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Posts by Reiny

Total # Posts: 38,320

Calculus
let the point of contact be P(a,b) let A be (1,7) slope of AP = (b-7)/(a-1) the closest point would be where the tangent at P is perpendicular to AP 2y dy/dx = 1 dy/dx = 1/(2y) so at P, the slope of the tangent is 1/(2b) so (b-7)/(a-1) = -2b b-7 = -2ab + 2b -b = -2ab + 7 2ab...

math
In a parallelogram Abcd angle add ??? side an ???? e ????? x+y ???? wow!

Math
Just follow the definition: a*b means 3a^2+b 3*1 means 3(3^2) + 1 = .....

Math
number correct --- x , 0 ? x ? 20 number wrong ---- y number skipped ---- 20-x-y 5x - y + 0 = 72 y = 5x - 72 y ? 0 if x = 14, y = -2 , not possible if x = 15 , y = 3 , skipped = 2 if x = 16, y = 8 , not possible , x+y>20 so he got 16 right, 8 wrong, and skipped 2 check: 5(...

Math
not arithmetic nor geometric gave up and checked with Wolfram found: term(n) = (7(3^n) - 3)/6 http://www.wolframalpha.com/input/?i=pattern+%7B3,+10,+31,+94%7D quite obscure, perhaps more terms would have helped.

Math
mmmhhhh when x=1 , 3+2x = 3+2(1) = 5 when x=2, 3+2x = 3+2(2) = 7 when x = 3 ..... continue

Math
number of girls --- x number of boys --- (5/11)x x - (5/11)x = 114 (6/11)x = 114 x = 114(11/6) = .... take over

Math
1:2:1/2 = 2:4:1 -----> ratios usually are not expressed in fraction form let their shares be 2x, 4x, and x but x = 48 so 2x = 96 and 4x = 192 add them up

Calculus
You did not do exactly the same, your slope was -3/5, different from mine. (another example of why I prefer traditional class room instructions, where the learning of math is not just "answer based" )

Calculus
How did you get the slope to be -3/5 ?? let the x-intercept be A(a,0) and the y-intercept be B(0,b) label point (3,5) as P By ratios in similar triangles: (a-3)/5 = 3/(b-5) ab-5a-3b+5 = 15 b(a-3) = 5a b = 5a/(a-3) Area of triangle = (1/2)ab = (1/2)(a)(5a/(a-3) ) = 5a^2/(2a-6) ...

Math
right now: x + 7x = 976 x= 122 Aaron has 122 cards and Ben has 854. after the give-away of k cards: ben has 854-k Aaron has 122+k Aaron has 3 times as many as Ben 122+k = 3(854 - k) 122+k = 2562 - 3k 4k = 2440 k = 610 check: after the exchange Ben has 854-610 = 244 Aaron has ...

Maths
3^9 + 3^12 + 3^15 + 3^n = 3^9(1 + 3^3 + 3^6 + 3^(n-9) ) = 3^9(757 + 3^(n-9)) 3^9 is a perfect cube, so all we need is (757 + 3^(n-9)) to be a perfect cube, clearly n >9 perfect cubes past 757 with 3^(n-9) as the 2nd number: 1000 243 <---- well, that was lucky 1331 574...

Calculus
let the height be h then h^2 + b^2 = 20^2 h = (400-b^2)^(1/2) Area = (1/2)(bh) = (1/2)(b)(400 - b^2)^(1/2) d(Area)/dt = (b/2)(1/2)(400-b^2)^(-1/2) (-2b db/dt) + (1/2)(db/dt)(400 - b^2)^(1/2) = -b^2 (db/dt)/?(400-b^2) + (1/2)(db/dt)?(400-b^2) when b = 11 and db/dt = 4 d(Area)/...

math
number of ways to give the fruits = 5!/(3!2!) = 10 (you could list them) Bananas at least two days in a row: BABAB is the only case where two or more B could not be together. Look at your list from above prog(at least two B's in a row) = 9/10

maths
Susan's age now ---- x Mary's age now ------3x Three years ago: Susan ---- x-3 Mary ----- 3x-3 x-3 + 3x-3 = 22 continue

Algebra
good road ---- x km poor road ----- 48-x km time on good road = x/72 time on poor road = (48-x)/48 x/72 + (48-x)/48 = 3/4 times 144 , the LCD 2x + 3(48-x) = 108 carry on, easy from here

Maths
without a calculator... let a=20142014 then 20142015 = a+1 then 20152015 = a + 1 + 1000 = a+1001 then 20152014 = a+1000 20142015×20152014 – 20142014 ×20152015 = (a+1)(a+1000) - a(a+1001) = a^2 + 1001a + 1000 - a^2 - 1001a = 1000

Algebra
2x^3 - 5x^2 - 5x - 1 = 0 let f(x) = 2x^3 - 5x^2 - 5x - 1 try f(1) = 2 - 5 - 5 - 1 ? 0 try f(-1) = -2 - 5 + 5 - 1 ? 0 try f(1/2) = 1/4 - 5/4 - 5/2 - 1? 0 try f(-1/2) = -1/4 - 5/4 + 5/2 - 1 = 0 , yeahh! so (2x + 1) is a factor and x = -1/2 by long algebraic division, which I ...

Math -fractions word problems
total number of students ---- x number of boys ----- (3/7)x number of girls ------(4/7)x (4/7)x = (3/7)x + 4 times 7, the LCD 4x = 3x + 28 x = 28 boys: (3/7)(28) = 12 girls = 28-12 = 16

intergrated science
I will assume that Calculus is part of your integrated science course. a = 2 then v = 2t + c at the beginning of the observation, t = 0 , v = 24 so 24 = a(0) + c ----> c = 24 v = 2t + 24 when t = 8 v = 2(8) + 24 = 40 m/s or, simply .... for each of the 8 seconds the ...

calculus
your values of x = -2, 3 are the x-intercepts, and you don't need a derivative to find them dy/dx = (x-3)(2/3)(x+2)^(-1/3) + (x+2)^(2/3) = (1/3)(x+2)^(-1/3) [2(x-3) + 3(x+2)] = (1/3)(5x)(x+2)^(-1/3) = 0 for a max/min of y ----> 5x = 0 or (x+2)^(-1/3) = 0 ---> no way ...

math- Trigonometry
I agree with Scott. For the given date, the calculations are correct. In reality, the question is absurd. Using Pythagoras, the height of the lighthouse would have to be appr 8.9 km high. and, using our given angle of 65.91..° tan 65.91 = height/4 height = 4tan 65.91 = ...

Math
or 15 machines 15 minutes to make 500 raviolis 75 machines 15 minutes to make 2500 raviolis 75 machines 15(2.4) minutes to make 2500(2.4) raviolis 75 machines 36 minutes to make 6000 raviolis (the 2.4 comes from 6000/2500)

maths
I assume you are solving? from the 2nd: y = -2x-4 sub into the first 3x - 2(-2x - 4) = 1 3x + 4x + 8 = 1 7x = -7 x = -1 back into y = -2x - 4 y = -2(-1) - 4 = -2 x = -1 , y = -2

Math
Assuming that x is the length of the missing parallel side ... area of trapezoid = (x+15)(10)/2= 5x + 75 area of triangle = (1/2)(15)(10) = 75 5x + 75 < 2(75) 5x < 75 x < 15 but clearly x has to be positive 0 < x < 15 looks like a common sense type of question ...

finite math
mortgage after downpayment = 140,000 i = .09/12 = .0075 n = 30(12) = 360 payment = p p(1 - 1.0075^-360)/.0075 = 140000 p(124.2818657.) = 140000 p = $1126.47

finite math
Follow the same steps I just showed you here http://www.jiskha.com/display.cgi?id=1478848733

Math
1/6 of the 3/2 pepperoni's remain or 1/4 this is (14)/4 or 1/16 of the original amount

Math
distance covered in one rotation = 25? inches 65 miles/hr = 65*12*5280 inches/hour = 65*12*5280/3600 inches/sec number of rotations = 65*12*5280/3600 ÷ (25?) = 14.56.. / sec or appr 15 rotations per second check: distance in 1 second = 14.56*25? = appr 1143.5 inches = ...

Statistics
prob(ace) = 4/52 = 1/13 prob(5 aces with card replaced each time) = (1/13)^5 = ....

Math
did you notice that the third difference is 3 ? So it is a cubic messing around a bit I got term(n) = (n^3 - n^2 - 4)/2 so term(6) = (216 - 36 - 4)/2 = 88

math
68/104 = 17/26 This question has two correct choices as answers. Poorly designed question.

matha
What part of my previous reply to your same question did you not like ? http://www.jiskha.com/display.cgi?id=1478784506

Math
This year: number of middle schoolers --- 2x number of high schoolers ----- 7x but 2x = 18 x = 9 So this year there are 18 middle schoolers, and 63 high schoolers. Total = 81 Since all we know from the previous year is the ratio of 1:8 , and there were more last year: possible...

Math
I have no idea what that first part of your post is supposed to be. your problem: 53+59+65+...+233 We have to know how many terms. a=53, d=6, n= ? term(n) = a + (n-1)d 233 = 53 + 6(n-1) 180 = 6n - 6 6n = 186 n = 31 sum(31) = (31/2)(first + last) = (31/2)(53+233) = 4433 which ...

Math
(Log75+log9+log5)÷(log5+log45) = log(75*9*5) / log(5*45) = log 3375 / log 225 = log(25*9*15) / log(25*9) = log(5^2 * 3^2 * 15)/log(5^2 * 3^2) = log( 15^2 * 15) / log (15^2) = (log 15^2 + log 15)/ log 15^2 = (2log15 + log15)/(2log15) = 3log15/(2log15) = 3/2 I think I ...

math
After eliminating all the weird symbols, I got: Triangle ABC is a right triangle with right angle at A. Suppose AX is an altitude of the triangle, AY is an angle bisector of the triangle, and AZ is a median of the triangle, and angle XAY = 13°. If X is on BY, then what is ...

Math
let the sides be 2x, 3x, and 4x (notice 2x:3x:4x = 2:3:4 ) but 2x = 15 find x, then sub into my definitions

Algebra
one number ---- x the other ------(1/2)x x + (1/2)x = 18 double each term 2x + x = 36 continue

matha
I think you missed a zero in the original value, if the present value is 1,000,000, then after a 5% depreciation you have 95% left or 950,000. Insert or delete the zero as needed.

Math grade 6, 4 operations
Let the number of years be x 10+x + 7+x = 41 2x = 41 - 17 2x = 24 x = 12 It will happen in 12 years. check: in 12 years: Deepak will be 22 his brother will be 19, the sum will be 41

Math grade 6, 4 operations
Retype your question in English please.

Maths
Translate into English. "One-fourth of the sum of a number and seven is four less than three times the number." If the number is x (1/4)x + 7 = 3x - 4 x/4 - 3x = -11 times 4 x - 12x = -44 -11x = -44 x = 4

math
how about 3457 ?

math
4-8 -(-2) -17 = -4 + 2 - 17 = -2 - 17 = -19

math
17(1/2)^(t/5730) = 10 (1/2)^(t/5730) = 10/17 take log of both sides and use rules of logs (t/5730) log .5 = log10 - lot17 t/5730 = (1 - log17)/log.5 t = 5730(1 - log17)/log .5 = appr 4387 years

statistic
enter your data http://davidmlane.com/normal.html

Algebra- Word Problem
your second equation: 4x + 2y = 56 2x + y = 28 2x+y = 28 x+y = 40 subtract: x = -12 you are correct, the question is bogus!

Math algebra
amount of water added ---- x gallons .6(2500) + 0.0x = .25(2500 + x) solve for x

Math
rate = distance/time = 3(.25)miles / 4.5 min but 4.5 min = 4.5/60 hrs = .0075 hrs = .75/.0075 mph = 10 mph

maths
n = 5 payment --- p i = .06 p(1.06^5 - 1)/.06 = 30000 I get p = $5321.89

Algebra 2
It appears that there are at least 3 numbers let the first be x then the second is x+2 and the third is x-4 x + x+2 + x-4 ? 30 3x ? 32 x ? 10 2/3 Assuming that your numbers are whole numbers x could be 5, 6, 7, 8, 9, or 10 possible cases: 5, 7, 1, .... ---> others that add ...

Math
Number of games in one round = C(10,2) = 45 but they are playing two rounds, so total number of games = 90

Math
I read that as: ?(2x - 1) = x-2 square both sides 2x-1 = x^2 - 4x + 4 x^2 - 6x + 5 = 0 (x-5)(x-1) = 0 x = 5 or x = 1 since I squared, both answers must be verified in the original equation, if x = 1 LS = ?(2x-1) = ?1 = 1 RS = 1-2 = -1 so x ? 1 if x = 5 LS = ?(10-1) = 3 RS = 5-...

Math
remember, consecutive angles in a parallelogram have to be supplementary, that is, they add up to 180° let the angles be x and 3x x + 3x = 180 continue ....

math
Volume of water rise = ?(6^2)(2) = 72? volume of 1 sphere = (4/3)?(1.5)^3 = 4.5? number of spheres that caused the rise = 72?/4.5? = 72/4.5 = 16

Math
x+y=82 x-y = 16 add them to solve for x subtract them to solve for y

Calculus AB
first find the point where y = 1 x^2 + 2x(1) + 1 = 4 x^2 + 2x - 3 = 0 (x+3)(x-1) = 0 x = -3 or x = 1 but in quad I, the point is (1,1) use implicit differentiation: 2x + 2x(dy/dx) + 2y + 3y^2 (dy/dx) = 0 dy/dx (2x + 3y^2) = -2x - 2y dy/dx = (-2x - 2y)/(2x + 3y^2) = (-2-2)/(2+3...

Math
8/12 = x/9 solve for x

Math
(f o g)(x) is defined as f(g(x)) so f(g(x)) = f(x-1) , remember f(x) = 3x+4 f(g(x)) = 3(x-1) + 4 = 3x + 1 , same as bob or f(g(x)) = 3g(x) + 4 = 3(x-1) + 4 = 3x + 1 , like bob had in #2 (f o g)(-2) = f(g(-2)) ----> g(-2) = (-2)^2 = 4 = f(4) = 3(4) + 2 = 14 last one: Here is...

The Tangent Function
Label the original position as A and the second position as B, top of the lighhouse as P and its base as Q. ABQ is a straight line, AB = 40, angle B=25°, angle PAQ = 30°, AQ = x, and PQ = h I used to teach this question is 2 ways: 1. In triangle PBA, angle PAB = 150&...

9th grade algebra (completing square)
You seem to have a good grasp of doing these. I verified most of your answers by subbing them back into the original equation. All the ones I tried were correct. I suggest you take your calculator and test your answers.

correction - math
Y = 2x^2 + 3?x is NOT a function, since a quadratic must have the form y = ax^2 + bx + c that is, the exponents of the x term can only be 2 or 1 the term ?x is x^(1/2) Furthermore, the graph of a quadratic function is a parabola, the graph of Y = 2x^2 + 3?x looks like this, ...

Math
Since no condition is stated, that number would be C(9,5) or 126 There seems to be something missing here.

pre calc
amount = a (1/2)^(t/k), where k is the half-life period when t = 2, amount = .7a .7a = a(1/2)(2/k) .7 = (.5)^(2/k) take log of both sides and use log rules log .7 = (2/k)log .5 2/k = log .7 / log .5 = .514573... k = 2/.514573.. = 3.887 days the half-life is 3.89 days check: ...

Math HELP HELP
x^2+4x-41 = x^2+4x + 4 - 4 - 41 = (x+2)^2 - 45 expand and simplify to verify my answer

pre calc
N = a (2)^(t/20), where N is the number of bacteria, t is the number of minutes, a is the initial count, our problem. counting 7:00 as zero time and 5:00 am as t = 10 hrs = 120 minutes 1000000 = a(2)^(120/20) 1000000 = a(2)^6 64a = 1000000 a = 1000000/64 = 15625 of the germs ...

Math
Did you even look at the solution I gave you here http://www.jiskha.com/display.cgi?id=1478637677 This is the same type of problem. btw, the denominator on the right side factors to (x+3)(x-1)

Algebra
"j vaires directly with m and inversely with p" ----> j = km/p plug in the given, and solve for k

MATH
Your second equation IS a quadratic function. since the highest power you see is x^2. Sorry if you misunderstood. btw, don't say "square root of x", that would be ?x the term is "x squared"

MATH
Small change to your definition. The highest power must be a square term. The degree of a polynomial is determined by the highest power, so in your case you would have a cubic because of the x^3 term a quadratic must have the form y = ax^2 + bx + c, where the a,b, and c are ...

Math
I will assume you meant: 2x/(x+1) + 3/(5x+5) = 0 the whole thing falls apart when the denominators are zero, since then we would be dividing by zero When does that happen? when x+1 = 0 x = -1 and 5x+5 = 0 5x = -5 x = -1 so x ? -1

Math
Look up the definition of a function in your text or in your notes. In a nutshell, it says that for every x there is one and only one y value So, if you see two or more y values for the same x, then it is NOT a function e.g. in the first I see (5,2) and (5,10) , so NOT a ...

Calculas-Differentiation
I have now done 2 of your quite straightforward questions. You MUST know how to do these type of relatively easy Calculus problems. Show me the steps of your solution so I can check it.

Calculas-Differentiation
The line y=1/4x+1 has a slope of 1/4 So the perpendicular has a slope of -4 y = 6 - x^2 dy/dx = -2x set -2x = -4 , and solve, then use your grade 9 method of finding the equation of the tangent

Algebra
amount of the 20% stuff ---- x gallons amount of the other stuff ---- 700-x .2x +.3(700-x) = .24(700) solve for x to reveal the mystery.

Calculas-Differentiation
dA/dt = 6t + 1/5 plug in t = 2 for dA/dt

trigonometry- hight and distance
At 45° the length of the shadow will also be h m

Math
x+y=16 x-y=3 just add them, to find x subtract them to get y

Algebra
in its standard form , at centre (0,0) a^2 = b^2 + c^2 4^2 = b^2 + 2^2 b^2 = 12 x^2 / 16 + y^2 / 12 = 1

Math
If you are picking just one student, prob(boy) = 12/29

Math
why not try it with something like (x+4)(2x-1) expand it and see how many products you have before simplifying

Math
to have an undefined slope, the line must be a vertical line. A vertical line has the form x = c, where c is a constant look at our point, its x value is -3 so the equation of your line is x = -3

math
radish seeds --- x pumpkins ----- x+6 x + x+6 + 40 = 80 solve for x

correction - Math
forget my previous post, did not notice the x^3 f(x)=4x^2-2x+3 ; g(x)=2x^3+4x-7 (f-g)(x) = 4x^2 - 6x + 10 - 2x^3 (f-g)(2) = 16 - 12 + 10 - 16 = -2 bobpursley was correct

Math
3rd one: f(x)=4x^2-2x+3 ; g(x)=2x^3+4x-7 (f-g)(x) = 2x^2 - 6x + 10 (f-g)(2) = 8 - 12 + 10 = 6

Math
let's take $100 interest earned = 100/9 let the rate be r then the number of years = r 100(r/100)(r) = 100/9 r^2 = 100/9 r = 10/3 = 3 1/3 % for 3 1/3 years in general: amount invested --- x interest earned ---- x/9 rate ----- y/100 time ---- y I = PRT x(y/100)(y) = x/9 y^2...

math last question asap ples :P
Well, for A, is 36 + 9 = 64 ?? or , is 6^2 + 3^2 = 8^2 ?? for B, is 144 + 25 = 169 ?? or, is 12^2 + 5^2 = 13^2 ?? btw, just because one of these statements is true, does not "prove" the Pythagorean Theorem, it merely illustrates it.

math
difference of squares 16s^2 - 9 = (4s+3)(4s-3)

MATH ..can you guys help??? also ASAP :p
simply look what happened to the x and y. It should be clear that (x,y) ----> (x-5, y + 8)

stats
prob(right) = 1/4 prob(wrong) = 3/4 prob(at least 15 right) = prob(15 right) + prob(16 right) + ... + prob(40 right) or = 1 - (prob(none right) + prob(1 right) + prob(2 right) + ...+prob(14 right) I hope you have lots of patience and don't make any errors. I will do one of...

math
I assume that you mean: "Luis rides his bicycle 3/4 of a mile in 5 minutes" Since 5 minutes is 1/12 of an hour, like you stated rate = distance/time = (3/4) / (1/12) mph = 9 mph

pre-calc.
ln(100) = ln(10^2) = 2ln10 so ln100/ln10 = 2ln10/ln10 = 2

Pre-Calc
cot x = 1/2 can be written in an infinite number of ways, the 1/2 is simply the ratio expressed in simplest form how about cot x = .5/1 or how about cotx = .378/.756 etc by definition cotx = adjacent side/opposite side in a right-angled triangle so in the original given cotx...

Math
x^2 + 2^2 = 5^2 solve for x

If y= (2x + 2)^3 find dy/dx using chains rule
I would just do it in one step dy/dx = 2(2x+3)^2 (2) = 4(2x+3)^2 using the steps asked for: let u = 2x+2 du/dx = 2 then y = u^3 dy/du = 3u^2 dy/dx = (dy/du)(du/dx) = (3u^2)(2) = 4u^2 = 4(2x+2)^2 Once you see the pattern of these type of derivatives, you should be able to ...

Algebra 2
two consecutive even integers ---> x and x+2 x + x+2 ? 130 2x ? 128 x ? 64 so how about 62 and 64 as the largest pair

Math
3 + 6*4 + 3

Math
I recognize this to be an circle. Do you want it in standard form? if so, then ... 8x+x^2-2y=64-y^2 x^2 + 8x + ... + y^2 - 2y + ... = 64 complete the square x^2 + 8x + 16 + y^2 - 2y + 1 = 64 + 16 + 1 (x + 4)^2 + (y-1)^2 = 81 centre is (-4,1), radius is 9

Calculas
Steve did this for you http://www.jiskha.com/display.cgi?id=1478532807 Why are you reposting?

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