Sunday
August 30, 2015

Posts by Reiny


Total # Posts: 30,686

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

Math
yes, you got it. it would be x = nπ/2, where n is an integer.
May 1, 2015

Math
since csc Ø = 1/sinØ csc (2x) has asymptotes when sin(2x) = 0 (the amplitude won't matter) sin(2x = 0 then 2x = 0 , ±π, ±2π , ±3π .... x = 0 , ±π/2, ±π, ±3π/2 ... http://www.wolframalpha....
May 1, 2015

Calculus
just notice that 0 < a < 4, so our answers would be the two shown in my solution a = 1.11415714 and a = 2.772605
May 1, 2015

Calculus
no, you were right the first time if y = x + cos(ax) , then dy/dx = 1 - asin(ax) so for a max, asin(ax) = 1 but we are told that x=1 a sin a = 1 sin a = 1/a very hard equation to solve, if you have a good calculator, set it to radians and start trying some values. clearly a &#...
May 1, 2015

math
Let's see how many cubes we can lay along the length, 4.5 ÷ .25 = 18 and along the width, 5 ÷ .25 = 20 and how high can we stock them? 3.75 ÷ .25 = 15 So there would be 18 x 20 x 15 of them or 5400 (and you spent 3 hours on this? not possible!) another...
April 30, 2015

Math 12
A four-of-a-kind is four cards showing the same number plus any other card. If we order the 5-card hand with the four-of-a-kind first, we have C(13,1) choices for the number showing on the first four cards. Since we will have all four suits, we have only C(4,4) = 1 way to ...
April 30, 2015

Math Check
No Prob(first is white) = 4/14 = 2/7 now there are only 13 socks left, so prob(2nd is blue) = 8/13 prob(1st white, then blue) = (2/7)(8/13) = 16/91
April 30, 2015

math homework
that's better, that would simply be 4 x 5 x 2 or 40 ways
April 30, 2015

math homework
This question makes no sense. You say that there are "about" 5 different Star Wars issus, "about" 5 ..... and then you ask for "exactly" how many .... Please clarify.
April 30, 2015

math
Betty ? Kyle ? , please stick to one name No, how can it be simply 40 when the first answer was 59280 ?? You are just guessing and hope that I will give you the solution. Look at my solution for the first one, and tell me why my second multiplier is only 39 instead of 40 and ...
April 30, 2015

math
yes, the first one. How would you do the second one ? How would the solution change ?
April 30, 2015

math
yes, remember there were actually two questions. Which of the two did we answer, and how would you do the other one?
April 30, 2015

math
so there are 40 numbers to pick from. first choice -- 40 2nd choice -- 39 3rd choice -- 38 what is 40*39*38 ?
April 30, 2015

Math
surely you have those in your text or notes. first one: term(n) = a + (n-1)d and you know both a and d term(n) = 4 + (n-1)(8) = 4 + 8n - 8 = 8n - 4 for the second, go to your text, find the formula for term(n) of a GS , and plug in your given values
April 30, 2015

ALGEBRA
part at 4% --- x part at 5% --- 7500-x .04x + .05(7500-x) = 325 after you multiply each term by 100 to get rid of the decimals this is an easy equation to solve. Go for it.
April 30, 2015

ALGEBRA
prob(repair) = 3/100 expected cost = (3/100)($39) = $1.17 cost of agreement = $9.00 so profit per agreement = 7.83 Percentage of profit = 7.83/9 = .87 or 87% (not bad, that is why I never buy these agreements) another way to look at it. Suppose 100 people bought the agreement ...
April 30, 2015

math
First make a sketch, here is Wolfram's version http://www.wolframalpha.com/input/?i=y+%3D+cosx+%2B+1%2Fcosx+for+-%CF%80+to+%2B%CF%80 The vertical lines are asymptotes, and thus will not yield any values. You can see that the min value is appr 2 Here is a larger picture, ...
April 30, 2015

math
1 + 4x + 4x^2 - 16x^4.. ,1 + 2x - 8x^3 - 16x^4.., 16x^4 + 4x^2 + 1 is there a significance to the .. at the end of the first term? if not, then 1 + 4x + 4x^2 - 16x^4 = (1+4x) + 4x^2(1 - 4x^2) = (1 + 4x) + 4x^2(1 - 2x)(1 + 2x) 1 + 2x - 8x^3 - 16x^4 = (1+2x) - 8x^3(1 + 2x^2) 16x...
April 30, 2015

Math
every pair of same factors must be a perfect square and any integer base raised to an even exponent must be a perfect square, so all factors are perfect square except 7^15 which is 7^14 x 7 7^14 is a perfect square, but if I multiply that by 7 it no longer is. we could write ...
April 29, 2015

Please help -_-
Sadie, there was only about 1 hour between the time you first posted this and your second posting. Have some patience, we are volunteers and don't sit here all the time just waiting for questions. In my case I might come here a few times a day, if I see questions ...
April 29, 2015

Calculus-limits
since the power of the numerator is one degree higher than that of the denominator we get y = (9x-x^2-7x^4)/(x^3+12x) = -7x + ?? so as x gets bigger, y gets bigger, so the limit is undefined, (approaches negative infinity, or we can say the limit does not exist
April 29, 2015

easy math
done, always check back before reposting
April 29, 2015

Math
Assuming he picks one topping number = 2 x 16 x 2 = 64
April 29, 2015

mathssss
I will assume you mean: (2c+5)/-5 * (2c+5)/-5 + (4c-2)/5 * (4c-2)/5 = 20 major difference from what you typed, those brackets are critical (4c^2 + 20c + 25)/25 + (16c^2 - 16c + 4)/25 = 20 20c^2 + 4c + 29 = 500 20c^2 + 4c - 471 = 0 solve using the formula
April 29, 2015

math
lw = 60 ---> l = 60/w 2l + 2w = 38 ---> l + w = 19 60/w + w = 19 times w 60 + w^2 = 19w w^2 - 19w + 60 = 0 (w-15)(w-4) = 0 w = 15 or w = 4 , then l = 4 or l = 15 the length is 15 and the width is 4
April 29, 2015

Algebra
always check back before reposting http://www.jiskha.com/display.cgi?id=1430287921
April 29, 2015

Calculus
For any point (a,b) |12a - 9b - 5| /√(144+81) = 2 12a - 9b - 5 = 30 12a - 9b = 35 Now test which ordered pair satisfies this linear equation.
April 29, 2015

algebra 2
no matter what the function f(x) ---> f(x-5) results in a horizontal translation of 5 units to the right look at the graph http://www.wolframalpha.com/input/?i=plot+y+%3D+log%28x%29+%2C+y+%3D+log%28x-5%29+for+0%3C+x%3C30
April 29, 2015

math
arc length of a circle = rØ, where Ø is in radians 5Ø = 10 Ø = 2 radians or appr 114.59°
April 29, 2015

Math
looks like experimental , and the results don't match the theoretical or mathematical probability When rolling a die, the real prob(5) = 1/6
April 29, 2015

Analytic Geometry
given: 4x+3y - 10 = 0 a) easiest way: since the new line is parallel it must look like 4x+3y + c = 0 using your distance formula from a point to a line |4(2) + 3(-1) + c|/√(4^2 + 3^2) = 3 8 - 3 + c = 15 c = 10 4x + 3y + 10 = 0 or -8 + 3 - c = 15 -c = 20 c = -20 4x + 3y...
April 29, 2015

Math
Wasn't there an "experiment" of rolling the dice 160 times? And it came up "2" 39 times So the experimental prob must be 39/160 The theoretical probability is the actual mathematics one, so the "2" is one of the 6 sides, so the experimental ...
April 29, 2015

ALGEBRA
distance = √( (4-(-2))^2 + (-5-3)^2 ) = √(36 + 64) = √100 = 10
April 29, 2015

Algebra
25000(.8)^n = 5000 .8^n = .2 take log of both sides , and using log rules n log.8 = log.2 n = log .2/log .8 = appr 7.2 years
April 29, 2015

Algebra
Choc chip -- 12 oatmeal ---- 12 no-bake ---- 12 peanut butter --12 gingerbread ---12 Sample space = C(60,6) selections of six gingerbread from 12 = C(12,6) prob = C(12,6)/(C(60,6) = .000018456
April 28, 2015

Math
Did you check if the slope between any two points is always the same ? Hint: the point (0,0) is a good point to check in the given equations. Which equation does it satisfy ?
April 28, 2015

Math
I suggest you make a table of sums for 6 rows and 6 columns from the numbers from 1 to 6 Fill in the sums, e.g. the first row and last row would be 2 3 4 5 6 7 .... 7 8 9 10 11 12 count up all the odd ones, obviously 18 of them Remember 2 is a prime number so it must be ...
April 28, 2015

Math
In the first one I think Bob forgot about the other 5 cards that have to be drawn I am going to do these by using combinations P(exactly 2 wild, 5 non-wild) = ( C(8,2) x C(100,5) / C(108,7) = .0756 or using bob's method P(exactly 2 wild, 5 non-wild = 8/108 * 7/107 * 100/...
April 28, 2015

math
make a sketch and let our point needed be (x,y) for the x: (x-(-5))/(6-x) = 2/3 3x + 15 = 12-2x 5x = -3 x = -3/5 for the y: (y+4)/(-2-y) = 2/3 3y + 12 = -4-2y 5y = -16 y = -16/5 your point is (-3/5 , -16/5) or, using vectors (x,y) = (3/5)(-5,-4) + (2/5)(6,-2) = (-3 , -12/5...
April 28, 2015

maths
2a + 2m = 5a + m so m = 3a if 3a = m and m = 2.40 3a = 2.4 a = .8 So each apple costs 80 cents, and a mango $2.40 check: 2apples + 2 mango = 1.60 + 4.80 = 6.40 5apples + 1 mango = 4.00 + 2.40 = 6.40 yes, they are equal My answer is correct
April 28, 2015

mathematics
Kayla, in your solution you defined variables but then never used them Jerry's marbles --- x Tom's marbles ---- 4x Ali's marbles ---- 4x + 36 their sum is 279 x + 4x + 4x+36 = 279 9x = 243 x = 27 Jerry has 27 marbles Tom has 108 marbles Ali has 144 marbles Tom has ...
April 28, 2015

Algebra
10t^5 + 5t^4 - 50t^3 = 0 t^3( 2t^2 + t - 10) = 0 t^3(2t+5)(t-2) = 0 t = 0 or t = -5/2 or t = 2
April 27, 2015

Algebra
well, you created the perfect square on the left, so state it , and simplify the right side (x - 3/8)^2 = -39/64 ahhh, I see the problem. How can anything squared be negative, so there is no REAL number solution. Have you studied complex numbers? If so, then x - 3/8 = ±...
April 27, 2015

Algebra
repeat the procedure I just showed you, tell me what you got.
April 27, 2015

Algebra
divide by 2 and bring constant to the right side x^2 - 3x + .... = 18 x^2 - 3x + 9/4 = 18 + 9/4 (x - 3/2)^2 = 81/4 x - 3/2 = ± 9/2 x = 3/2 ± 9/2 x = -3 or x = 6
April 27, 2015

College Algebra
You defined x as the price, but did not use it as such I will re-define x as the number of $1 increases new price = (100+x) number of rooms rented = 95-x Revenue = R(x) = (100+x)(95-x) = 9500 - 5x - x^2 R ' (x) = -5 - 2x = 0 for a max of R(x) 2x=-5 x = -2.5 I will assume ...
April 27, 2015

Calculus
the hardest part is finding the intersection of the two curves, x^2 - 1 = cosx I will let Wolfram do it: http://www.wolframalpha.com/input/?i=x%5E2+-+1+%3D+cosx Because of the symmetry we could go from 0 to 1.1765 and double the answer area = 2 ∫(cosx - x^2 + 1)dx from 0...
April 27, 2015

Math 222
Stop switching names and stick to one name only -x^2 - 3x + 5 = 0 x^2 + 3x - 5 = 0 use the quadratic formula x = (-3 ± √29)/2
April 27, 2015

The villages
I will take a giant leap of faith and assume you want it simplified, (x+3)/(x^2-2x-8)- (x-5)/(x^2-12x+32) = (x+3)/((x-4)(x+2)) - (x-5)/((x-4)(x-8)) LCD is (x-4)(x+2)(x-8) = [(x+3)(x-8) - (x-5)(x+2)]/((x-4)(x+2)(x-8) ) = ... expand the top and simplify / (x-4)(x+2)(x-8)
April 27, 2015

Algebra
Now: Dana ---- x Renee --- 2x 4 years ago: Dana = x-4 Renee = 2x-4 "Four years ago Renee was three times as old as Dana" ---> 2x-4 = 2(x-4) solve for x, very straight-forward
April 27, 2015

Math, please help
insufficient data
April 27, 2015

Math
−22.75 cos (π/6(m − 1)) + 52.55 = 48 -22.75 cos ((π/6)(m-1)) = -4.55 cos ((π/6)(m-1)) = .2 ((π/6)(m-1)) = 1.369438... or ((π/6)(m-1)) = 4.9137459.. m-1 = 2.61543.. or m-1 = 9.38456.. m = 3.615435 or m = 10.38457 adding/subtracting 2π ...
April 27, 2015

Math help!
hint: multiply each term by 6x and rearrange.
April 27, 2015

Math help!
x of the vertex is -b/(2a) -----> good formula to memorize = -(-16)/(4) = 4 f(4) = .... so now you have the vertex. easy to read off the max/min and the axis of symmetry. for x intercept let y = 0 in y = 2x^2 - 16x + 27 for y intercept let x = 0 in y = 2x^2 - 16x + 27 ...
April 27, 2015

Math help!
miles on the highway --- x miles in the city ----- 465-x gallons used on highway = x/24 gallons used in city = (465-x)/18 x/24 + (465-x)/18 = 23 multiply each term by 72 , the LCD 3x + 4(465-x) = 1656 3x + 1860 - 4x = 1656 -x=-204 x = 204 Miles on the highway were 204 check: ...
April 27, 2015

Math help!
number of dimes ---- x number of quarters -- 43-x 10x + 25(43-x) = 760 etc.
April 27, 2015

polynominals
1975 ---> x = 5 y = 5^2 + 3(5) + 2 = 42 million repeat for the other years (silly question, assumes the number of trout keeps increasing, e.g. in 2020 we would have 50^2 + 3(50)+2 or 2652 million trout)
April 27, 2015

probability
3 red 2 green 4 white 2 purple ---> total = 11 let's do the prob that she had the 3 reds number of such choices = C(3,3) x C(8,5) = 56 number of choices of 8 from 11 = C(11,8) = 165 prob(all 3 reds) = 56/165 so prob(not all the reds) = 1 - 56/165 =109/165
April 27, 2015

Math 222
Was not meant to be scarcastic, simply trying to figure out the best way to explain it, there are several ways.
April 27, 2015

Math 222
first equation: -5x + 2y = 16 subbing in y = 2x+7 ----> -5x + 2(2x+7) = 16 -5x + 4x + 14 = 16 -x = 2 x = -2 now put that back into y = 2x+7 = 2(-2) + 7 = 3 all done curious, at what grade level are you taking this?
April 27, 2015

Math 222
-5x+2y=16 y = 2x+7 Tika, Doesn't the 2nd equation tell you what the value of y is ?? Just replace the y in the 2y of the first equation with the value of y in the second. Give it a try, it is really easy. Let me know what you got.
April 27, 2015

Math
since sinØ = opposite/hypotenuse = -3/5 you should recognize the 3-4-5 right-angled triangle. You are also told the the angle (or triangle) is in the I, II, or IIIrd quadrant. But isn't sinØ negative only in III of those given? so x = -4, y= -3 thus tan&...
April 27, 2015

Math 222
solve each one separately if you want 2x-1 ≥ -3 2x ≥ -2 x ≥ -1 4x+5 ≥ -19 4x ≥ -24 x ≥ -6 but they are connect with AND, so ... x ≥ -1 AND x ≥ -6 Now thing about, what numbers are both greater than or equal to -1 AND -6 Place the...
April 27, 2015

MATH
This question makes little sense to me. Are the times given based on how long each one could row the boat? Why would you let Dale row for 10 minutes, if Abby ran do it it 1 minute? Anyway, taking your data at "face-value" .... A=1 B=2 C=5 D=10 I would use A for all ...
April 27, 2015

Math 222
rate charged by first mechanic --- x rate charged by second mechanic -- y "sum of their rates is 165" ---> x+y = 165 "first mechanic worked 10 hours" ---> 10x "the second mechanic worked 5 hours" --- 5y "Together they both charged a ...
April 27, 2015

Math 222
-2x + 9y = 3 -3x - 4y = 22 first equation times 3 -6x + 27y = 9 second equation times -2 6x + 8y = -44 add the new equations: 35y = -35 y = -1 sub back into original -2x + 9y = 3 -2x - 9 = 3 -2x = 12 x = -6 x= -6 , y = -1 of course you should realize that there are many other ...
April 27, 2015

Math 222
Both our last two replies posted at the same time. NO, both numbers are NOT 12 Look at your question, it said one is 23 less than the other, how can they be both 12 ? This is why definitions of your variable are so important. I defined by smaller as x, so it is 12 I defined by...
April 27, 2015

Math 222
yes, that would be one of the answers, remember it asked for two answers. You should verify your answers against the original conditions to eliminate any doubt
April 27, 2015

Math 222
smaller number --- x larger number ----- x+23 x + x+23 = 47 easy to solve....
April 27, 2015

math
How did you decide it was B ?
April 27, 2015

Statistics PLEASE HELP
prob(both defective) = (2/8)(1/7) = 1/28 prob(at least one good) = 1 - 1/28 = 27/28
April 27, 2015

math
True , the surface area of similar objects is proportional to the square of the sides (1/2)^2 = 1/4
April 26, 2015

Math
multiply each term by 3 3y + 9 = x x - 3y - 9 = 0
April 26, 2015

calculus check
correct
April 26, 2015

Calculus
how about L'Hopital's Rule limit = 7/( (1/2)(x+4)^-(1/2) ) = 14(√(x+4) = 14(2) as x---> 0 = 28
April 26, 2015

Calculus
number ' (t) = 100e^t + 75t number (t) = 100e^t + (75/2)t^2 + c assuming at opening (t=0) no people were in the zoo, 0 = 100e^0 + (75/2)(0) + c c = -100 number(t) = 100e^t +(75/2)t^2 - 100 so when t = 2.666.. (at 9:40 am) number(2.666...) = 100e^2.6667 + 37.5(2.666..) - ...
April 26, 2015

Analytic Geometry
slope of 1st line = (-2-6)/(5+1) = -8/6 = -4/3 slope of 2nd line = (7+4)/(1-3) = -11/2 angle made by 1st line = tan^-1 (-4/3) = 126.87° angle made by 2nd line = tan^-1 (-11/2) = 100.30° angle between them = 26.565° or tan(angle between) = (-4/3 + 11/2)/(1 + (-4/3...
April 26, 2015

algebra
9(x^2 - 8x + ....) + 4(y^2 + 4y + ....) = -124 9(x^2 - 8x + 16) + 4(y^2 + 4y + 4) = -124 + 144 + 16 9(x-4)^2 + 4(y+2)^2 = 36 divide each term by 36 (x-4)^2 /4 + (y+2)^2 /9 = 1
April 26, 2015

Math
18sin^2 Ø +3cosØ - 17 = 0 18(1- cos^2 Ø) + 3cosØ - 17 = 0 18 - 18cos^2 Ø + 3cosØ -17 = 0 18cos^2 Ø - 3cosØ -1 = 0 (6cosØ + 1)(3cosØ - 1) = 0 cosØ = -1/6 or cosØ = 1/3 Ø = 1.738.. or &...
April 26, 2015

math
Sales of the $12000 which are over $5000 = $7000 so total commission = .06(5000) + .12(7000) = ..
April 26, 2015

math
Let the side parallel to the highway be y ft let each of the other two sides be x ft So 2x + y = 680 y = 680-2x area = xy = x(680-2x) = 680x - 2x^2 which is a parabola opening downwards, and you want its vertex. Since you are doing this type of question, you must have learned ...
April 26, 2015

calculus
integral of (3x^2+2x+4) dx f(x) = x^3 + x^2 + 4x + C given (f(1) = 10 10 = 1 + 1 + 4 + C C = 4
April 26, 2015

Calculus
need their intersection: x^2 - 4x + 3 = x + 4 x^2 - 5x - 1 = 0 was hoping for "nicer" values, but anyway.... x = (5 ± √29)/2 height of our region within those x values = x+4 - (x^2 - 4x + 3) = 1 + 5x - x^2 area = ∫(1 + 5x - x^2)dx from x = (5-&#...
April 26, 2015

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