Friday
April 18, 2014

Posts by Reiny


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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