Saturday

January 31, 2015

January 31, 2015

Total # Posts: 28,795

**Calculus**

I made a sketch showing the distance covered by the plane after it passed over the kangaroo as x miles let the angle of elevation be Ø I have : tanØ = 2/x xtanØ = 2 x sec^2 Ø dØ/dt + tanØ dx/dt = 0 when the distance between the ...
*October 7, 2014*

**Calculus help please**

sin^-1 (2/7) means, find the angle Ø , so that sinØ = 2/7 sketch a right-angled triangle with base angle Ø, opposite side 2 and hyptenuse 7 by Pythagoras, adj^2 + 2^2 = 7^2 adjacent = √45 = 3√5 then tanØ = 2/(3√5) thus tan(sin^-1 (...
*October 7, 2014*

**MATH**

this problem consists of finding the vertex of the parabola, the x of the vertex is -b/(2a) = -40/-8 = 5 when x = 5 A = -4(25) + 40(5) = 100 So the maximum area is 100 ft^2 , when the width is 5 ft. I would suggest you have your caps lock fixed on your keyboard, it will be so ...
*October 7, 2014*

**Math**

depends if you round to the nearest tenth or the nearest hundredth to the nearest tenth it would be 1.6 for the nearest hundredth, the above is correct as 1.65
*October 7, 2014*

**calculus 1**

sin(anything) has a minimum of -1 and a max of +1 so 18sin(7t) has a min of -18 and a max of 18 since 18sin(7t) is added to 100 the minimum would be 100-18 or 82 the maximum would be 100+18 = 118 period of the function : 2π/7 = period period = appr .897 sec per period so ...
*October 7, 2014*

**math**

short piece --- x long piece ---- 9x x + 9x = 20 10x=20 x=2 the short piece is 2 m the long piece is 18 m
*October 7, 2014*

**MATH**

tan(x)sin(2x) = √3 sin (x) tanx(2sinxcosx) = √3sinx divide by sinx 2tanxcosx = √3 2(sinx/cosx)(cosx) = √3 sinx = √3/2 I recognize x as one of the special angles, x = 60° but sine is also positive in quadrant II so x = 180-60 = 120° x = 60&...
*October 7, 2014*

**Calculus**

cos−1(x) refers to an angle, let's call it Ø , so that cosØ = x = x/1 so sketch a right-angled triangle, label the base angle Ø, it's adjacent side as 1, and its hypotenuse as x then the other side is √(1 - x^2) and cotØ = x/&#...
*October 7, 2014*

**AP Calculus**

Darn!!! last line, forgot the +1 , but you figured that out, didn't you?
*October 7, 2014*

**AP Calculus**

sometimes called: find the derivative from First Priciples f(x) = 1/√x + x f(x+h) = 1/√(x+h) + x+h f'(x) = Lim ( f(x+h) - f(x) )/h , as h --->0 = lim( 1/√(x+h) + x+h - (1/√x + x )/h as h--->0 = lim ( (1/√(x+h) - 1/√x)/h + h/h) as h...
*October 7, 2014*

**Maths**

j : m : s = 12 : 5 : 1 or 12k : 5k : k there are 66 more juices than soft drinks 12k = k + 66 k = 6 milk = m = 5k = 30 30 cartons of milk check if k=6, we have 72 juices, 30 milk and 6 soft drinks 66 more juices than soft drinks ? , yes ratio: 72 : 30 : 6 = 12 : 5 : 1 , yes
*October 7, 2014*

**Maths**

boys -- b girls -- g b/g = 3/5 5b = 3g b = 3g/5 OR g = 5b/3 men --- m women -- w m/w = 3/1 m = 3w equation #1: 2/9 of the visitors were children: b+g = (2/9)( b+g+m+w) 9b + 9g = 2b + 2g + 2m + 2w) 7b + 7g = 2m + 2w 7(3g/5) + 7g = 6w + 2w times 5 21g + 35g = 40w 56g = 40w...
*October 7, 2014*

**Math**

According to the diagram I drew .... width --- w 5.5(2w) + .5w = 60.375 11.5w = 60.375 w = 5.25 or 5 1/4 ft
*October 7, 2014*

**bank loans**

I don't think any bank in 2014 would use simple interest, but anyway .... interest = 3000(18/12)(.12) = $540 (here is where the flaw comes in using simple interest. The $540 would be the simple interest on the full amount of $3000, but the balance is constantly decreasing ...
*October 7, 2014*

**statistics**

prob = C(12,3) x C(40,2)/C(52,5) = 220(780)/2598960 = 55/833 or appr .066
*October 6, 2014*

**Math Question**

I will assume you meant f(x) = -5√(-4x+4) + 2 or else they would have just added the 2 to the 4 y = -5√(-4x+4) + 2 = -10√(1-x) + 2 , I factored out √4 which is 2 inverse: interchange x and y variables x = -10√1-y) + 2 solve this new equation for y...
*October 6, 2014*

**Math**

1 inch = 2.54 cm then 5/6 inches = (5/16)(2.54) cm = appr .794 cm = 7.94 mm , yes it will fit but very loosely 2nd way 2.54 cm = 1 inch 1 cm = 1/2.54 10 mm = 1/2.54 inches 5 mm = 1/5.08 inche = appr .1969 inches which is less than 5/16 inches so it will fit, but just as loose ...
*October 6, 2014*

**Math**

yes
*October 6, 2014*

**Pre-Calc/Trig...**

vertex form: y = - (x-4)^2 + 4 your text or your notes should have the definitions and properties of that form
*October 6, 2014*

**math**

Think! It can't be isosceles, you would need two equal sides. It is not right-angled or else 8^2 would have to be equal to 6^2 + 3^2 definition of scale: a triangle with all sides different.
*October 6, 2014*

**Math**

72 ft, 10 inches = 72.8333... ft cos 57 = base/72.8333.. base = 72.8333..(cos 57°) = appr 39.668 ft so I would pick D, 40 ft
*October 6, 2014*

**Algebra**

√( (x-7)^2 + (0-6)^2 ) = 10 square both sides and expand x^2 - 14x + 49 + 36 = 100 x^2 - 14x - 15 = 0 (x - 15)(x + 1) = 0 x = 15 or x = -1 interpret my results.
*October 6, 2014*

**Math, ASAP Please**

Think about it 5% on $100 would be $5.00 so on a $1000 it would be $50 since it is a bit more than 5% , the only logical choice is $52.50
*October 6, 2014*

**Rational Functions**

x-intercept of 3 ---> needs a multiplier of x-3 vertical asymtote of x = -2 ----> needs a divisor of x+2 so far y = (x-3)/(x+2) horizontal asymptote of y = 2 lets slap a 2 infront y = 2(x-3)/(x+2) , as x gets huge y ---> 2 , ( try x = 100,000 ) we want y-intercept of...
*October 6, 2014*

**trig**

I assume you made a diagram Because of the symmetry, let's just look at the top part of the diagram Let the centre of the smaller circle be O and the centre of the larger circle be P Let the point of contact of the belt to the smaller circle be A and to the larger circle B...
*October 6, 2014*

**Math**

Did you enter 2.98333 , which was my answer using linear approximation method ? , (we can't use a calculator for this)
*October 5, 2014*

**Math**

What is the least common multiple (LCM) of 15 and 12 ?
*October 5, 2014*

**Math**

Did you look at my previous answer to this problem? Why are you changing names? http://www.jiskha.com/display.cgi?id=1412554250
*October 5, 2014*

**finding the interest**

You probably want to use Ms Sue's answer. I did not read the question carefully and read it as finding the interest rate.
*October 5, 2014*

**finding the interest**

So loan = 450-90 = 360 let the monthly rate be r 22.8( 1 - (1+r)^-20)/r = 360 1 - (1+r)^-20 = 360r/22.8 very difficult equation to solve, I will use Wolfram http://www.wolframalpha.com/input/?i=solve+1+-+%281%2Br%29%5E-20+%3D+360r%2F22.8 using the logical answer of r = ....
*October 5, 2014*

**Statistics**

prob(odd on blue) = 1/2 prob(5 or 6 on yello) = 2/6 = 1/3 prob(odd on blue AND 5or6 on yellow) = (1/2)(1/3) = 1/6 Proof and check: There are 36 possible ways for the 2 dice to fall the ones you want are: 1 5 1 6 3 5 3 6 5 5 5 6, which is 6 of them so prob(as stated) = 6/36 = 1/6
*October 5, 2014*

**Math**

If we let L(x) represent the linear approximation for some value of x L(a) = f(a) + f'(a)/(x-a) , were a is a number for which I know the value of f(a) so for √8.9 I know that √9 = 3 , so let a = 9 f(9) = √9 = 3 for f(x) = √x = x^(1/2) f'(x) - (...
*October 5, 2014*

**ALGEBRA**

equation #1: |3x-1| + 7 = 2 |3x-1| = -5 but by definition, the |anything| cannot be negative, the same is true for the 2nd equation. So neither one has a solution
*October 5, 2014*

**Math Check**

I answered a similar question yesterday http://www.jiskha.com/display.cgi?id=1412431497 The way you placed your brackets, none of your choices are correct
*October 5, 2014*

**Math**

at a time of t min, height of water level = h, radius of water level = r V = (1/3)πr^2 h by ratios: r/h = 10/22 = 5/11 11r = 5h r = (5h/11) V = (1/3)π(25h^2/121)h = (25/363)π h^3 dV/dt = (25/121)π h^2 dh/dt given: dV/dt = 30 ft^3/min find: dh/dt when h = 14...
*October 5, 2014*

**Math**

Most questions of this type appear to disregard pressure, so in the following solution I will do the same (physics expert will surely groan) V = (4/3)π r^3 dV/dt = 4πr^2 dr/dt so when r = 5 and dr/dt = -12 dV/dt = 4π(25)(-12) = appr -3769.91118
*October 5, 2014*

**Math**

at a time of t min, let the height of the water level be h m, and the radius of the water level be r m By ratios: r/h = 4.5/9 = 1/2 2r = h or r = h/2 Volume of cone = (1/3)π r^2 h = (1/3)π (h/2)^2 h = (1/12)π h^3 dV/dt = (1/4)π h^2 dh/dt given: when h = 4 m...
*October 5, 2014*

**Algebra**

by definition: p-10 = 20 OR -p+10 = 20 p = 30 or -p = 10 p = 30 or p = -10
*October 4, 2014*

**Math**

-80=8b-15+5b -80 + 15 = 13b or 13b = -65 b = -5 Solving an equation means finding that value of the variable which makes the original equation a true statement. We found that value to be b = 5 Now sub that value into the left side and the right side of the ORIGINAL equation. ...
*October 4, 2014*

**Math Help**

should have noted that the original function is only valid for x ≤ 1
*October 4, 2014*

**Math Help**

I will assume you meant f(x) = -5√(-4x+4) + 2 or else they would have just added the 2 to the 4 y = -5√(-4x+4) + 2 = -10√(1-x) + 2 , I factored out √4 which is 2 inverse: interchange x and y variables x = -10√1-y) + 2 solve this new equation for y...
*October 4, 2014*

**Pre-Calc**

number of apples processed = P(22) = .... do the arithmetic cost = C(P(22)) = put the answer of P(22) into C(n)
*October 4, 2014*

**Math**

I assume you meant √(21x) , and not the way you typed since 21 = 3x7 , you want either another 3 or 7 in x so that we have at least one perfect square. none of the first 3 choices contain a 3 or 7 ,but 54 does so √(21x54) = √3x7x3x9x2) = √(81*14) = 9&#...
*October 4, 2014*

**Math**

sum of all exterior angles of an n-gon is 360 so 360/n = appr 30 n = 12 It is a 12-gon
*October 3, 2014*

**Math**

sum of angles of a regular polygon = 180(n-2) so 180(n-2)/n = 165 180n - 360 = 165n 15n = 360 n = 24 sum of inside angles = 180(22) = 3960°
*October 3, 2014*

**Math**

sum of interior angles of a heptagon = 5(180) = 900 so we have 520 + x + x + (3/2)x = 900 2x + 1.5x = 380 x = appr 108.57° take it from here
*October 3, 2014*

**(MCV4U) Vectors**

ignore the first part of my solution, start with My diagram ...
*October 3, 2014*

**(MCV4U) Vectors**

Since you labeled your subject as vectors I will use them let the wind vector be (rcosØ, rsinØ (rcosØ, rsinØ) + (200cos180,200sin180) = (180cos170,180sin170) ( rcosØ, rsinØ) = (22.7346 , 31.2567) 2r^2 = 22.7346^2 + 31.2567^2 r = 27....
*October 3, 2014*

**Algebra**

6x/16 + 1/16 = (6x+1)/16
*October 3, 2014*

**Math**

Are you sure the sum of the other two regions is 25a and not 24a ? then the sum of the area would be a^2 + 144 + 24a = (a+12)^2 which would make it a square of sides a+12 for a perimeter of 4a + 48
*October 3, 2014*

**math**

2 chicken lay 8 eggs in 3 days 1 chicken lays 4 eggs in 3 days 1 chicken lays 8 eggs in 6 days 5 chicken lay 40 eggs in 6 days
*October 3, 2014*

**5th grade math**

16/5 - 2 = 6/5 (6/5)/2 = 3/5 or 60%
*October 3, 2014*

**math**

(x+2y)^2 = (x+2y)(x+2y) = x^2 + 2xy + 2xy + 4y^2 = x^2 + 4xy + 4y^2 The method I used is sometimes referred to a FOIL
*October 3, 2014*

**Pre-Calc/Trig...**

You are correct
*October 3, 2014*

**Analytic Geometry CHECK MY ANSWER**

the slope is (6-3)/(2-2) = 3/0 which would be undefined. None of the choices are correct Your line is a vertical line.
*October 3, 2014*

**Analytic Geometry CHECK MY ANSWER**

your equation should read: t = 85n + 25 Doesn't the value of t "depend" on what you put in for n ?? So t would be the "dependent" variable, so that implies that ....... your choice of answer makes no sense. You mean to say that the total t is not ...
*October 3, 2014*

**Pre-Calc/Trig...**

yes and yes
*October 3, 2014*

**Pre-Calc/Trig...**

how about letting t = 1, 2, 3, 4, ... minutes and then interpret the results. What do you notice about the distance for every minute of change in time.
*October 3, 2014*

**Pre Calc**

so you want: 7000(1.07^t) = 1400 1.07^t = 2 take log of both sides, and by the rules of logs t log 1.07 = log 2 t = log2/log1.07 = appr 10.245 years
*October 3, 2014*

**Pre-Calc/Trig...**

so in f(x) = 1/(x+2) you are replacing x with 3+h so f(3+h) = 1/(3+h + 2) = 1/(h+5)
*October 3, 2014*

**Algebra 1 Check**

correct do you know why ?
*October 3, 2014*

**Math Questions**

I will do the first one: 6√24x = 18√24 divide by √24 6x = 18 x = 3 do the others the same way, #1 and #3 are incorrect, you had #2 correct btw, I interpreted you question as you typed it. I assume you did not mean 6√(24x)
*October 3, 2014*

**Math**

for y = cos kt the period would be 2π/k since the period of sec is the same as the period of sin period = 2π/(π/5) = 2π(5/π) = 10 Didn't it tell you that at the beginning ?
*October 3, 2014*

**math**

You must have been given some choices in the range to give you .34
*October 3, 2014*

**Math**

V = πr^2 h, but h = 2r so V = πr^2 (2r) = 2πr^3 then 2πr^3 = 250 r^3 = 125/π r = cuberoot(125/π) h = 2r = 2 cuberoot(125/π) = appr 6.83 cm
*October 3, 2014*

**Math**

correct
*October 3, 2014*

**math**

depends what results you want. Incomplete question .
*October 2, 2014*

**Math Question**

so y = k/x sub in the values 63 = k/3 k = 189 so .......
*October 2, 2014*

**Algebra**

since each bracket has a +1 understood in front of it, you can just drop the brackets. Collect all like terms and you are done
*October 2, 2014*

**Math 3 quick questions**

For the first two, do you notice that the binomial appears both as a square and as a first degree expression? When you first learn to do these types, it might be a good idea to replace the binomial with a single variable. e.g. in the first: let 3x+1 = a , then your equation ...
*October 2, 2014*

**algrebra**

number of dimes --- x number of quarters --- x+17 value of money: 10x + 25(x+17) = 600 , all in cents 10x + 25x + 425 = 600 35x = 175 x = 5 so 5 dimes and 22 quarters. check by finding the value of 5 dimes and 22 quarters.
*October 2, 2014*

**Math**

14 g = 53 L 1 g = (53/14) L then 25 g = (53/14)(25) L = appr 94.6 L
*October 2, 2014*

**Math**

what happens when you multiply something by 10? what happens when you multiply something by 100? by 1000? etc so look at 60x50 as 6x10 x 5x10 = 6x5x10x10 = 30x100 = 3000
*October 2, 2014*

**geometry**

You are obviously looking at some diagram, which we can't see.
*October 2, 2014*

**math**

It is unfortunate that measurement of angles, and time, has escaped the metric system. Things would be so much easier. K = 90° - 48° 26' 8" = 89° 59' 60" - 48°26'8" = 41° 33' 52" Hint: If you have a good scientific ...
*October 2, 2014*

**HELP! Algebra. DONT UNDERSTAND**

Niezel is correct from a - e explanation of e) (a+b)(c+1)-(a+b) = ac+bc = c(a+b) by common factor of (a_+b) = (a+b)(c+1 - 1) = c(a+b) f) x^2 - 9y^2 ----- standard difference of squares = (x+3y)(x-3y) g) (x^2 - y^2) + x + y = (x-y)(x+y) + (x+y) , difference of squares at the ...
*October 2, 2014*

**Financial Mathematics**

i = .07/12 = .0058333... (I stored that in memory on my calculator for good accuracy) 2000(( 1.0058333..^20 - 1)/.0058333)(1.0058333..)^40 + 2500( (1.00583333..^20 - 1)/.0058333..)(1.0058333..)^20 + X(1.005833..^20 - 1)/.0058333.. = 180000 , X = 2000+R 53375.555 + 59392.5459...
*October 2, 2014*

**Probability**

a) prob(red) = 5/10 = 1/2 b) prob(red or white) = 7/10 c) prob( as stated) = 5/10 or 1/2 , there are still 10 balls, since you replaced it whatever happened in first draw has no effect on the second draw d) prob( as stated) = 5/9 , now it matters, there are only 9 balls left e...
*October 2, 2014*

**math**

First of all the area of a circle is π r^2 , not (πr)^2 so πr2= 658 r^2 = 658/π r = √(658/π) = appr 14.47
*October 1, 2014*

**Math**

prob(fail) = 6/100 = 3/50 prob(not fail) = 47/50 prob(2 of 6 will fail) = C(6,2) (3/50)^2 (47/50)^4 = appr .042 Since the prob (anything) must be a number from 0 to 1, your answer makes absolutely no sense at all. I don't even understand your notation.
*October 1, 2014*

**Math**

y - y1 = mx - mx1 mx1 = mx - y + y1 x1 = (m - y + y1)/m
*October 1, 2014*

**Trigonometry**

safe ramp: tanØ = 1/12 Ø = 4.76° Since your angle is greater than that, it is not safe
*October 1, 2014*

**Math**

4√(1280r^4t^12) = 4√1280 √r^4 √t^12 = 4(16√5)r^2 t^6 = 64√5 r^2 t^6
*October 1, 2014*

**Math Definition Help**

Definitions are easy to check Let Google or your texbook be you friend.
*October 1, 2014*

**Math Help**

I will assume you meant f(x) = (3x+4)/5 or y = (3x+4)/5 step1: interchange the x and y variables x = (3y+4)/5 step2: solve this inverse equation for y 5x = 3y + 4 3y = 5x - 4 y = (5x-4)/3 f^-1 (x) = (5x-4)/3
*October 1, 2014*

**Pre-Calc**

A and B are inverses. (you can check by picking any number, subbing that into the original function. Take that answer and sub it into the "inverse" function. If you don't get back the original number it is not a true inverse. e.g. for D let x = 3 f(3) = 7 f(7) = ...
*October 1, 2014*

**MATH**

I will assume you meant: ln ( (3x-2)/(x-1) ) < 0 I would establish the boundary by letting ln ( (3x-2)/(x-1) ) = 0 then (3x-2)/(x-1) = e^0 , yes e^0 = 1 (3x-2)/(x-1) = 1 3x-2 = x-1 2x = 1 x = 1/2 So we need either x < 1/2 or x > 1/2 But remember x = 1 is not allowed ...
*October 1, 2014*

**Math**

1. Use the sum of n terms of an arithmetic sequence sum = (n/2)(first + last) (16/2)(first + 12500) = 800000 divide by 8 first + 12500 = 80000 first = 80000-12500 = 67500 2. museum A: a = 50,000 , d = 2500 museum B: a = 45,000 , d = 2750 find term(12) or a+11d for each one ...
*October 1, 2014*

**Maths**

Your formula makes no sense, because I could just cancel the d's and get l = k check your typing. Is there a square root somewhere I suspect something like: " intensity is proportional to the square of the distance"
*October 1, 2014*

**Pre Calculus**

I did the same question on Monday http://www.jiskha.com/display.cgi?id=1412031500
*October 1, 2014*

**MATH**

Lena,did you not check your answer? It does not work, mine does. Always check your results by testing them for the original conditions 14(.25) + 22(.50) ≠ $15.00
*September 30, 2014*

**MATH**

You should check your "caps lock" key, it appears to be stuck. number of 1/2 cups ---- x number of whole cups --- 37-x 25x + 50(37-x) = 1500 25x + 1850 - 50x = 1500 -25x = -350 x = 14 etc
*September 30, 2014*

**7th grade math**

Correct, there are 10 of them and you found them all
*September 30, 2014*

**Math**

Here is how I would do this in a formal way: Would like to have a zero on the right side, so ((3x-2)/(x-1))<1 ((3x-2)/(x-1))-1 < 0 (3x-2 - (x-1))/(x-1) < 0 (2x - 1)/(x-1) < 0 "critical values" are x = 1/2 and x = 1 This splits a number line into 3 parts, ...
*September 30, 2014*

**math**

helicopters --- H airplanes ----- 4H H+4H = 35 5H = 35 H = 7 so .....
*September 30, 2014*

**Math .**

#1 yes #2: a+5 = (1/5)(5a+25) a+5 = a+5 ----> 5=5 , statement is true infinite number of solutions #3 3(4x - 3) - 7x = 5x - 9 12x-9-7x=5x-9 5x-9 = 5x-9 true, so infinite number of solutions #4 yes
*September 30, 2014*

**Calculus**

the original fractions had 7 and 5 in the denominator which is the same as (1/7) times .... e.g 9/4 = (1/4)(9)
*September 30, 2014*

**Calculus**

recall that if y = secx dy/dx = secx tanx y= [(sec^7 x)/7] - [(sec^5 x)/5] dy/dx = (1/7)(7)(sec^6 x)(secx)tanx - (1/5)(5)(sec^4 x)secx tanx = sec^7 x tanx - sec^5 x tanx = sec^5 x tanx(sec^2 x - 1) but sec^2 x - 1 = tan^2x = (sec^5 x)(tan^3 x) nice question
*September 30, 2014*

**Pre-caluclus**

so ln(x-2e)+ln(x-3e)=2 ln ( (x-2e)(x-3e) ) = 2 by definition (x-2e)(x-3e) = e^2 x^2 - 5ex + 6e^2 - e^2 = 0 x^2 - 5ex + 5e^2 = 0 x = (5e ± √(25e^2 - 4(1)(5e^2))/2 = (5e ± √5e^2)/2 = (5e ± e√5)/2 = ( (5±√5)/2 )e
*September 30, 2014*

**analytic geometry**

horizontal distance --- x I see it as: tan 3.5° = 120/x x = 120/tan3.5 = appr 1962 ft
*September 30, 2014*

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