Friday
September 4, 2015

Posts by Reiny


Total # Posts: 30,720

trigonometry 28
This basic proof should be found in your textbook or in your notes. If not, just Google it, you will found many proofs.
July 2, 2015

calculus
the largest area of course is contained within a circle. So if the perimeter is 15 m then 2πr = 15 r = 15/(2π) area = π(15/(2π))^2 = 225/(4π) m^2 or appr 17.9 m^2
July 2, 2015

calculus
Ok, I will go with that assumption. As I made my diagram, I also noticed that you did not state the speed of the car B. I will also assume that the speeds are the same. At a time of t hrs, let the distance between them be x miles so by the cosine law: x^2 = (30+30t)^2 + (30t)^...
July 2, 2015

calculus
How are the two cars positioned relative to each other ? e.g. is car A directly west of car B ? is car A north of car B ?
July 2, 2015

trigonometry
use the fact that cos Ø = sin (90° - Ø) cos(3x - 10) = sin(90 - (3x-10) ) cos(3x - 10) = sin(100 - 3x) so sin(x-20) = sin(100 - 3x) then: x-20 = 100-3x 4x = 120 x = 30 check with your calculator
July 2, 2015

trigonometry
given: sinØ = a/b so y = a , x = ? r = b r^2 = x^2 + y^2 b^2 = x^2 + a^2 since we are in quad I, x = +√(b^2 - a^2) now use your definitions to state the trig ratios
July 2, 2015

Math
#1 is the interesting question Since the annuity payments become your "salary", I will assume they are made at the beginning of the year. IF x is the first payment made now , the Present Value is: PV = 8,503.05 + (1.03)(1.075)^-1 (8,503.05) + (1.03)^2 (1.075)^-2 (8,...
July 2, 2015

Math
I did this one yesterday http://www.jiskha.com/display.cgi?id=1435760969
July 2, 2015

Math
done yesterday http://www.jiskha.com/display.cgi?id=1435761181 why did you repeat the question?
July 2, 2015

Math
did you mean a = (√5 + 1)/(√5 - 1) and b = (√5-1)/(√5 + 1) ?? or the way you typed it
July 1, 2015

Math
27x^3+8y^3 --- the difference of cubes = (3x + 2y)(9x^2 - 6xy + 4y^2) = 12(9x^2 - 6xy + 4y^2) but 9x^2 - 6xy + 4y^2 = (9x^2 + 12xy + 4y^2) - 18xy = (3x+2y)^2 - 18xy = 144 - 108 = 36 so 27x^3 + 8y^3 = 12(36) = 4320 or: y = 6/x back in the first: 3x + 2(6/x) = 12 times x 3x^2 + ...
July 1, 2015

Maths
You will have 2 congruent triangles, so we need to find only the area of one of them Heron's formula: Area = √(s(s-a)(s-b)(s-c)) , were a, b, and c are the sides and s= half the perimeter s = (26+28+30)/2 = 42 s-a = 16 s-b = 14 s-c = 12 area = √(42x16x14x12...
July 1, 2015

math in distress
the second oldest could be either 9, 10, 11, or 12 All of the following satisfy the given conditons: 5 5 9 9 12 5 5 9 10 12 5 5 9 11 12 5 5 9 12 12
July 1, 2015

math in distress
one book weighs 2.5 lbs so 5 books weigh 5(2.5) or 12.5 lbs one notebook weighs 4 ounces 5 notebooks weigh 20 ounces = 1 lbs and 4 ounces , (if I recall the non-metric stuff) total = 12.5 lbs + 1 lb + 4 ounces, you were correct here = 13.5 lbs + .25 lbs = 13.75 lbs or 13 lbs ...
July 1, 2015

math
set up a simple ratio ... 1/x = (3/4) / 4 (3/4)x = 4 3x = 16 x = 16/3 I will take 5 1/3 quarts You will need to buy 6 quarts, (best bought as 1 gallon and 2 quarts) or, (by the 3 step process) 3/4 wall takes 1 quart one wall takes 1 / (3/4) quarts or 4/3 quarts 4 walls take 4(...
July 1, 2015

correction - maths
logx (1/8) = -3/2 means: x^(-3/2) = 1/8 x^(3/2) = 8 (√x)^3 = 8 √x = 2 x = 4 check: log4 (1/8) = log41 - log48 = 0 - 3/2 , (since 4^(3/2) = 8) = -3/2
July 1, 2015

mathematics :geometric progression
If geometric, then (2k-4)/(k-3) = (4k-3)/(2k-4) (2k-4)^2 = (k-3)(4k-3) 4k^2 - 16k + 16 = 4k^2 -15k + 9 -k = -7 k = 7 so the first 3 terms are: 4, 10, 25 a = 4, r = 2.5 sum(8) = a(r^8 - 1)/(r-1) = 4(2.5^8 - 1)/(2.5-1) = 4(390625/256 - 1)/(3/2) = 4(390369/256)(2/3) =4(130123/128...
June 30, 2015

Tupper
Never heard of a subject called Tupper. anyhow.... let the number of Katies truffles be x after first gifting: Katie had (3/4)x left she gave 1/2 of those away leaving her with (1/2)(3/4)x or (3/8)x truffles (3/8)x = 18 3x = 144 x = 48 So she started with 48 check: she gave 1/...
June 30, 2015

math
actually it is 1/18 since we are counting all 36 possible outcomes, our desired event could be 1,2 or 2,1 so 2/36 = 1/18
June 30, 2015

math
we have 1 - 7/9 + (7/9)^2 - (7/9)^3 + ... a = 1 , r = -7/9 sum∞ = a/(1-r) = 1/(1 - (-7/9) ) = 9/16
June 30, 2015

MRGS SCHOOL.
It says that any whole number greater than 1 is either prime itself or can be expressed as a product of two or more primes. e.g. 600 = 2x2x3x5 247 = 13x19 the factors in both examples are all made up of primes
June 30, 2015

Math
I know, I know, 6+2+5 ≠ 15, but maybe in the far distant past it was. That's what happens when you have to switch to the second hand to count, I always get confused if I have to count a finger as a carry.
June 29, 2015

Math
prob = (2/15)(5/12) = ...
June 29, 2015

Mah
prob of 2 nickels = (4/12)(4/12) = 1/9 so prob of not picking 2 nickels = 8/9 odds in favour of 2 nickels = (1/9) / (8/9) = 1 : 8 none of the choices are correct for the ODDS if you wanted the probability of getting 2 nickels it would be 1/9 the odds of an event is NOT the ...
June 29, 2015

calc
Maybe I should become a politician. Never actually answer the question, rather give an answer to some other question. Thanks for the catch Steve, that is two for one evening, I should get more sleep.
June 29, 2015

calc
slope = x/y = 3/1 = 3 so the equation of the tangent at the point (3,1) is y-1 = 3(x-3) y = 3x -8 or 3x - y - 8 = 0
June 29, 2015

Calculus
let the piece of paper be x inches wide and y inches long area of printed part = (x-4)(y-8) = xy - 8x - 4y + 32 but that equals 72 xy - 8x - 4y + 32 = 72 y(x-4) = 8x + 40 y = (8x+40)/(x-4) , clearly x > 4 amount of paper used = A A = xy = x(8x+40)/x-4) = (8x^2 + 40x)/(x-4) ...
June 29, 2015

Cycle geometry
So the exterior angle = 180-162 = 18° sum of exterior angles = 360° so 18n = 360 n = 20 It is a 20-gon
June 29, 2015

Physics
let's assume that for the first 1.95 seconds, the given acceleration of 44.3 m/s^2 includes the effect of gravity, and for any time thereafter the effects of gravity of -4.9 m/s^2 takes over for the first part: a = 44.3 v = 44.3t + c but when t = 0 (at the start) v = 0...
June 29, 2015

Algebra
amount of 15% juice --- x amount of 5% juice ---- 10-x .15x + .05(10-x) = .12(10) solve for x
June 29, 2015

algebra
Steve answered a similar question: http://www.jiskha.com/display.cgi?id=1435406901
June 28, 2015

math
the way you typed it, it is not a quadratic but a cubic e.g. 10x^2 - 1/x = 3 times x, 10x^3 - 1 = 3x 10x^3 - 3x - 1 = 0 , which is a cubic equation appr x = .67023 if you meant: (10x^2 - 1)/x = 3 then 10x^2 - 1 = 3x 10x^2 - 3x - 1 = 0 (2x - 1)(5x + 1) = 0 x = 1/2 or x = -1/5 ...
June 28, 2015

Math
I assume you are rounding to the nearest thousand since it rounds to 4000, the hundreds digit could only be 0,1,2,3, or 4 if the number starts with a 4 or only 5,6,7,8,9 if it starts with a 3 but the hundreds digit is twice the tens, so the hundreds digit must be even so cases...
June 28, 2015

MATH
number of 5RS coins --- x number of 2RS coins = .15x 5x + 2(.15x) = 1272 5.3x = 1272 x = 240 so 240 of the 5 RS coins, and 36 of the 2 RS coins
June 28, 2015

Maths
let the number of cookies be x let the number of friends by y x - 5y = 0 x - 3y = 36 subtract them: -2y = -36 y = 18 x - 5(18) = 0 x = 90 John has 90 cookies.
June 28, 2015

Math
starts with x spends half, so amount left = (1/2)x Spends 1/3 of that, so left with (2/3)of (1/2)x thus amount left = (2/6)x or (1/3)x but (1/3)x = 20 x = 60
June 28, 2015

Geometry
no, one other piece of information , such as one of the angles or one of the diagonals must be given. Many years back on Sesame Street, Oscar the Grouch took a rectangle and squished it, so its angles were no longer 90°. He then called it a wrecked-angle. Notice that if ...
June 27, 2015

ahhh #2 - Math
looks like our replies crossed. So there was an actual direction to your problem. Now you state: "Write each expression as a single logarithm" Why didn't you say that at the beginning and avoid all this confusion.?
June 27, 2015

ahhh - Math
Just thought I would play some "Jeopardy" with your post Alex Trebek : log3 (3x^2) me: What is 1 + log3 (x^2) simplified expanation: log3 (3x^2) = log3 3 + log3 (x^2) = 1 + log3 (x^2) so the two expressions are the same.
June 27, 2015

Math
1 + log3(x^2) is not a question 1 + log3(x^2) is an algebraic expression What do you want to do with it ? Do you want to solve something like 1 + log3(x^2) = 0 ? Do you want to colour it blue? Do you want to sent it to Donald Trump as a campaign slogan? etc The way it stands, ...
June 27, 2015

Math
just replace y with x, since it says y = x 2x^2 - x^2 = 1 x^2 = 1 x = ±1 if x = 1, then y = 1 if x = -1, then y = -1
June 27, 2015

Maths
arrangements in a line = 5! = 120 around a circle, with no specified position around the table = 5! / 5 = 4! = 24 e.g. for any arrangement of the 5 people around the table, everybody could get up, move once to the left, and the arrangement would not change, etc . We could do ...
June 27, 2015

Math
A: x > 14 , so NO B: x > 77/2 , so NO C: x = -8 , so NO D: x ≤ 26/3 or x ≤ 8 2/3 , YEAH, since 8 ≤ 8 2/3
June 26, 2015

Geometry
Just use ordinary keyboard keys According to the properties of tangents to circles, AO is perpendicular to PA making angle PAO = 90°, thus angle angle POA = 90-32 = 58° The same property is true for angle POB since PA = PB , angle POB = 58° Then angle AOB = 116°...
June 26, 2015

math
possible numbers: 111111 222222 .... 999999 largest such number: 999999 number from above with a sum of 6 : 111111 999999 - x = 111111 x = 888888
June 26, 2015

Probability
sounds like conditional probabilty Prog(A|B) , (read as the prob of A, given B) = prob(A AND B)/prob(B) prob(A and B) = 1/15 prob(B) = 7/15 prob( as stated) = (1/15) / (7/15) = 1/7 (of course, since the 4 is one of the 7 even numbers from 1 - 15)
June 25, 2015

Algebra
I agree with Ms Sue To show us that you are not merely sponging off us, for the question above, I would be interested in your thinking to solve the problem So you want whole numbers m and n so that 3^m + 2^n ≤ 999
June 25, 2015

Algebra
make a list of possible coins to give you 38 cents e.g. Q D N P 1 1 0 3 1 0 2 3 ... 0 0 7 3 ... then pick the one where the sum of coins is 8
June 25, 2015

Advanced Algebra
Use your definition of an arithmetic sequence. The difference between any pair of consecutive terms must be the same, if subtracted in the same direction, that is .... (4m-8) - (m) = (m^2 - 6) - (4m-8) 4m - 8 - m = m^2 - 6 - 4m + 8 0 = m^2 - 7m + 10 (m - 2)(m - 5) = 0 m = 2 or...
June 25, 2015

Math: Compounded Interest
for semi-annually .... amount = 200( 1.025)^(1/2) = 202.48 , not 201.20
June 25, 2015

Math
Steve, your graph does not agree with your solution, so looking at it carefully, I had the same up to 3(√(x^2 + y^2) = 1 + 4y square both sides 9(x^2 + y^2) = 1 + 8y + 16y^2 9x^2 + 9y^2 - 16y^2 - 8y = 1 9x^2 - 7y^2 - 8y = 1 you forgot to square the 3 I am sure Justine ...
June 25, 2015

math
1 km = 1,000 metres = 100,000 cm = 1,000,000 mm so 18 mm = 18/1000000 km = .000018 km nobody using the metric system would measure mm in km !
June 25, 2015

Math (arithmetic)
In your arithmetic series: a = 21 d = 1 n = ?? sum(n) = 1065 1065 = (n/2)(2(21) + (n-1)(1) ) 2130 = n(42 + n - 1) 2130 = n^2 + 41n n^2 + 41n - 2130 = 0 (n-30)(n + 71) = 0 n = 30 or n = -71 , but n > 0 there are 30 rows
June 25, 2015

math 2
prob = (8/18)(6/18) = .....
June 25, 2015

mathematics
"product" is the result of multiplication, so ... just multiply them.
June 25, 2015

Math
Just translate .... "My hundreds digit means nothing." ----> XX0XX "Six more than my hundreds digit is my thousand’s" --->X60XX "ones less than my thousands’ is my ten thousands" ---> 560XX "My tens digit is four more than ...
June 25, 2015

Math
Review the laws of exponents First of all √2 = 2^(1/2) then √(1/2) = √1/√2 = 1/√2 = 1/2^(1/2) = 2^(-1/2) based on 1/a^n = a^-n
June 24, 2015

Math
It would be so much easier if we could identify you by some name other than Anonymous.
June 24, 2015

Algebra
Damon did a whole bunch of those for you yesterday. The idea is to use a previous solution and apply it to a new question. x^2 + ax + 25 = (x + ???)^2 Gee what do you think we need so when squared we will get 25? And what will be the middle term if we expand that?
June 24, 2015

Math
You will have to know the 3 prime properties of logs 1. logk (AB) = logk A + logk B 2. logk(A/B) = logk A - logk B 3. logk (A^n) = n logk A where k is any positive number , k ≠ 1 so log2√36 - log2 log2</sub√72 = log2 (√36/√72) = log2 √(36...
June 24, 2015

math
You posted the same question yesterday, and Steve pointed out to you that you are missing some important data http://www.jiskha.com/display.cgi?id=1435116033 and yet you posted it again exactly the same way.
June 24, 2015

Geometry
The diagonals of the prism are formed by the height of the prism, which is 12 cm, and the diagonals of the base rhombus. I will do one of the diagonals , you do the other. for acute angle of the rhomus: sinØ = 9.6/10 Ø = 73.7° the the obtuse angle is 106.3&...
June 24, 2015

dav public
Not enough information, you need either another angle or another side
June 24, 2015

Algebra
R(P) = .37 ln P + .05 when P = 532 walking speed = .37ln 532 + .05 = 2.372 ft/s ?????
June 23, 2015

math
when is 5,592,000(1.038)^n = 14,000,000,000 5.592 x 10^6 (1.038)^n = 1.4 x 10^10 1.038^n = 2503.576... n log 1.038 = log 2503.576.. n = 209.8 years What a silly question.
June 23, 2015

math
Are you sure these logs weren't added ? then we could do something, but the way it sits, I see no simplification
June 23, 2015

math
correct
June 23, 2015

math
What is 5000(1.035)^16 ?
June 23, 2015

math
log2 8 = 3 <-----> 2^3 = 8 I actually had my students write this down in their notebooks, highlight it, and memorize it It clearly shows where the numbers go in the conversion of one format to the other.
June 23, 2015

Math
3/5 < n/7 < 4/5 multiply by 35 , the LCD 21 < n < 28
June 23, 2015

Math
The question only makes sense if we know the definition of x. Is x the number of years since 2000?
June 23, 2015

Math
A = 2 , term(10= ar^9 = 1024 then 2 r^9 = 1024 r^9 = 512 take 9th root r = 2
June 23, 2015

math
Possible cases: 3A0AA0 5A2AA1 7A4AA2 9A6AA3 , where A can be any number from 0-9 since those positions have not been defined If we make the unit digit 4, then the thousand digit is 8 and the hundred thousand digit would be 11 ???? Now fill in any digits for A that you like.
June 23, 2015

math
x + 317849 - 126527 = 648274 x = 648274 - 317849 + 126527 x = ....
June 23, 2015

Math
I ignored this question when you first posted it as "Phil" because the poor punctuation and grammar made it hard to understand. e.g. "sales of 58-inch HDTV's are expected to be equal." Equal to what?
June 22, 2015

Algebra
typo ? I count only 4 marks for the first 5 tests Once you found your error, replace A with your 5th test and solve for x (A+70+80+79+69+x)/6 ≥ 80
June 22, 2015

MATH
x - 12 - 6 = 2(12+6) take over
June 22, 2015

Math
mmmh, if it took him 4 hrs to 144.6 miles then in 1 hr he went 144.6/4 or ...... miles if 12 gallons took him 144.6 miles then 1 gallon took him 144.6/12 or .... miles
June 22, 2015

math
so it must start with a 6 6X,XXX The unit digit can only be 5 so we have 6XXX5 then 6 + 3X+5 = 23 3x = 12 x = 4 your number is 64445
June 22, 2015

Algebra
Since there is no t term in the equation the ball was "dropped" from a height of 240 ft. So the maximum height was 240 ft
June 22, 2015

math
umhhh, don't you look back at your previous post ? http://www.jiskha.com/display.cgi?id=1434968282
June 22, 2015

correction - math
or basic algebra .... let her total amount of money be x x - (1/3)x - (2/5)x = 60 multiply all terms by 15 15x - 5x - 6x = 900 4x = 900 x = 225 Jane had $225 check: snacks = (1/3)(225) = 75 book = (2/5)(225) = 90 , expensive book! amount left = 225-75-90 = 60
June 22, 2015

math
The fifth digit can only be 4,5, or 6 let's start with the largest case 6X,XX7 , where X is the same 6 + 3x + 7 = 19 3x = 6 X = 2 one case: 62227 if the unit digit is k, it should be clear that 19-(6+k) must be a multiple of 3 and that is true only of x = 2 how about ...
June 22, 2015

math
Your question is not clearly stated. Do you want the number of elements in a particular subset of a given set? or Do you want the number of subsets possible for a given set? or ... e.g. suppose the have a set of 6 elements such as {A,B,C,D,E,F} The number of subset is 2^6 or ...
June 22, 2015

math
2^x = 2x no simple formula method to do this type of equation. If you know Calculus , you could use Newton's method. A good way to start is to graph y = 2^x and y = x^2 to see that there are two intersection points. However, they made it easy for you and picked a system ...
June 22, 2015

balayan national highschool
Possible cases: 3A0AA0 7A4AA2 , where A can be any number from 0-9 since those positions have not been defined If we make the unit digit 4, remember your number has to be even, then the thousand digit is 8 and the hundred thousand digit would be 11 ???? ) Now fill in any ...
June 22, 2015

Calculus(math)
if v(t) = 2t + 1 then s(t) = t^2 + t + c s(5) = 25+5+c = 30+c s)0) = c effective distance = s(5) - s(0) = 30+c - c = 30 what you found is the difference in the velocities
June 21, 2015

CASS ? Bea ? ALGEBRA
check for previous post of this http://www.jiskha.com/display.cgi?id=1434803510
June 20, 2015

Calculus
let the angle be Ø given: dØ/dt = 2° per minute = 2(π/180) radians = π/90 radians (I switched to radians, since trig derivatives are valid for radians) let the third side be x x^2 = 10^2 + 19^2 - 2(10)(19)cosØ x^2 = 461 - 380cosØ 2x dx...
June 20, 2015

ALGEBRA
If after 20 minutes past "now" the minute hand is just as far ahead of the hour as it is behind, the time then clearly must be 3:30 so 20 minutes ago, it must have been 3:10
June 20, 2015

ALGEBRA
smaller number --- x larger number ---- x+40 arithmetic mean = (x + x+40)/2 = x+20 geometric mean = √(x(x+40)) x+20 - 2 = √(x^2 + 40x) square both sides x^2 + 36x + 324 = x^2 + 40x 324 = 4x x = 81 one number is 81 and the other is 121 check: AM = (81+121)/2 = 101 ...
June 20, 2015

oops - Ndmc
Steve is right, I misread the question Nevertheless, that is some dangerous speed the bus is going The math is correct, the bus will catch the car after 20 seconds
June 20, 2015

Second thoughts - Ndmc
Even though the above solution is mathematically correct, it makes no sense and the question is ridiculous. let's look at what time their speeds are the same 5t = 50 t = 10 after 10 seconds, the bus is going at 50 m/s and the car is going at a constant speed of 50m/s but ...
June 20, 2015

Ndmc
The question is poorly worded. It says, "At the same time" a car .... overtakes and passes the bus. So the time would be zero. I will assume that the car was a certain distance behind the bus bus: a = 5 v = 5t + c but when t=0, v=0 , so c=0 v = 5t s = distance = (5/2...
June 20, 2015

math
7 = 1x7 8 = 2x2x2 12 = 2x2x3 Everybody must be represented, so LCD = 1x2x2x2x3x7 = 168
June 20, 2015

geometry
d miles correspond with 9 inches on the map so 1 mile corresponds to 9/d inches d+1 miles corresponds to (9/d)(d+1) inches on the map doodle with (9/d)(d+1) any way you want.
June 19, 2015

Math
The period: 2π/k = 5 then k = 2π/5 the amplitude = 35/2 = 17.5 your ferris wheel behaves like h = 17.5sin(2π/5) but you said it is 50 m high and the max height of the function is 17.5 so we need h = 17.5sin(2π/5) + 32.5 looks like I am overthinking this ...
June 19, 2015

algebra
However, since both sides were squared, all answers must be checked in the original equation √(10-x) + x = 8 if x = 6 LS = √4 + 6 = 8 = RS if x = 9 LS = √1 + 9 = 10 ≠ RS so the only solution is x = 6
June 19, 2015

Math
how about this approach: Simone's money --- 2x Fiona's money --- 3x after mom's gift: 2x/(3x+5) = 4/7 14x = 12x + 20 2x = 20 x = 10 so Simone had 2x or $20 Fiona had 3x or $30
June 18, 2015

Math (Need help Urgent)
I am sure you meant: y ≤ -2(x - 2)^2 - 2 which would be everything below and including the parabola, which itself opens downwards and has a vertex of (2,-2) http://www.wolframalpha.com/input/?i=y+%E2%89%A4+-2%28x+-+2%29%5E2+-+2
June 18, 2015

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