# Posts by Reiny

Total # Posts: 38,649

calculus
base of box: x by x inches height of box : y inches V = x^2 y 1600 = x^2 y y = 1600/x^2 cost = 3(2x^2) + 5(4xy) = 6x^2 + 20x(1600/x^2) = 6x^2 + 32000/x d(cost)/dx = 12x - 32000/x^2 = 0 for a min of cost 12x = 32000/x^2 x^3 = 8000/3 x = 20/3^(1/3) = appr 13.867 sub that into y...

math
correct A = 25000 e^(.084t) dA/dt = Pr e^(rt) we know r = .084 dA/dt = .084(25000) e^(.084t) = 2100 e^(.084t) when A = 30,000 30,000 = 25,000 e^(.084t) 1.2 = e^(.084t) ln 1.2 = .084t ---> I assume you know log rules t = ln 1.2 / .084 = appr 2.17 Plug that into 2100 e^(.084t)

Math
V = (4/3)? r^3 dV/dt = 4? r^2 dr/dt when r = 6, dV/dt = 5 5 = 4? (25) dr/dt dr/dt = 5/(100?) = 1/(20?) cm/s A = 4? r^2 dA/dt = 8? r dr/dt = 8?(5)(1/100? ) = 2/5 cm^2 /s

math
d = 2p+2 - p = p+2 or d = 5p+3 - (2p+2) = 3p + 1 but those d's must be equal, so 3p+1 = p+2 2p = 1 p = 1/2 which makes d = 1/2 + 2 = 5/2 the terms are: 1/2 , 3, 11/2 , 8 , 21/2 , 13

Maths
By the midpoint theorem, DE = (1/2)AB and DE || AB so we have similar triangles EDC and ABC let the altitude from C to DE be h then by similar triangles the altitude from C to AB = 2h and AB = 2DE area of triangle DEC = (1/2)(DE)h area of triangle ABC = (1/2)(AB)(2h) = (1/2)(...

math
Draw perpendiculars to create a rectangle and 2 congruent right-angled triangles. Look at one of those right-angled triangles. let the missing side be x x^2 + 4^2 = 8^2 x^2 = 48 x = ?48 = 4?3 Let the acute angle of the parallelogram be Ø In the triangle, sinØ = 4...

Algebra2
(fog)(4) = f( g(4) ) , g(4) = -2(4)-6 = -14 = f(-14) = 3(-14) - 7 = -49 or f( g(x) ) = f(-2x-6) = 3(-2x-6) - 7 = -6x - 25 f( g(4) ) = -6(4) - 25 = -49

Algebra2
what is (-2x+4) - (-6x-7) ?

Math
?(x-3) - ?x = 3 ?(x-3) = ?x + 3 square both sides: x-3 = x + 6?x + 9 -12 = 6?x ?x = -2 by definition of ? , this has no solution. proceeding anyway ... square both sides again: x = 4 since we squared, all answers must be verified: if x = 4, LS = ?1 - ?4 = 1 - 2 = -1 ? RS There...

Maths
What is (3/7)(5/9) ?

math
looks like the hyperbola is vertical, so (x-4)^2 /a^2 - (y-2)^2/b^2 = -1 we know b = 3 , (the distance between (4,2) and (4,5) ) 4y-3x=-4 3x - 4y = 4 slope of asymptote = 3/4 that is b/a = 3/4, but b = 3, so a = 4 (x-4)^2 / 16 - (y-2)^2 /9 = -1 confirmation: http://www....

Physics
The three legs of the trip are 70 km , 15 km , and 30 km for a total time of 1 hour average velocity = (70 + 15 - 30)/1 = 55 km/h average speed = (70+15+30)/1 = 115 km/h velocity involves both magnitude and direction. Since the direction was reversed for the last part, I used -30

maths
let log3 x = a and log3 y = b then: 3^a = x and 3^b = y 3^a (3^b) = xy 3^(a+b) = xy (9^(1/2))(a+b) = xy 9^(a+b)/2 = xy log9>/sub> xy = (a+b)/2 can you do anything with that? btw, what does log 9 mean? is 9 the base, as I assumed ? But then the logarithm had no argument. ...

Mathe
Just plug it in. 2(-1) + 5(2) = a evaluate

math
One rotation = 30? inches, you had that 65 miles per hour = 65(63360) inches per 60 minutes = 68640 inches/min number of rotations = 68640/(30?) = 728.3 rotations correct!!!

trig
I will use a sine curve amplitude = 25 so let's start with y = 25 sin t , where t is in seconds period = 16 seconds 2?/k = 16 16k = 2? k = ?/8 so far y = 25 sin ?/8 t we want the lowest point to be +8, so we have to raise the sine curve 33 units so far: y = 25 sin ?/8 t + ...

MATH
Why not just say, x^2 + 2x = 80 ? x^2 + 2x - 80 = 0 (x+10)(x-8) = 0 your number was either 8 or -10 both work

math
Don't "guess" in mathematics, it is a precise language, be sure. x/(45-5x)=1/[5(x-1)] x/(5(9-x)) = 1/(5(x-1)) multiply by 5 x/(9-x) = 1/(x-1) multiply both sides by (x-1)(9-x) x^2 - x = 9 - x x^2 = 9 x = ± 3 so the product of the solutions is -9

Math (Algebra 2)
correct, see my reply to your previous post of this

math
Lisa's present age --- x Richard's present age --- x+6 5 years from now: Lisa ---- x+5 Richard -- x+11 4 years ago: Lisa --- x-4 Richard --- x+2 x+5 + x+11 = 2(x-4 + x+2) 2x + 16 = 4x - 4 20 = 2x x = 10 Lisa is 10 and Richard is 16

Math
The nickel will have two branches. For each of those the die will have 6 branches and for each of those the quarter will have two branches, thus 2x6x2 = 24

To do these kind of questions, you MUST know how to find the midpoint between two given points. That is what I did to find (7,-5) You must also know that the equation of a line in point slope form for a given slope m and a given point (a,b) is y - b = m(x - a). that is what I ...

The first thing you would have done of course is to make a sketch, it does not have to be perfect. Secondly, watch your sloppy typing, I will read point B as (4,4) and point C as (18,-8) In the first part, you want the equation of the line BD, where D is on AC, and BD is ...

math
1 km/5 minutes = 1000 m / 300 seconds = 10/3 m/s

Maths
What is 7000(.9)^2 ?

MATH
solve for p, 3p = 15

Álgebra
Easy to translate from English to Math. Let the 2nd number be x and the first one y "The first number is three times the second" y = 3x "The second number is five less than two times the first" x = 2(3x) - 5 -5x = 5 x = 1 then y = 3 The first number is 3 ...

math
I will assume that your question will ask "How many shirts does he have ? " number of shirts ---- x , where x is a whole number (1/2)(x - 4) = (3/10)x times 10 5(x-4) = 3x 5x - 20 = 3x 2x = 20 x = 10

Pre-cal
your graph should look like this http://www.wolframalpha.com/input/?i=plot+y%3D+-2-4sin(%CF%80%2F2(x-1%2F3))

MATH
GOOD GRIEF, Just realized I did this same question a week ago. At least I ended up with the same answer. http://www.jiskha.com/display.cgi?id=1484278204

MATH
Let the perpendicular distance from C to AB meet AB at D vector AB = [9,8,12] equation of plane through C and D having AB as a normal: 9x + 8y + 12z = c but (6,2,3) lies on it , so the plane is 9(6)+8(2)+12(3) = c = 106 plane equation: 9x+8y+12z = 106 equation of line AB: x = ...

Math
LS = sec? - tan?sin? = 1/cosØ - (sinØ/cosØ)sinØ = 1/cosØ - sin^2Ø/cosØ = (1 - sin^2 Ø)/cosØ ---> you had it up to there = cos^2 Ø/cosØ ---> since sin^2 Ø + cos^2 Ø = 1 = cosØ...

math
Should be in your textbook. projection of vector u onto vector v = (u dot v)/|v|

math
use the dot product. [4,4,2] dot [4,3,12] = |[4,4,2]| |[4,3,12]| cosØ 16 + 12 + 24 = ?36 ?169 cosØ 52 = (6)(13) cosØ cosØ = 2/3 Ø = appr 48.19° or .841 radians let u be the projection vector of [4,3,12] onto [4,4,2): cosØ = |u|/|[4...

Math
nope! Area of circle with radius r = ?r^2 so combined area of two of those circles = 2?r^2 twice the circumference = 2(2?r) = 4?r e.g. suppose the radius = 5 cm area of 2 such circles = 2(?(25)) = 50? twice the circumference = 2(2?(5)) = 20? clearly different!

Math
Repeat without typos and with correct grammar.

math
Repeat without typos and with correct grammar. Are we talking about arithmetic or geometric sequences or what?

math - word problem
red apples ---- x green apples ---- x+35 (x+35)/x = 8/3 8x = 3x + 105 .. x =

math
4th term is 3 ---> ar^3 = 3 7th term is 8/9 --> ar^6 = 8/9 divide them: r^3 = 8/27 r = 2/3 in ar^3 = 3 a(8/27) = 3 a = 81/8 GP is 81/8 , 27/4 , 9/2 , 3 , .....

maths calculus also
Two parabolas, one opening up the other down Intersection: x^2 - 2x = 4x - x^2 2x^2 - 6x = 0 2x(x - 3) = 0 x = 0 or x = 3 effective height of region = 4x-x^2 - (x^2 - 2x) = 6x - 2x^2 area = ? (6x - 2x^2) dx from 0 to 3 = [3x^2 - (2/3)x^3] from 0 to 3 = 27 - (2/3)(27) - 0 = 9 ...

MATHS
(x^4 +2x^3 + 3x + 4) by (x^2 +x) , those brackets are essential = (x+1)(x^3 + x^2 - x + 4)/( x(x+1)) = (x^3 + x^2 - x + 4)/x = x^2 + x - 1 + 4/x x^2 + 2x + 8 is an irreducible polynomial because it cannot be factored over the rationals. that is, we cannot find two numbers that...

maths help calculus
A = ? r^2 dA/dt = 2? r dr/dt given: dA/dt = 3 , find dr/dt when r = 2 3 = 2? (2) dr/dt dr/dt = 3/(4?) cm/s

mathss
2 + 3x + 4x^2 + 5x^3 = ?(i+1) x^(i-1) for i= 1 to 4

Maths
(1+x)(1-x) = 1 - x^2 (1+x+x^2)(1-x) = 1 - x^3 (1+x+x^2+x^3)(1-x) = 1 - x^4 mmmhhh??? (1 + x + x^2 + . . . + x^16)(1 - x) = ......

geometry
let the point be (x,y) (?(x^2 + y^2) = 2?(x-3)^2 + y^2) = 0 square both sides x^2 + y^2 = 4(x^2 - 6x + 9) + y^2) x^2 + y^2 = 4x^2 - 24x + 36 + 4y^2 3x^2 + 3y^2 - 24x + 36 = 0 x^2 + y^2 - 8x + 12 = 0 complete the square x^2 - 8x + 16 + y^2 = -12 + 16 (x - 4)^2 + y^2 = 4 indeed ...

math
follow the order of operation (5-2*.5)(4-2*.5)(63) = (5-1)(4-1)(63) = 4(3)(63) = ..

Algebra
smaller number --- x larger number ---- x+4 3(x+4)/x = 4 + 5/x times x 3(x+4) = 4x + 5 3x + 12 = 4x + 5 7 = x the smaller is 7 , the larger is 11 check: 33/7 = 4 with remainder 5 OK, all is good

Pre calc
cos a = 4/5, and a is in quad I Make your sketch and use Pythagoras: x^2 + y^2 = r^2 16 + y^2 = 25 y^2 = 9 y = 3 in quad I so sin a = 3/5 do the same for sin b = -15/17 , b in quad IV x^2 + 225 = 289 x = +8 in quad IV evaluate WHAT expression ? but you now have both sines and ...

Pre-Cal
the centre of this one is (0,0) and the major axis lies horizontally, so x^2/a^2 + y^2/b^2 = 1 ** for such an ellipse: a^2 = b^2 + c^2, but c = 4 a^2 = b^2 + 16 sub back into ** x^2/(b^2+16) + y^2/b^2 = 1 but (4,1) lies on it, so 16/(b^2+16) + 1/b^2 = 1 16b^2 + b^2+16 = b^2(b^...

Math
from x=7t-2 t = (x+2)/7 from y=-4+3t t = (y+4)/3 (x+2)/7 = (y+4)/3 3x + 6 = 7y + 28 3x - 7y = 22 ---> slope = 3/7

math
think of it as y = 0x - 4 and compare it with your famous y = mx + b what do you think?

Math
Did you make your sketch? On mine, I have a triangle with sides 100 and 400 and the contained angle of 135° Using the cosine law: x^2 = 100^2 + 400^2 -2(100)(400)cos135° x = 475.992.. To get the angle opposite the side of 400: sinØ/400 = sin135/475.992.. sin&...

Calculus algebra review
I think you have a typo and you meant: ((1/(2+h)) -(1/2)) / h if so: = ( (2 - 2 - h)/(2(h+2)) / h = -h/(2(h+2))/h = -1/(2h+4)

Math
from the last: 2X+2z= 4 x+z=4 z = 4-x from the first: -X-y-z= -8 z = 8-x-y so 4-x = 8-x-y y = 4 from the 2nd: -4+4y+5z =7 -4 + 16 + 5z = 7 5z = -5 z = -1 then in z = 4-x -1 = 4-x x = 5 x=5, y=4, z=-1

Math
3/6 ? why not just say half of the 24 students are boys? So ....

math
number bought --- n cost price = 50n selling price = 1.2(50)n = 60n 60n = 600 n = 10

Math
Explain what an "over" is.

math
amount of pure acid added ---- x litres .1(2) + x = .2(x+2) 2 + 10x = 2(x+2) 2+10x = 2x + 4 8x = 2 x = 1/4 L

math
I assume you made the simple sketch and translated the angles of depression given to be the base angles of the two right-angled triangle. Let the distance of the hut with the 60° angle be x, let the other distance be y case1: tan60 = 150/x x = 150/tan60 case 2: ..... y = ...

Math
area of smaller = 16 perimeter of smaller = 16 area of larger = 36 perimeter of larger = 24 area of smaller : larger = 16:36 = 4 : 9 perimeter of smaller:larger = 16:24 = 2:3

Algebra
width --- x length ---x+9 2x + 2(x+9) = 62 2x + 2x + 18 = 62 4x = 44 x = 11 the width is 11 and the length is 20 check: 2(11) + 2(20) = 62 , as needed

math
The question seems too simple. Since there are 16 books, you could pick any of them. So 16 different ways to pick a book. Are you sure that that was all it said?

DPS ( Math)
If I understand your question .... 1+2+3+4+...+n = 300 you have an AS with a=1, d=1 sum(n) = (n/2)(2a + (n-1)d) = 300 n(2 + n-1) = 600 n^2 + n - 600 = 0 (n+25)(n-24) = 0 n = 24, since n > 0 term(24) = a + 23d = 1 + 23 = 24

math
let the two numbers be 4x and 7x 4x = 36 x = 9 So what is the larger of the numbers ?

math
So 2/9 of the full tank remain, (2/9)x = 14 x = 14(9/2) = 63 L

AP Calculus
When you say, "I don't understand any of this", I am troubled. This question is as fundamental in beginning Calculus as it gets. Are you taking this course in a traditional classroom setting? What is your background in math that enables you to take Calculus? ...

math
open http://davidmlane.com/normal.html enter 70 into SD click on <above> and enter 850 adjust Mean until you get .16 in the area (probability) window I had 780.39 days as the mean.

Algebra 2
number of dimes ---- x number of quarters --- x-4 equation based on value: 10x + 25(x-4) = 320 etc

Math
How about just using the cosine law? let the distance be x x^2 = 500^2 + 1050^2 - 2(500)(1050)cos 86°

Math
Of course you made a diagram. let the distance to the first connection be x let the distance to the second connection by y x < y from the smaller right-angled triangle: sin55 = x/15 x = 15sin55 from the larger triangle: sin 63 = y/22 y = 22sin63 distance between the two ...

Algebra 2
correct, it is a) another way would be to look at the regions that each defines and see if the point lies in that region. since you only have two boundaries to worry about, that would be quite easy. So sketch y = 3x -1 , (y-intercept of -1 and slope of 3) and y = -x+1 , (y-...

Algebra 2
test your point in each of the cases. I will try c) is 1 > 12-1 and 1 < -4+1 is 1 > 11 and is 1 < -3 I guess not! , so not c) remember , since they use the logical operator "and", both parts must be true

Math
6x +12 + 2cosx = 0 or 2cosx = -6x - 12 No straight-forward or easy way to get a reasonably accurate number. Let's start by looking at the graphs of y = 2cosx and y = -6x-12 http://www.wolframalpha.com/input/?i=plot+y+%3D+2cosx+,+y+%3D+-6x-12 looks like there is a solution ...

help in "logic" needed - Math
I have seen your post several times. Have not answered it since I am not familiar with the topic. The last time I would have seen something like that must be about 55 years ago and it has long since gone into my "delete" part of my memory.

MATH
simply use the "length of line between 2 points" formula. I will do PQ, you do the other two PQ = ?( (7+3)^2 + (3-5)^2 ) = ?(100 + 4) = ?104 = ?4 ?26 = 2?26

math
assuming you mean: 225 ÷ 15[60 ÷ 3|10+18 ÷ (9-7)-14|+11] and the | .. | means absolute value = 225 ÷ 15[60 ÷ 3|10+18 ÷ (2)-14|+11] = 225 ÷ 15[60 ÷ 3|10+9-14|+11] = 225 ÷ 15[60 ÷ 3|5|+11] = 15[20|5|+11] = 15...

Algebra
y/5+y-3/2=7 I would multiply each term by 10 and see it fall apart and become easy

maths
one angle ---- x the other angle ---- 3.5x x + 3.5x = 180° 4.5x = 180 x = 180/4.5 = ... then 3.5x = ...

trigonometry
I am sure you made a sketch. On mine, I labeled the window position W, the top of the building across the street T and the bottom of the building B. I also labeled the point where the horizontal from W meets TB as M In triangle WBM, tan20° = 30/WM WM = 30/tan20° in ...

Math
4 1/4 + 3 5/8 = 17/4 + 29/8 = 34/8 + 29/8 = ... = ...

Geometry
let each side of the square be x then the diagonal is ?2 x by Pythagoras let the short side of the rectangle be a let the longer side be b then (1/2)ab = (.6)(1/2)x^2 ab = .6x^2 10ab = 6x^2 x^2 = (5/3)ab also a^2 + b^2 = 2x^2 , again by Pythagoras, and we are told the ...

Geometry
Good link here: https://en.wikipedia.org/wiki/Varignon's_theorem contains a proof which is easy to follow

Pre Calc
what is 4(4!/(4-4)! ( 9!/(4!5!) ?

Math
Sheena's present age --- x her dad's present age --- 3x in 12 years: Sheena's age = x+12 dad's age = 3x+12 x+12 = (1/2)(3x+12) 2x+24 = 3x + 12 x = 12 Shenna is pesently 12 and her dad is 36

Math
let the unit digit be x let the tens digit be y let the hundred digit by (y+1) y+1 + y + x = 20 2y+ x = 19 x = 19-2y, where both x and y must be whole numbers from 0 to 9. the number is 100(y+1) + 10y + x = x + 110y + 100 reverse the hundreds and unit digit: 100x + 10y + y+1...

Math
Both are correct In the first one, you don't say how the dot is labeled. Is it a solid dot or an open dot If the dot is solid, it means that value is include and you would have p ? 1 choice C 5x+6<11 5x < 5 x< 1 choice D 5x+6?11 5x ? 5 x ? 1 You decide.

math
3/4 on chocolates rest on gum, so 1/4 on gum choc : gum = 3/4 : 1/4 = 3 : 1

Math
Don't know what all this is. let the first be x then the second is x+5 and the third = 3(x+5) x + x+5 + 3(x+5) = 75 x+x+5+3x+15 = 75 5x = 55 x = 11 the numbers are 11, 16, and 48

Math
Well, 1 teaspoon is half of 2 teaspoons. So what is half of 3.2 cups of sugar ?

math
2x dx/dt - 2dy/dt = 0 dy/dt = x (dx/dt)

Finance
What did you get so far ?

Finance
First find the payment using: Present Value = payment (1 - (1+i)^-n)/i where i is the rate expressed as a decimal , i = .09, and n is the number of interest periods. n = 5 outstanding balance after 2 years = 15000(1.09)^2 - payment( 1.09^2 - 1)/.09 let me know what you get

Math - Algebra
Just like it says: 6s +4l = 30 ---as is ---> 6s + 4l = 30 7s + 2l = 23 --times 2--> 14s + 4l = 46 subtract them: 8s = 16 s = 2 in the first ----> 12 + 4l = 30 4l = 18 l = 9/2 or 4.5 the large marble weighs 4.5 g, the smaller 2 g

Algebra 2
what is 26x26x10x10x10x10 ?

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

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