 2x/3 + 4/9 - 2√5/9 - x&#...
May 5, 2015

Math
e.g. in 5x^2 + 7x - 18 a=5 b=7 c=-18 Your question is poorly worded a stands for the coefficient of the x^2 term b stands for the coefficient of the x term c stand for the constant
May 5, 2015

math
let the total be x A got (3/7)x = 3x/7 B got (2/3)(3x/7) = 6x/21 = 2x/7 C got 3x/7 - 49 3x/7 + 2x/7+ 3x/7 - 49 = x times 7 3x + 2x + 3x - 343 = 7x x = 343 A has 147 B has 98 C has 98 ratio of B:C = 1:1
May 5, 2015

Math
you are saying there are 3 points on the graph, but the table shows 4 points. mmmhhh? anyway: take the slope of all possible pair of points, what do you get ?
May 5, 2015

Algebra
f stands for the number of $5 bills, so by saying f = 5, you are saying there are five $5 bills. It does not say that anywhere ---------- let f be the number of fives let t be the number of tens so the VALUE of our fives = 5f and the VALUE of our tens = 10t 5f + 10t = 595 ...
May 5, 2015

Math - 7th grade
Good job, I agree with all your answers
May 5, 2015

Calc 1
let the point of contact be (x,y) or (x, -6sinx) Then for a tangent, slope = m = (-6sinx - 0)/(x-0) = -6sinx/x m = (-6sinx - 0)/(x-0) = -6sinx/x dm/dx = (x(-6cosx - (-6sinx))/x^2 , by quotient rule = 0 for a max/min -6xcosx + 6sinx = 0 xcosx - sinx = 0 xcosx = sinx x = sinx/...
May 5, 2015

Math
You are using the word "combinations" so it would be C(5,3) or 10 of them e.g. suppose you have A, B, C, D, E kind of trees ABC ABD ABE BCD BCE CDE ADE ACE BDE ACD
May 5, 2015

math
To form a triangle, the sum of any two sides must be greater than the remaining third side checking for a) is 17+13> 2 ? Yes is 17+2 > 13 ? Yes is 13+2 > 17 ? NO So 17,13,2 cannot form a triangle Repeat for the others.
May 5, 2015

Algebra Readiness
actually the correct table is C e.g. look at the first one x = -5 y = -5 - 6 = -11 try the others.
May 5, 2015

math
So the angle between them is 72° They both travel for 2 hours, so the 1st went 30 km, and the 2nd went 4 km This is just a cosine law question .... x^2 = 30^2 + 4^2 - 2(4)(30)cos72 = 841.83.. x = appr 29.01 km or, using the fact that the 2nd boat was directly north of the ...
May 5, 2015

Math
That would only be true if the height is equal to the radius
May 5, 2015

Algebra (Slope)
parallel lines have equal slopes, so slope = (6-4)/(2-3) = -2
May 5, 2015

Maths
I did this for you Always check back before reposting the same question.
May 5, 2015

Analytic Geometry
let the new point be (x,y) I will assume you mean XZ = 4XY by simple ratio: for the x's (x+1)/(4+1) = 4/1 x+1 = 20 x = 19 for the y's (y-2)/(11-2) = 4/1 y-2 = 36 y = 38 Z is (19,38) check: XY = √(5^2 + 9^2) = √106 XZ = √(20^2 + 36^2) = √1696 = 4...
May 5, 2015

algebra
speed of freigh --- x speed of passenger ---- x+6 time for passenger to go 330 miles = 330/(x+6) hrs time for freight train to go 300 miles = 300/x hrs but the times are the same 330/(x+6) = 300/x 330x = 300x + 1800 30x = 1800 x = 60 state the conclusion
May 5, 2015

Geometry
By definition of "obtuse", one of the angles must be greater than 90 So if all 3 angles would be obtuse, their sum would be greater than 270° But we know that the total sum of all 3 angles = 180° So, silly conclusion. As a matter of fact , a triangle can have...
May 5, 2015

math
nice problem: b) the easiest, just sub in (5,5) to show it works a) since y = 7x, sub the y into the circle equation x^2 + (7x)^2 = 50 x^2 + 49x^2 = 50 x^1 = 1 x = ± 1 if x=1 , y = 7 , call that A(1,7) if x = -1 , y = -7 , call that B(-1, -7) c) slope AC = (5-7)/(5-1...
May 5, 2015

Maths Problem
let the side of the larger square be x let the side of the smaller square be y 1. x^2 + y^2 = 65 2. y > 1/2x 2y > x initial thought: 65 must be sum of 2 squares, 8 and 1 immediately come to mind but 2(1) is not greater than 8 how about 7 and 4 ? is 7^2 + 4^2 = 65 ? YES ...
May 5, 2015

geometry
Which sides are parallel ?
May 5, 2015

math
i = .0825 n = 6 amount = 27000(1.0825)^6 = .....
May 5, 2015

math
number of total choices = 3 x 3 x 2 = 18 number of choices with yellow or green tofu and tea = 3 x 2 x 1 = 6 prob(stated event) = 6/18 = 1/3
May 5, 2015

college precalculus
i = .06/12 =.005 n = 8(12) = 96 P(1.005)^96 = 2000 solve for P
May 5, 2015

trigonometry
Clive probably meant: (1+sin 2A)/cos 2A = (cosA + sinA)/(cosA - sinA) LS = (sin^2 A + cos^2 A + 2sinAcosA)/(cos^2 A - sin^2 A) = (cosA + sinA)/( difference of squares) = ... I am sure you can take it from there
May 5, 2015

Algebra
original: 10 cm by 20 cm after cutting x cm at the corners new length = 20 - 2x new width = 10 - 2x height = x volume = x(10-2x)(20-2x) , 0 < x < 10
May 4, 2015

math
B worked for all of them when I tried it.
May 4, 2015

math
I would try subbing in the points e.g. (0,5) works in A,B, and D only (1,4) works in B try if the others work in B well ???
May 4, 2015

math
If it even works, the largest number must be the hpotenuse, so e.g. R is 26^2 + 20^2 = 46^2 ? test the others.
May 4, 2015

math
height/30 = sin60 height = 30sin60 = ....
May 4, 2015

math
2 fracture each third ?? I have no idea what that means.
May 4, 2015

Math
1. f(x) = x^2 - 3x + 2 for f(-2), put in -2 wherever you saw an x f(-2) = (-2)^2 - 3(-2) + 2 = 4 + 6 + 2 = 12 you are correct 2. correct again.
May 4, 2015

math 0312
speed in still water ---- x rate upstream = x-9 , where x is clearly > 9 rate downstream = x+9 17/(x+9) + 17/(x-9) = 13 times (x+)(x=9) or x^2 - 81 17(x-9) + 17(x+9) = 13(x^2 - 81) 17x - 153 + 17x + 153 = 13x^2 - 1053 13x^2 - 34x - 1053 = 0 x = (34 ± √55912)/26...
May 4, 2015

Math 222
is that g(x) = √x - 1 or g(x) = √(x-1) ? make a table of values, pick some x's , find the y's and plot the points
May 4, 2015

Math
A. for Carmen to run 3 times, Susan runs 4 times around the track for Carmen to run 1 times, Susan runs 4/3 around for Carmen to run 12 times, Susan runs 12(4/3) or 16 times around the track (notice that this is a straight ratio thing)
May 4, 2015

Further mathemactics
tan^2 Ø - sin^2 Ø = sin^4 Ø sec^2 Ø LS = sin^2 Ø/cos^2 Ø - sin^2 Ø = (sin^2 Ø - sin^2 Ø cos^2 Ø)/cos^2 Ø , using a common denominator. = (sin^2 Ø - sin^2 Ø(1 - sin^2 Ø)/cos^2 &...
May 4, 2015

trig
I assume you are solving this equation. btw, sec by itself is meaningless, since it is an operator, thus it needs an argument that's like saying 3 + √ = x anyway.... -2sec x = 3 sec x = -3/2 cosx = -2/3 the cosine is negative in quads II and III using my calculator ...
May 4, 2015

math functions
All three are correct #3 is correct assuming you are starting with n = 1
May 4, 2015

Math
Very simple LS = sin^2 x - cos^2 x = sin^2x - (1-sin^2 x) = 2sin^2 x - 1 = RS
May 3, 2015

math
Angles do not have area.
May 3, 2015

trigonometry
Did you not read my post? I told you how to do it.
May 3, 2015

trigonometry
let's just tackle the LS LS = sin(A+B)*sin(A-B) = (sinAcosB + cosAsinB)(sinAcosB - cosAsinB) = sin^2 Acos^2B - cos^2Asin^2B , the difference of squares pattern = (1 - cos^2A)(cos^2B) - cos^2A(1-cos^2B) = cos^2B - cos^2Acos^2b - cos^2A + cos^2Acos^2B = cos^2B - cos^2A = RS ...
May 3, 2015

Math
done look back when you posted it earlier
May 2, 2015

trigonometry
one rotation is 2π so -31π/6 ÷ 2π = -5 - π/6 so we have 5 clockwise rotations and another clockwise of π/6 (remember in trig, counterclockwise is positive and clockwise is negative) or consider the rotations in degrees 31π/6 radians = 930&...
May 2, 2015

trigonometry
Since arctan and tan are inverse operations, then logically arctan(tan(-31π/6)) = -31π/6 however .... since it probably wants the angle closest to the origin, and since tan(-31π/6) = tan(-π/6) arctan(tan(-31π/6) = arctan(tan(-π/6) = -π/6
May 2, 2015

Math - Trigonometry
Ls = 1/cosx - cos^2 x/cosx = (1-cos^2 x)/cox = sin^2 x/cosx = sinx sinx/cox = sinx tanx = RS How can you change 1/cosx - cosx to 1/cosx - cosx/cosx ?? you can't just toss in an extra cosx at the bottom that last term of cosx/cosx would reduce to 1
May 2, 2015

Math - Trigonometry
I have helped you with two of these now. I think it is time for you to try them. Hint: on the LS, find a common denominator and add the two terms Show me your steps and I will help you from there.
May 2, 2015

Math - Trigonometry
This one's really easy ... RS = sin^2 x - cos^2 x = sin^2 x - (1 - sin^2 x) = 2sin^2 x - 1 = LS
May 2, 2015

Math - Trigonometry
LS = 1/sinx + 1/cosx = (cosx + sinx)/(sinxcosx) = (cosx + sinx)(1/sinx)(1/cosx) = (cosx+ sinx)(cscx)(sec) = RS
May 2, 2015

Calc 1
Wasn't your tangent line supposed to pass through the origin?
May 2, 2015

algebra
well, let's just take the slope using the 2 given points slope = (y-2)/(3-1) = (y-2)/2 but we are told that the slope is 2 , so (y-2)/2 = 2 y-2 = 4 y = 6
May 2, 2015

algebra
what is (1/2)(1/2)(1/2) ?
May 2, 2015

Math Calc
You will need the vertex of this parabola I don't know what method you learned , so I will use the simplest way not using Calculus for y = ax^2 + bx + c, the x of the vertex is -b/(2a) so for yours, t = -112/-32 = 3.5 sub that back in to get the maximum height. when it ...
May 1, 2015

math
What is the question? Is this supposed to be an equation looking like 3x^2 - 27x^2 + 60x = 0 ?
May 1, 2015

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