Friday

April 18, 2014

April 18, 2014

Total # Posts: 26,010

**Trigonometry**

This is the second time you have posted this same question since Steve answered it for you. Please look back to your previous posts before reposting it .

**Steve - Trigonometry**

Steve, you are right, should have looked at that original restriction more carefully. ( must have automatically assumed the usual 0 ≤ Ø ≤ 2π ) So you will find my other solution comical, where I assumed that domain and got solutions in all 4 quadrants :...

**Trigonometry**

if cot 2Ø = 5/12 then tan 2Ø = 12/5 recognizing the familar 5-12-13 right-angled triangle, we would say sin 2Ø/cos 2Ø = 12/5 = (12/13) / (5/13) so sin 2Ø = 12/13 ----> 2sinØcosØ = 12/13 and cos 2Ø = 2cos^ Ø -1 =...

**trigonometry**

If cot(2Ø) = 5/12 , then tan(2Ø) = 12/5 and 2Ø is in either I or III tan 2Ø = 2tanØ/(1 - tan^2 Ø) let tanØ = u then 12/5 = 2u/(1 - u^2) , (for easier typing) 10u = 12 - 12u^2 12u^2 + 10u - 12 = 0 6u^2 + 5u - 6 = 0 (2u + 3)(3u - ...

**pre-calc help**

(9√2 , -π/4 or (9√2, 7π/4 or (-9√2, 3π/4)

**pre-calc help**

factor it (5sinx - 1)(sinx - 4) = 0 sinx = 1/5 or sinx = 4 the latter is not possible, so sinx = 1/5 x must be in I or II x = 11.537° or 168.463° if you need the answer in radians , set your calculator to RAD (DRG button) and repeat the inverse sin operation.

**Math**

LS = (1-cosx)/(sinx)+(sinx)/(1-cosx) = ( (1-cosx)(1-cosx) + sinx(sinx) )/(sinx(1-cosx)) = (1 - 2cosx + cos^2 x + sin^2 x)/(sinx(1-cosx)) = (1 - 2cosx + 1)/(sinx(1-cosx) = 2(1-cosx)/(sinx(1-cosx)) = 2/sinx = 2 cscx = RS

**math**

check if ratio of 48: 272 = 3:17 Is it? If yes, you are right.

**math**

I am sure that you can push buttons on a calculator as well as I can change the percents to decimals first .... e.g. 67.95% = .6795 5% = .05 etc

**math**

I will read it as 31,760,000 / (1 - 0.0781 ) = 34450591.17

**Pre-Calc**

check your typing, is this the way you wanted it to look like ? Don't try to form fractions instead place numerator and denominatr within brackets and use / to show the division bar. e.g. (4x -9)/(x^2+6x-7)

**geometry**

If by vertical angles you mean opposite angles when 2 lines intersect, then they must be equal, so ... 4x- 34 = 3x + 17 x = 51 and angle1 = 3(51) + 17 = 170

**math help**

I will assume you want an equation which is parallel to the given line and passing through (-3,12) Then new line will have the same slope, so it will differ from the given line only in its y-intercept: new line: y = 4x + b but (-3,12) lies on it, so 12 = 4(-3) + b b = 24 y = 4...

**german**

Ich muss mit den anderen Lehrern mitstimmen. Sie haben dir die richtige Antwort gegeben. (notice that in both sentences, the verb is at the end)

**Math**

Had that first equation not mysteriously changed we would have; 1st times 3 ---> 12x - 9y = 15 2nd times 4 ---> 12 - 20y = 28 subtract: 11y = -13 y = -13/11 into 1st: 4x -3(-13/11) = 5 4x = 5 - 39/11 = 16/11 x = 4/11

**Trigonometry**

Do you not have a calculator? if cotØ = .791 then tanØ = 1/.791 = appr 1.264 Ø = 51.656° secØ = 1/cosØ = 1.612 2. sin^2 Ø + cos^2 Ø = 1 , one of the major trig identities, which you MUST know.

**math**

First of all the equation should say: h = -16t^2 + 140t + 40 you want h = 30 30 = -16t^2 + 140t + 40 16t^2 - 140t - 10 = 0 t = (140 ± √20240)/32 = 8.8 or a negative, which we will reject it would take about 8.8 seconds to reach a height of 30 ft (on its way down)

**Precalc**

Egg on face (intentions were honourable)

**However ..... Precalc**

But in log (7-4x) since we can only take logs of positives, 7-4x > 0 -4x > -7 x< 7/4 or x < 1.75 since 7400/401 > 1.75 there is no solution to this equation.

**Math help, anyone?**

12. 7x =24 x = 24/7 13. 22:36 = 11:18 14. 24/20 = 6/5 15. 4:12 = 4/12 = 1/3 16. 46:54 = 23:27 = 23/27

**algebra**

one obvious solution: d = 0 then 1/3t + 1/4.5(t+1.5) = 1 multiply each term by 9 3t + 2(t+1.5) = 9 3t + 2t + 3 = 9 5t = 6 t = 6/5 d = 0, t = 6/5

**math ergent please**

http://www.jiskha.com/display.cgi?id=1385391935

**math**

Again, I answered this question for you yesterday, when you posted it as Kevin http://www.jiskha.com/display.cgi?id=1385420924

**math ergent please**

I did this same question when it was posted under the name of "Kevin" now it is "kavi", mmmhhhh? http://www.jiskha.com/display.cgi?id=1385421276

**analytic**

so (7,3) is the midpoint remember how to find the midpoint between (a,b) and (c,d) midpoint = ( (a+c)/2 , (b+d)/2 ) so if the endpoints are (x,6) and (9,y) then ( (x+9)/2 , (6+y)/2 ) = (7,3) (x+9)/2 = 7 x+9 = 14 x = 5 and (6+y)/2 = 3 6+y = 6 y = 0 x = 5 , y = 0 check: what is ...

**math**

A's rate = 1/16 B's rate = 1/12 combined rate = 1/16+1/12 = 7/48 let the total time taken be t days so ... 2(1/16) + (t-2)(7/48) = 1 1/8 + (7/48)t - 7/24 = 1 , ----- 1 for whole job 7t/48 = 1 - 1/8 + 7/24 7t/48 = 7/6 7t = 56 t = 8 days So it took 8 days, with A working...

**Algebra 1`**

so you want to write the equation in the form y = ....... This usually requires two steps: 1. move everybody except the y term to the right side 3y = 12x + 15 2. divide each term by the coefficient of the y term y = 4x + 5 you can do this with every linear equation in x and y.

**College Algebra**

since the zeros of the quadratic are -4 and 3 we can say: f(x) = a(x+4)(x-3) so the only thing we don't know is a possible coefficient. but f(1) = - 30 -30 = a(1+4)(1-3) -30 = -10a a = 3 f(x) = 3(x+4)(x-3) expand if so needed

**Algebra 1**

let's look again at the third if you had √-47 there would be no answer but if you had - √47 then it would be -6 to the nearest integer.

**Algebra 1**

The first two are correct to the nearest integer. The third is a trick question, you cannot take the square root of a negative number

**math**

6 = 2x3 9 = 3x3 so the LCM of 6 and 9 is 18 so how many multiple so 18 are there from 1 to 1000 ? ...18 ....36 ... etc ... 990 term 1 = 18 term 2 = 36 ... term ? = 990 can you determine which term ? is equal to 990 ?

**math**

depends on what arithmetic operation you perform the "equation" of two negative fractions is not an operation. Please clarify your problem.

**algebra**

height of penny = -16t^2 + 5t + 4 to reach bottom of well, h = -100 -16t^2 + 5t + 4 = -100 16^2 - 5t -104 = 0 using the formula: t = appr 2.7 or a negative, which we'll reject

**math ergent please**

"the remainder is -2 when f(x) is divided by x+1" --> f(-1) = -2 and similarly f(1) = -4 yielding you two equations: f(-1) = -k - m - 3 + 7 = -2 k+m = 6 f(1) = k-m+3+7=-4 k - m = -14 solve these two equations for k and m

**math**

PM(x)=-x^3+7x^2-10x = -x(x^2 - 7x + 10) = -x(x-5)(x-2) so the x-intercepts of this function are 0, 5, and 2 and it is a cubic with a negative cubic term Make a sketch and you should be able to answer all your questions quite readily.

**math**

I use synthetic division for this type of question -2 | 1 -3 1 2 ........ -2 10 -22 ....... 1 -5 11 -20 (hard to line up nicely) x^3-3x^2+x+2 = (x+2)(x^2 - 5x + 11) - 20

**math**

first try, x=1, turns out to be a zero So ... synthetic division 3x^3+x^2-8x+4 > 0 (x-1)(3x^2 + 4x - 4) > 0 (x-1)(x+2)(3x - 2) > 0 so the corresponding function y = 3x^3 + x^2 - 8x + 4 has x-intercepts of -2, 1 and 2/3 and knowing the shape of this standard cubic to o...

**math**

How do you propose we show a "graphing calculator" solution on here ? since choices of x+ ±1, ±2 are the obvious first guesses and x = 2 can be found to be a solution in a few seconds, I then did a synthetic division to get 6x^3-13x^2+x+2=0 (x-2)(6x^2 -...

**Calculus - Volume By Integration**

I also checked my calculation in our previous post http://www.jiskha.com/display.cgi?id=1385311297 I carelessly dropped the π in my last 3 lines, and should have used my calculator to add up the terms in my last line. My last line should have been 500π which then als...

**math**

using the factor theorem, I tried x = ±1, ±2, ±5 I found x=1 and x=-1 to work as well as x=-2 so factors would be (x+1)(x-1)(x+2)(........) I can reason that the first term of the missing factor is x and it must end in -5 so x^4-3x^3-11x^2+3x+10 = (x-1)(x+...

**math**

let rate of the stream be x km/h So speed with the current = 5+x speed against the current = 5-x 2/(5-x) - 2/(5+x) = 10/60 times ((5-x)(5+x) 2(5+x) - 2(5-x) = (1/6)(25 - x^2) 4x = (1/6)(25-x^2) 24x = 25-x^2 x^2 + 24x - 25 = 0 (x+25)(x-1) = 0 x = 1 or x = a negative, which we w...

**Math Word Problem**

1. common sense solution: if it takes 10 carpenters to do a house in 8 days, then 1 carpenter would take 80 days, and 4 carpenters would take 20 days. 2. by the "constant" method number of days = k/number of carpenters given: 8 = k/10 k = 80 so number of days = 80/nu...

**Calculus Area between curves**

Here is a sketch of the region http://www.wolframalpha.com/input/?i=solve+x%2B6y%3D8+%2C+x%2B8%3Dy%5E2 I will do it the easiest way. The intersection points are (-4,2) and (56,-8) I would take horizontal slices effective width of a horizontal slice = 8-6y - (y^2 - 8 = 16 - 6y ...

**math**

prob = C(30,2) x C(13,1)/C(43,3) = 435(13)/12341 = .4582..

**compound interest**

do it the same way I just showed you in your previous post.

**compound interest**

time = 77-21 = 50 years amount = 1000(1.1)^50 = $ 117,390.85

**Math**

Use Pythagoras ... shorter side = x longer side = x+5 diagonal = 32 x^2 + (x+5)^2 = 32^2 x^2 + x^2 + 10x + 25 - 1024 = 0 2x^2 + 10x - 999 = 0 by formula: x = 19.99 or appr 20 or a negative so the two sides are appr 20 inches by 25 inches

**cv**

7n−(9n+1)>5 7n - 9n - 9 > 5 -2n > 14 n < -7

**Algebra 2**

#3 - #1 y - z = 0 or y = z 2x#1: 2x + 4y + 4z = 12 #2 : -2x + 4y + 6z = -3 add them, 8y + 10z = 9 sub in z=z 8z + 10z = 15 z = 9/18 = 1/2 y = 1/2 in #3 x + 3/2 + 1/2 = 6 x = 6-4/2 = 4 x=4, y=1/2, z = 1/2

**college problem solving**

let the tens digit be x and the unit digit be y then the number is 10x + y 10x+y = (x+7y) - 6 9x - 6y = -6 3x - 2y = -2 , #1 the number reversed would be 10y + x so 10y+x = 10x+y + 27 9x - 9y = -27 3x - 3y = -9 , #2 #1 - #2 y = 7 then from #1, x = 4 the number is 47 check: rev...

**Calculus - Volume by Integration**

A quick look at the region bounded by y=(x-2)^3-2, x=0, y=25 http://www.wolframalpha.com/input/?i=plot+y%3D%28x-2%29%5E3-2%2C+x%3D0%2C+y%3D25 shows me that I should scan horizontally from y = -10 to y = 25 using V = π∫ x^2 dy from y = -10 to 25 I need x^2 y = (x-2)^...

**Geometry**

make a sketch and reflect the point (4,6) in the vertical line x = 1 to get (-2,6)

**math**

Huh? What previous question ?

**Calc**

At a time of t hrs, let the position of ship A be P and let the position of ship B be Q Join PQ, and complete the large righ-angled triangle having a base of 100 and a height of 15t + 30t or 45t (the horizontal distance between them is always 100 km PQ^2 = 100^2 + (45t)^2 2 PQ...

**Math**

One of the popular questions in Calculus texts. Let the radius of the circle be x then the width of the rectangle = 2x let the height of the rectangle be y 2x + 2y + halfcircle = 30 2x + 2y + (1/2)(2πx) = 30 2x + 2y + πx = 30 2y = 30 - 2x - πx y = 15 - x - π...

**math problem grade 8!!**

14 saves, 1 goal let in ----> 15 shots probability of letting in a goal = 1/15 so for 90 shots, prob of likely goals = (1/15)(90) = 6

**math**

it isn't. prob of drawing a queen = 4/52 = 1/13 prob of not drawing a queen = 12/13 so the odds in favour of drawing a queen = (1/13) / (12/13) = 1/12 or 1 : 12

**math**

Ricardo ----- x Miriam ------ x+4 10 years ago: Ricardo -- x-10 Miriam --- x+4-10 = x-6 at that time she was 3 times as old as Ricardo x-6 = 3(x-10 x-6 = 3x - 30 -2x = -24 x = 12 Ricardo IS now 12 and Miriam is now 16 You check the answers to make sure the conditions fit.

**Math**

mmmh, let's see - I don't see any absolute value symbols - I don't see any fractions with variables in the denominator - I see a cubic term, so it is not quadratic. well , by the process of elimination......

**Math**

If you increase the radius of a circle, does its diameter increase or does it decrease?

**Algerbra**

from the 2nd ---> y = x+4 sub into the 1st x^2 + (x+4)^2 = 58 2x^2 + 8x+16-58 = 0 x^2 + 4x - 21 = 0 (x+7)(x-3) = 0 x = -7 or x = 3 if x = -7, y = -7+4 = -3 if x = 3 , y = 3+4 = 7 x=3, y=7 or x=-7, y = -3

**finance charges**

very vague question the way it is presented m, r, and t are not defined Do you want Present Value or Future amount the formulas should be in your text or are easily looked up.

**finance**

Let P be the semiannual payment P(1.065^30 - 1)/.065 = 50000 P = 578.87

**math**

???? check your typing.

**Algebra**

If your variables disappear after performing valid algebraic operations, and -you end up with true statement, there are an infinite number of solutions -you end up with a false statement, there are no solutions. so in your case the statement 0 = 0 is true, so .....

**Calculus**

Let the point be P(x,y) , point (-4,1) be A Since the shortest distance must be where AP is perpendicular to the given line. slope of given line = 6/5 so slope of AP is - 5/6 equation of AP: y-1 = (-5/6)(x+4) times 6 6y - 6 = -5x- 20 5x + 6y = -14 , #2 6x - 5y = -1 , #1, the g...

**Math help plz check my answers!**

1. 10:2 is not in lowest terms, both numbers divide by 2 10:2 = 5:1 2. r/5= 9/21 r = 45/21 = 15/7 which is appr 2.143 They should have given 15/7 as the correct choice, the rounded off number is not exact. 3. puzzled by your choice. it takes 3 cups to make 9 dozen so it takes ...

**Math-Algebra 1**

Different texts use slightly different names for the form of the linear equation. e.g 4x + 3y -12 = 0 -----> I would call general form 4x + 3y = 12 -------> standard form y = (-4/3)x + 4 ---- > slope-y intercept form point-slope form is a starting equation, usually en...

**math**

you have to do in in two parts we need the x-intercept: 0 = √x-3 √x = 3 x = 9 area from 0 to 9 + area from 9 to 16 (If you do it in one calculation from 0 to 16, the area which is below the x-axis will work its way into the answer as a negative area) y = √x -...

**algebra 2**

2(x-5)>6(x-3) 2x - 10 > 6x - 18 2x - 6x > -18+10 -4x > -8 x < 2

**math**

A very common formula for the area of a triangle with sides A and B with Ø the contained or included angle between them is Area = (1/2)(A)(B)sinØ then (1/2)(12)(9)sinØ = 48 sinØ = .88888.. Ø = appr 62.7° or 117.3° make a sketch to see...

**math**

monthly rate = .04/12 = .003333... time from 23rd to 65th birthday = 504 months amount = 100( 1.003333..^504 - 1)/.003333.. = $130,517.61

**algebra 1**

w = -3 is a "reasonable" answer because it satisfies the original inequation, and it falls within the domain of my solution. There are an infinite number of reasonable answers. check: if w = -3 LS = |4 - 3(-3)| = |4+9| = 13 Is 13 > 8 ??? YES, so w = -3 is one of t...

**algebra 1**

Here would be the correct solution ... 4-3w > 8 OR -4 + 3w > 8 -3w > 4 OR 3w > 12 w < -4/3 OR w > 4 You didn't state what Paul had said.

**algebra 1**

10 ???? How much spread is there between 10 and 14 ?? So , are you malik or nicki? don't switch names.

**algebra 1**

The domain is -40 < x<40 which I interpret at 40 days before Sept 21 and 40 days after Sept 21 (you do the counting) the range would be .... well if x = -40 y = -.05(-40) + 12 = 2+12 = 14 and if x = +40 y = -.05(40)+12 = -2+12 = 10 The numbers 14 and 10 would be the numb...

**algebra 1**

Here is a graph of the situation. http://www.wolframalpha.com/input/?i=plot+y%3D-0.05x+%2B+12+%2C+-40%3Cx%3C40 The way it is stated the equation makes little sense to me. Is x the time relative to Sept 21 ? Is -40<*<40 supposed to mean -40 < x <40 ? that is, are yo...

**algebra 1**

Last night , I had given you a full explanation, set-up and even the solution for this problem, even though it only asked for the two inequations at the beginning of my solution. http://www.jiskha.com/display.cgi?id=1385177236 and you responded with, I am confused. What part d...

**cal**

I think you meant: f(x) = x/(x^2 + 1) (or else why not just reduce it to f(x) = 1/x + 1 ? ) for concave upwards, f ''(x) > 0 f'(x) = (1 - x^2)/(x^2 + 1)^2 using the quotient rule and again f''(x) = 2x(x^2-3)/(x^2+1)^3 so when is f''(x) positive ?...

**math**

Huh ? What question above ?

**Math**

use my favourite stats webpage http://davidmlane.com/hyperstat/z_table.html make sure you click "area from a value" enter 20 as the mean 4 as the sd click on "between" and enter 9.5 and 23 calculate to get 0.769

**algebra 1**

Aren't they supposed to be in-equalities? profit = revenue - expenses = 100x + 5y - 30x - 2y = 70x + 3y but 100x + 5y - 30x - 2y ≥ 400 70x + 3y ≥ 400 also 30x + 2y ≤ 200 15x + y ≤ 100 " Marissa can sell up to 8 framed photographs" --- >...

**math**

jhon: i want to add 34+85% i tryed it and i got 62.9 Reminds me of one of my favourite Bert & Ernie cartoons of years ago: temperature: 29° time : 6:15 ---------------- total: 6 : 44

**cal**

even though both Jai and I had the same answer, which is different from the one you picked ? Where would the 8 even come from ????

**cal**

f(x) = x^2 + x^(1/2) f ' (x) = 2x + (1/2)x^(-1/2) f '' (x) = 2 - (1/4)x^(-3/2) or 2 - 1/(4x√x) explanation: (x^(-3/2) = 1/x^(3/2) = 1/(x^(1/2)^3 = 1/(√x√x√x) = 1/(x√x)

**Math help please**

well, zero out of three is not that great. 1. did you notice 4^0 = 1 4^1 = 4 4^2 = 16 4^3 = 64 and 4^4 = 256 ?? 2. The height of the tree in my backyard "depends" on how long it has been there, so .... 3. suppose we have an area of 20 cm^2 and it stays at 20 if the w...

**math(help)**

1. what is 1/6 + 2/6 2. what is 8/8 - (4/8 + 1/8) 3. what is 7/8 - 5/8 4. what is 11/20 - 9/20

**Math**

Some rational numbers are integers. (all I need is one example) fraction--- 6/2 ineger ---- 2 is 6/2 = 2 ? The circumference of a circle varies directly with its radius f(x) = .08x^3 + .6x + 2.8 - certainly not a quadratic , (I see a cub) - I certainly don't see any variab...

**math**

You posted this before, it made no sense then, and it makes no sense to me now. what does x ≥ -13 , -13 mean ?

**math**

What a lot of extra verbiage to state the simple question: How many place settings can I make from 3 kinds of place mats, and 3 kinds of napkins (she can't use the orange ones, since she has only 3) Since all the setting have to be the same, we just have to find one number...

**Pre-Calc Help!!!**

LS = (tanx - tan(π/4)/(1 + tanx(tan(π/4)) ) = (tanx - 1)/(1 + tanx) = RS I used the identity tan(A-B)= (tanA - tanB)/(1 + tanAtanB) and the fact that tan π/4 = tan 45°= 1

**Math**

your equation says: y = -5 now in the given point (-3,1) is the y value equal to -5 ?

**Geometry**

actually, there is an infinite number of solutions one of the properties of a circle is that a triangle is formed with the diameter as a base and the other point on the circle, you will always have a right angle. so the centre would be (5,3) and the radius would be 2√2 e...

**cal**

some patterns you should just recognize. I know how to differentiate and integrate sin (?), but in both cases the derivative of the "angle" which would be the x from the x^2 has to be considered. Sure enough, the derivative of x^2, which would be 2x , is hanging arou...

**cal**

wouldn't that just be 5 cos(x^2) + c ?

**Geometry**

notice the points given form a horizontal line, so the length of the side must be 7 the x coordinate of the third point must be midway between the two points (simple geometry, look at your sketch) let the third point be P P is (-3/2, y) so the distance from P to (2,3) must be ...

**math(help)**

29/59 = appr .4915.. or about 1/2

**math in focus**

number of girls --- x number of boys --- x+121 number of females -- y number of males ---- 3y number of women = y - x number of men = 3y - x - 121 "5/6 of the males were boys " ---> (5/6)(3y) = x + 121 15y = 6x + 726 6x - 15y = -726 2x - 5y = -242 ---- A "2/3...

**Calculus Help!!!**

notice that one parabola opens up, the other down. their intersection ..... x^2 - c^2 = c^2 - x^2 2x^2 = 2c^2 x^2 = c^2 x = ± c ---- y = 0 in both they intersect at (-c,0) and (c,0) using symmetry area = 2∫(2c^2 - 2x^2) dx from 0 to c = 2(2c^2 x - (2/3)x^3) | from...

**Kelly - Amy - Chrissy Calculus**

Why are you switching names ???? Follow the method I showed you in the other two questions of this type. Did you look at the solutions? Let me know how far you get.

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