# Posts by Reiny

Total # Posts: 38,755

**math**

The direction of vector AB is (9,8,12) So a plane perpendicular to vector AB will be 9x + 8y + 12z = c, where c is a constant. Let's find the plane such that C(6,2,3) lies on it 9(6) + 8(2) + 12(3) = c c = 106 so the plane containing C and having AB as a normal is 9x + 8y...

**Calculus**

first line derivative: dy/dx = 3(x^2 -4x)^2 (2x-4) = 3(x^2)(x-4)^2 (2)(x-2) = 6x^2 (x-2)(x-4)^2 B is the correct choice, but it is not fully simplified

**Calculus**

k(x)=sin x cos x think: k(x)= (sin x)(cos x) , and use the product rule

**algebra**

The way it was typed and following the order of operation, we have: (v^2 + 6v+8)/(v^2 + v - 12) / (v+2)/(2v-6) = (v+2)(v+4)/( (v+4)(v-3)(v+2)(2)(v-3) ) = 1/(2(v-3)^2) If you meant: (v^2 + 6v+8)/[ (v^2 + v - 12) / ((v+2)/(2v-6)) ] then we would have (v+2)(v+4)/[ (v+4)(v-3)/((v+...

**Pampers**

English ----> Math 4x - 6 = x + 15 solve for x, very easy

**algebra**

I agree if you got -(7c - 25)/p

**Math**

yes!

**Math**

3b + 2m = 7 ---times 2 ---> 6b + 4m = 14 2b + 5m = 6.5 --times 3--> 6b + 15m = 19.5 subtract them: 11m = 5.5 m = .50 sub into first: 3b + 2(.50) = 7 3b = 6 b = 2 Books cost $2 each and magazines cost 50 cents each (wow, good prices, old textbook ??)

**Calculus**

base will be 12 - 2x by 12-2x, height will be x V = x(12-2x)^2 range of x: 0 < x < 6

**Algebra**

5x+3y=9x-7y 10y = 4x y = 2x/5 Not sure what you mean by "solve". Since you have 2 unknowns but only one equation, there is no unique solution. by letting x equal multiples of 5, you will get whole integer solutions for both x and y. e.g. x = 5, y = 2 x = 10, y = 4 x...

**Calculus**

At the max/min of f(x), f ' (x) = 0 , so ?x sinx = 0 ?x=0 ---> x = 0 or sinx = 0 ---> x = 0, ?, 2? We have to find f(x) ? ?x sinx dx ??? ---> nasty tried integration by parts, got messy how about this approach? ?xsinx = ? [?x(x - x^3/3! + x^4/4! - x^5/5! + ...] ...

**Precalculus**

u=4(cos102°i+sin102°j) = 4[cos102° , sin102°] the direction angle is clearly 102° magnitude = ?(16(cos^2 102 + sin^2 102) = ?(16(1)) = 4

**trigonometry**

Make a sketch. I used your A and B as points on the ground, P as the position of the plane and R as a point on the ground directly below P. I let angle A = 50° Enter your given data. angle ABP = 113° Therefore angle APB = 17° by the sine law: PB/sin50 = 3.9/sin17 ...

**Calculus**

your solution and conclusion are correct

**FAST Angle Help! (Math)**

Not enough information. There has be an angle given. What the angle 90°, as I supect? then h^2 = 5^2 + 12^2 = 169 h = 13 (you should remember from now on that the 5-12-13 triangle is right-angled, as well as the most-famous 3-4-5 triangle)

**math**

Just translate ... x = 3y , and y = 3z y+z = 50 3z + z = 50 4z = 50 z = 25/2 or 12.5 then y = 3z = 3(12.5) = 37.5 x = 3y = 3(37.5) = 112.5

**Math grade 6, quadrilateral logic**

False. All parallelograms are trapezoids, but not all trapezoids are parallelograms pictures of trapezoids: https://www.google.ca/search?q=trapezoids&biw=1674&bih=926&tbm=isch&imgil=HGp-jIvhG8bzwM%253A%253B3qIYFYBU0gqV6M%253Bhttps%25253A%25252F%25252Fwww.youtube.com%...

**value**

Interpretation: The simple interest of a certain sum of money for 5 years at 8% is ?200 less than the simple interest on the same sum for 3 years and 4 months at 18%. Find the sum of money. Let the sum of money be x first case: interest = x(.08)(5) = .4x second case: 3 years ...

**math**

In a cyclic quad, opposite angles must add up to 180° let the angles be 2x and 3x so 5x = 180 x = 36 The two angles are 72° and 108°. More information is needed to find the remaining two angles.

**Math**

Who is x and y ? In a rhombus, opposite angles are equal and adjacent angles add up to 180° So the equal angle pairs are 50° and 130°

**Math**

rate = 27 km/hr = 2700000 cm / 60 minutes = 45000 cm/min so in 1 minute, the water flows 45000 cm volume = area of base x height = 5.4 cm^2 x 45000 cm = 243000 cm^3

**Math**

unit cost price = 6/7 or appr .8571 unit selling price = 7/6 or appr 1.1667 profit per unit = 7/6 - 6/7 = 13/42 = appr .3096 or appr 30.96% 13/42 x = 65 x = 65(42/13) = 209.95 or appr 210 210 lemons must be sold

**9th grade algebra (recursive formula)**

or term(18) = 3362 ----> a+17d = 3362 term(38) = 7362 ----> a + 37d = 7362 subtract them: 20d = 4000 d = 200 sub into a+17d = 3362 a = -38 so recursive: term(n) = term(n-1) + 200, term(1) = -38 general: term(n) = a+(n-1)d = -38 + 200(n-1) = 200n - 238

**Math**

You are driving your rental cars only about 1/2 mile and the other at 1/4 mile? I would just walk the distance. Check your typing or the wording of the question.

**Grade 8 math**

I don't know what level of math you are studying at in grade 8 in your region, but you have to know several facts of geometry 1. the Pythagorean Theorem 2. In a right-angled triangle, if a median is drawn from the right angle to the hypotenuse, the length of that median is...

**Marh**

Restate your question in proper English and I will look at it.

**Math grade 8**

not even true, e.g. let x = 1 x^6-x^5-x^4-x^3-x^2-x+1>0 1 - 1 - 1 - 1 - 1 - 1 - 1 + 1 > 0 is false all I needed was ONE exception and the statement is false. see: http://www.wolframalpha.com/input/?i=plot+y+%3D+x%5E6-x%5E5-x%5E4-x%5E3-x%5E2-x%2B1

**math**

2science + 1 auto ----> 5/6w pounds 4science + 2 auto = 2(2science + 1 auto) = 2(5/6w) = 5/3w pounds

**Math**

dR/dq = 30 - .6q so when q = 10 dR/dq = 30 - .6(10) = 24

**Math**

It helps to look at the graph of y = - x^2/(x+3) http://www.wolframalpha.com/input/?i=plot+y+%3D+-(x%5E2)%2F(x%2B3) look at the second graph, the first one is a close-up of the second. The "forbidden" value is x = -3 now look at just a bit to the right of x = -3 What...

**Math**

Sketch your right-angled triangle. sin 32° = 150/x x = 150/sin32 = ....

**algebra sir reiny sir steve&bob damon help**

Confirming Steve's answer, using Wolfram http://www.wolframalpha.com/input/?i=3x%5E2%3Dx%5Ex

**Math**

from : 2p-q-10=0 q =2p-10 sub into the 2nd: (p+10)(q+30) = 7200 (p+10)(2p-10 + 30) = 7200 (p+10)(2p+20) = 7200 divide by 2 (p+10)(p+10) = 3600 p^2 + 20p + 100 = 3600 p^2 + 20p - 3500 = 0 (p-50)(p+70) = 0 p = 50 or p = -70, but p ? 0 p = 50, q = 100-10 = 90

**algrbra**

proper steps: present age of Brandon ---- x present age of Brittney ----- x+5 Three years from now: Brandon------> x+3 Brittney -------> x+5+3 = x+8 x+3 + x+8 = 23 2x = 12 x = 6 Brandon is now 6, and Brittney is 11

**Math**

your choice of A is not correct (2x^5y^2)^3 = 2^3 (x^5)^3 (y^2)^3 = ... review the difference between (x^a)(x^b) and (x^a)^b also what is the meaning of 2^3, it certainly is not (2)(3) like your choice indicates

**math**

why not just solve the equation, they are perfectly set up. subtract them: 6x = -3 x = -1/2 back in #1: -2 + y = 2 y = 4

**maths**

third term of an A.P is 9 ---> a+2d = 9 tenth term is 21 ---> a+9d = 21 subtract them: 7d = 12 d = 12/7 in a+2d=9 a+ 24/7 = 9 a = 39/7 sum(12) = (12/2)( 78/7 + 11(12/7)) = 180

**maths**

I would use substitution. From the 2nd, x = 2y sub into the first: 4(2y) + 2y = 5 solve for y, then find x from x = 2y

**math**

John's present age --- x Uncle's present age ---- 6x in 4 year's time: John will be x+4 Uncle's age will be 6x + 4 6x+4 = 4(x+4) 6x+4 = 4x + 16 2x = 12 x = 6 John is now 6 and the uncle is now 36 in 6 years time the uncle will be 42 uncle's in 6 years time...

**math**

Make a sketch of the 20 by 20 square pool sketch the 2 m wide path all around the square pool Notice that each side is now 24 What is 4 times 24 ?

**Maths**

What is 3x3x2 ?

**Math**

Henry said: 10/35 = 8/W then 10W = 280 W = 28

**math**

so the rate would be 3400/34000 = .1 or 10% so on 38000 the tax would be 3800

**Math**

Damon did this for you on Saturday. What part of his solution did you not like ?? http://www.jiskha.com/display.cgi?id=1483831115

**Pre-Calculus**

radius ---- x height ---- x+5 V = ? r^2 h = ?(x^2)(x+5) , but x = d/2 = ?(d^2/4)(d/2 + 5) = ?( d^3/8 + d^2/4) or = (1/8)?(d^3 + 2d^2) or = (1/8)? d^2(d + 2) or ....

**Pre-Calculus**

make a sketch to see that V = x(11-2x)(8.5 - 2x) = x(93.5 - 39x - 4x^2) = 93.5x - 39x^2 - 4x^3 dV/dx = 93.5 - 78x - 12x^2 = 0 for a max of V solve for x

**Math- Sequences and Series**

n = 1 , S(1) = 1 - 4 = -3 n= 2, S(2) = 4 - 8 = -4 n = 3, S(3) = 9 - 12 = -3 n = 4, S(4) = 16 - 16 = 0 term(1) = -3 term(2) = sum(2) - sum(1) = -4-(-3) = -1 term(3) = sum(3) - sum(2) = -3 -(-4) = 1 term(4) = sum(4) - sum(3) = 0 -(-3) = 3 so the first 4 terms are -3, -1, 1, 3 ...

**Math**

sum(10) = a(r^10 - 1)/(r-1) 699050 = a(4^10 - 1)/3 2097150 = a(1048575) a = 2

**Math**

H(x)= -3x^2+24x-46 = -3(x^2 - 8x + ....) - 46 = -3(x^2 - 8x + 16) - 46 + 48 = -3(x - 4)^2 + 2 vertex is (4, 2) or for f(x) = ax^2 + bx + c the x of the vertex is -b/(2a) for H(x)= -3x^2+24x-46 x of the vertex is -24/-6 = 4 H(4) = -48 + 96 - 46 = 2 vertex is (4,2)

**Math**

What is the method you were taught for this procedure, since there are several ways to do this?

**Math**

a@b = 3a + 2b u@v = 3u + 2v = 20 v@u = 3v + 2u = 20 add them: 5u + 5v = 40 u + v = 8 then 2u@3v = 6u + 6v = 6(u+v) = 6(20) = 120

**math**

Let the number of boys be 3x let the number of girls be 4x ( notice 3x : 4x = 3 : 4 ) given : 4x = 200 x = 50 So we have 150 boys and 200 girls, for a total of 350. ( notice 150:200 = 3:4 , as required)

**MATHS**

yes, join the centroid to each of the vertices

**Math(simple interest)**

amount invested at 7.5% ---- x amount invested at 9% ----- 2x amount invested at 8% = 10000-2x-x = 10000 - 3x .08(10000-3x) + .09(2x) + .075x = 845 times 1000 80(10000-3x) + 90(2x) + 75x = 845000 now it is easy, just solve for x, then back-substitute into my definitions

**Math**

prob(picking a red, then a green) = (5/11)(2/10) = 1/11 Working in the prob that he will also eat it needs more information. e.g. How hungry is he? Will he eat it now, or later, etc

**math**

Too many unknowns here. Is this compound interest or simple interest? Are the instalment payments made monthly or ? Since it will take more than a year to pay it with monthly instalments, I will assume compound interest. i = .10/12 = .00833... then 500(1 - 1.008333...^-n)/....

**Algebra 1**

everything factors nicely. Things are already partially factored giving you clues as what the other factors will be (X^2 - 9)(7x + 21) / (x- 3)(x^2 + 6x + 9) = (x+3)(x-3)(7)(x+3) / ( (x-3)(x+3)(x+3) = 7 , x ? ± 3

**Algebra**

look back at your previous post where I answered this. How did your name change from Clarise to Clary?

**Math**

cost of hat ---- x cost of shoes ---- x+9 x + 2(x+9) = 60 solve for x

**Math**

Did you make a sketch? You did not state where the right angle is, I will assume it is at L In triangle JMK, we have bisected angles of 60° and 30°, so angle JMK = (180 - 30 - 15)° = 135°

**Math**

1.5 hens can lay 1.5 eggs in 1.5 days 3 hens can lay 3 eggs in 1.5 days 3 hens can lay 12 eggs in 6 days double the hens would double the number of eggs without changing the time multiplying the the time would multiply the eggs without changing the number of hens

**Algebra 1**

?6 + ?54 + ?150 = ?6 + ?9?6 + ?25?6 = ?6 + 3?6 + 5?6 = 9?6

**Math**

number of large tables ---- x number of smaller tables = 19-x 6x + 4(19-x) = 90 solve for x

**Math**

The five friends received 7 marbles each, so that accounts for 35 marbles. Including the 12 he kept for himself, the brother received 47 marbles from Natalie. But that was only 1/3 of what she had , so she had 3(47) or 141 marbles to begin with.

**Algebra 8th**

a(1)=17 a(n+1)=a(n)-3 a(2) = a(1) - 3 = 17-3 = 14 a(3) = a(2) - 3 = 14-3 = 11 decreases by 3 each time, ? - 3 = 17 looks like a(n) = -3n+ 20 a(1) =20. a(n+1)=1/2*a(n) a(2) = (1/2) a(1) = 10 a(3) = (1/2) a(2) = 5 so 20, 10, 5 <---- a GS with a = 20 r = 1/2 t(n) = ar^(n-1) t(...

**Math**

weight of each melon ---- x kg 8x + 1.25 = 19.25 solve for x

**Math**

doesn't matter what the first roll is, but there are 6 ways to match it so prob(of your case) = 1/6

**math**

number of books ---- x number of pens ----- y number of pencils --- 30-x-y (we know x and y must be whole numbers) 30x + 24y + 6(30-x-y) = 300 30x + 24y + 180 - 6x - 6y = 300 24x + 18y = 120 4x + 3y = 20 y = (20 - 4x)/3 try x = 1 , 2, 3, or 4 for y to be a whole number, x has ...

**math**

h/53 = tan 61° solve for h

**Math**

let the smaller be x then the larger is x+4 x^2 + (x+4)^2 = 520 x^2 + x^2 + 8x + 16 = 520 2x^2 + 8x - 504 x^2 + 4x - 252 = 0 (x+18)(x-14) = 0 x = -18 or x = 14 2 cases: if x = -18 , the smaller is -18, the larger is -14 if x = 14, then the larger is 18

**pre cal**

recall sinØ = y/r from the given: r^2 = 4^2 + (-8)^2 = 80 r = ?80 = 4?5 since (4,-8) is in quad IV , and in IV the sine is negative, sinØ = -8/4?5 = -2/?5 or -2?5/5

**algebra story problems**

when is 16t^2 = 16 ?? same question about 4 years ago? http://www.jiskha.com/display.cgi?id=1375384643

**Business Math**

when is 4000(1.031)^n = 12000 ? 1.031^n = 3 take log of both sides, and use log rules n log 1.031 = log 3 n = log3/log1.031 = appr 35.99 So it would take 36 half-years or 18 years check: 4000(1.031)^36 = 12005.27 , not bad

**Math**

you are both welcome

**Math**

When you multiply or divide an inequation by a negative number the inequality sign must be reversed. e.g. -5 < 4 is a true statement, but when I multiply be -1, the statement 5 < -4 would be false but 5 > -4 makes it true, so ..... -5p > -55 divide both sides by -5...

**plz sequence sir steve reiny bob damon i need u**

Here is my attempt: a,b, and c are in AS, so b-a = c-b c = 2b-a a, c, b are in GS, so c/a = b/c c^2 = ab (2b-a)^2 = ab 4b^2 - 4ab + a^2 = ab 4b^2 - 5ab + a^2 = 0 (b-a)(4b - a) = 0 b = a or b = a/4 but the numbers are supposed to be distinct, so can only go with b = a/4 also c^...

**seven lakes junior high school Math**

Visualize it. make a sketch of the x-y plane and grid on a piece of paper. Now fold it so that quadrant II falls on quadrant III. Does the crease fall along the horzontal (x-axis) or the vertical (y-axis) ??

**Calculus**

I agree with Damon's answer I followed your steps and found and error around the third last step ok at : dh/dt = -12 / (81*pi) , but then .... dh/dt = -4/(27?) ----> you had -4/(9?) = -.04716 you can also simplify your steps: from v = (1/12) * pi * h^3 why not just ...

**math**

If you meant the angle is 30°, then tan30° = h/10 h = 10tan30° = ...

**Grade 6, percentage**

original amount ---- $x amount spent on transport = .12x amount left = .88x he spends 1/4 of that on food leaving him with (3/4)(.88x) = .66x gives $1320 to parents, leaving him with .66x - 1320 actual cost of bike = .8(825) = 660 Assuming he spent all of his leftover money on...

**math**

other side = x hypotenuse = ?(x^2 + 12^2) x + ?(x^2 + 144) = 18 ?(x^2 + 144) = 18-x square both sides: x^2 + 144 = 324 - 36x + x^2 36x = 324-144 x = 5 your triangle is 5 by 12 with a hypotenuse of 13 check: is 5+13 = 18? YUP is 5^2 + 12^2 = 13^2 ? , YUP you should recognize ...

**Algebra**

correct There are some minor flaws in your presentation x+y=6300(-11) should have been -11(x+y)=6300(-11) to get -11x -11y = -69300 0.11x+ 0.08y=597(100) should have said 100(0.11x+ 0.08y)=597(100) to get 11x + 8y = 59700 The way you have it, the left side is not equal to the ...

**Grade 6, percentage**

fix this typo: "he gave 1320% to his parents"

**math**

Q={x|x is an integer and -4<x<-2} = {-3} How many integers lie between -4 and -2 ?

**Grade 6, percentage**

number who took the bus ---- x "there were 360 more pupils who walked than those who took buses" --> number who walked = x+360 (x+360) : x = 65% : 35% = 13 : 7 (x+360)/x = 13/7 13x = 7x + 2520 6x = 2520 x = 420 so 420 took the bus, and 780 walked total number of ...

**calculus**

I don't see the problem with this limit question other than your notation. I will assume you meant: lim 4^(2x -1) , as x ---> 0 Since you don't want to use substitution, which is always my first step, you could look at the graph of y = 4^(2x-1) and observe what it ...

**value**

Make your vector diagram. You should have a triangle with sides 200 and 100 and the contained angle of 135°. The third side is your resultant velocity, call it x by the cosine law: x^2 = 200^2 + 100^2 - 2(200)(100)cos 135° continue let me know what you get

**math**

I will assume that in each case, the first ball drawn is not returned. prob(2 blue) = (12/35)(11/34) = .. prob(2 yellow) = you do it prob(red, then yellow) = (14/35)(9/34) = ... prob(red, then yellow) = your turn again

**Pre calc**

the slope-yintercept form is y = mx +b so why not plug in your given data ?

**Math**

Since the new line is parallel to x+3y=5 it differs only in the constant: x+3y=c plug in (-1,4) to find c and you are done

**Maths**

let the amount he spent on food, utilities, socializing and savings be 2x , 7x, 3x, and 4x respectively 2x = 2500 solve for x, then sub back into my definitions add them all up to get the total expenses. divide this by .8 to get his total earnings.

**am I right ? or no?**

You did not show your answers, how can we check ?

**Trig**

make sketches of each triangle for sinx = 4/5 sin^2 + cos^2 x = 1 16/25 + cos^2 x = 1 cos^2 x = 9/25 cos x = 3/5, in quadrant I siny = 5/13 using your triangle and Pythagoras cosy = -12/13 , since we are in quadrant II sin(x+y) = sinxcosy + cosxsiny = (4/5)(-12/13) + (3/5)(5/...

**Algebra 2**

T)r) = 100 (1.1)^r plug in r = 8 and calculate

**algebra**

but the integers are consecutive, so smaller number --- x next integer ---- x+1 x + x+1 ? 9x - 5(x+1) 2x + 1 ? 4x - 5 2x ? -6 x ? -3 Also consider Steve's other possibility .

**Maths**

but Mike, you said that the two sides are equal, so the triangle is isosceles, and the angles would be (180 - 1/60)/2 ° = 89.99166.. ° each or your top angle is 1 minute of angle the base angles would be (10800 - 1)/2 minutes of angle = 5399.5 minutes = 89.99166.. °...

**Maths**

compare your answer of 14,730,933,173.9 with mine: 1.4725 x 10^10 they are the same answer correct to 4 significant digits.

**Maths**

Looks like you are doing some astronomical type of calculation. Make an exaggerated diagram of an isosceles triangle with a vertex angle of 1/60° or 1 minute of angle and mark each of the equal sides as 50,620,..... I am tempted to state your side as 5.0621 x 10^13 , or ...

**math**

number of metres of fencing = 3200/1.6 = 2000 m so each side of the square is 2000/4 or 500 m and its area is 500^2 m^2 cost of "reaping" = 500^2 /100 * 1.2 = 3000 rupees

**math**

a = 16 ar^4 = 9 sub in a = 16 16r^4 = 9 4r = ± 3 r = ± 3/4 7th term = ar^6 = 16(±3/4) = 16(729/4096) = 729/256