# 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

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

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.

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.

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

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° = ...

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 ...

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 ?

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?

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

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