Wednesday
December 7, 2016

Posts by Reiny

Total # Posts: 36,897

math
In any triangle , the sum of any two sides > the third side, so in triangle abd, ab +ad > bd ** in triangle bcd, bc+dc > bd *** in triangle adc ad + cd > ac **** in triangle abc ab+bc > bd **** add up *, **, ***, and **** 2ab + 2bc + 2dc + 2ad > 2bd + 2ac ...
September 25, 2016

Math
Since both the flight direction and the wind are due south, just add the two velocities to get 143 m/s draw a straight line pointing south, and label its length as 142 btw, 112 m/s for a small plane = 112(60)(60) or 403200 m/h = 403 km/h or appr 250 mph, average speed of a ...
September 25, 2016

Math
Just use the distance between two points formula. It will be found in your text or your notes.
September 25, 2016

Further mathf
number who play hockey ---- x number who play football -- 2x+5 x + 2x+5 = 80 x = 25 so 25 play hockey, 55 play football, and 15 play both now we can use a Venn diagram, filling in as follows: 15 in the intersection 55-15 or 40 in the football only part of the circle 25-15 or ...
September 25, 2016

maths
sum of first 6 terms = (6/2)(2a + 5d) = 6 2a + 5d = 2 ---> a = (2-5d)/2 ** (a+d)(a+4d) = -89 a^2 + 5ad + 4d^2 = -80 sub ** into that (2-5d)^2/4 + 5d(2-5d)/2 + 4d^2 = -80 times 4, the LCD (2-5d)^2 + 10d(2-5d) + 16d^2 = -320 4 - 20d + 25d^2 + 20d - 50d^2 + 16d^2 + 320 = 0 -9d...
September 25, 2016

maths
([-4.00000001 + 1])^5 = ([-3.00000001])^5 = (-3)^5 = -243
September 25, 2016

math
sister's age --- x the boy's age -- x-6 x(x-6) = 135 x^2 - 6x - 135 = 0 solve for x, Hint: it factors nicely
September 25, 2016

maths help me asap
y = 8x^2/(x-1) y' = ( (x-1)(16x) - 8x^2) )/(x-1)^2 = (16x^2 - 16x - 8x^2)/(x-1)^2 = (8x^2 - 16x)/(x-1)^2 y'' = ( (x-1)^2 (16x - 16) - (8x^2 - 16x)(2)(x-1) )/(x-1)^4 = (16x - 16)/(x-1)^4 = 16(x-1)/(x-1)^4 = 16/(x-1)^3 Well, that went well, from here on it is easy y...
September 25, 2016

maths need help log
log2 x = k^2+2k then x = 2^(k^2 + 2k) let log64 x^3 = y then 3 log64 x = y log64 x = y/3 64^(y/3) = x then: 64^y = x^3 = 2^(3k^2 + 6k) 2^(6y) = 2^(3k^2 + 6k) 6y = 3k^2 + 6k y = (1/2)k^2 + k log64 x^3 = (1/2)k^2 + k or (k^2 + 2k)/2 a quicker way might be to use a little-known ...
September 25, 2016

Math
6 years from now: son's age ---- x man's age --- 3x present time: (subtract 6) son's age --- x-6 man's age -- 3x-6 three years from now: (subtract 3) son's age = x-9 man's age = 3x - 9 3x-9 = 9(x-9) 3x - 9 = 9x - 81 72 = 6x x = 12 son's present age...
September 25, 2016

Math
If he kept his money at home in a coffee jar he would have 250 + 25(26) = $900 If he keeps it at this "bank" which pays no interest but charges you to deposit your money with them, you would have 250 + 25(26) - 12(3) = $864
September 24, 2016

No more Juan and his bookcase questions
Enough already with Juan and his bookcase. Besides this one, I count 8 others along the same line in the Related Questions below. Surely there is something there you might like
September 24, 2016

correction - Math
600 cm x 800 cm = 480000 cm^2, not 4800 cm each tile covers 2500 cm^2 number of tiles = 480000/2500 = 192 or you can lay 12 tiles along the 6 m side and 16 tiles along the 8 m side number of tiles = 12x16 or 192
September 24, 2016

Math
let the three numbers be 1/a, 1/(a+d), 1/(a+2d) 1/a = 2/(a+d) 2a = a+d a = d so the three numbers are 1/a , 1/(2a), 1/(3a) (1/a + 1/(2a) + 1/(3a) )/3 = 20 LCD = 6a 6/6a + 3/6a + 2/6a = 60 11/6a = 60 360a = 11 a = 11/360 , d = 11/360 the three numbers are: 360/11, 360/22, 360/...
September 24, 2016

Math
If you want to add 2/3 and 3/5, you will find the LCM of the denominators then divide the LCM by the denominators and multiply it with the numerators then add it... i.e. 2/3 + 3/5 , LCM = 15 15/3 x 2 = 10 15/5 x 3 = 9 2/3 + 3/5 = 10/15 + 9/15 = 19/15 or 1 4/15
September 24, 2016

maths need help
sum of n terms of an AP if you know the first and last is sum = (first + last)(n/2) sum = (80+160)(n/2) = 120n but we know that the sum of the interior angles of a polygon = 180(n-2) so 120n = 180n - 360 -60n=-360 n = 6 your figure is an irregular hexagon check: sum of angles ...
September 24, 2016

maths
Wow, as Steve pointed out to you yesterday for this same question, this is some serious and messy algebra. I attempted it with what looked like straightforward actual equations, and it got bad very quickly. With Wolfram helping me to check for correct in-between steps and ...
September 24, 2016

Math
lim(3x^5 + x + 2) / (8x^4 - 5) , as x ---> negative infinity divide top and bottom by x^4 = lim (3x + 1/x^3 + 2/x^4)/(8 - 5/x^4) when x ---> - infinity, the terms 1/x^3, 2/x^4, -5/x^4 all approach zero, so we are left with lim 3x/8 = lim (3/8)x now as x ---> - ...
September 23, 2016

VECTOR MATH
follow the method I showed you in the two previous posts. you could also make a sketch and solve it using basic trig I see a triangle with sides 100 and 60 and the contained angle of 160° by the cosine law x^2 = 100^2+60^2-2(100)(60)cos120 ....
September 23, 2016

MATH VECTOR
same type as your previous question resultant vector = 270(cos90, sin90) + 45(cos180,sin18) = .... then find the magnitude
September 23, 2016

MATH VECTOR
45 km/h vertically and then 75 km/h horizontally --->45(cos90°, sin90°) + 75(cos0, sin0) = (45(0,1) + 75(1,0) = (0,45) + (75,0) = (75,45) magnitude = √(75^+45^2) = √7650 = 15√34 direction vector: tanØ = 45/75 Ø = appr 30.96° or ...
September 23, 2016

math
for an "annuity due", payments are made at the beginning of the payment period. e.g. life insurance and car insurance payments on the other hand, salary or work payments would be made at the end of the period.
September 23, 2016

math
amount = 500( 1.08^8 - 1)/.08 = ...
September 23, 2016

Algebra
You could go through all the possibilities, after all there are only a limited number of cases, but let one integer be x and the other one y x+y = -3 y = -3-x product = xy = -12 x(-3-x) = -12 -3x - x^2 + 12 = 0 x^2 + 3x - 12 = 0 x = (-3 ± √(9 - 4(1)(-12)) )/2 = (-...
September 23, 2016

Math
Unrealistic question. Of course the minimum number of tiles would be obtained when the shape is as close to a square as possible, but we can't control the shape of the region based on the number of tiles. (The architect had decided the shape, perhaps it is not even ...
September 23, 2016

math
solve x(x+1) = 12 x^2 + x - 12 = 0 it factors.
September 23, 2016

maths trig
Ok, hard to visualize the diagram, but I think I got it. (I have no idea why they would have the corner of the flag touch the ground) My diagram is as follows Flagpole #1 , top A bottom B , AB = 4 Flagpole #2, top C, bottom D , CD = 3 Have BD the distance on the ground between...
September 23, 2016

Newtons Cooling Method
I agree with T(t) = 89.5 - 53 e^(kt) using your data, 54 = 89.5 - 53 e^(4k) 53 e^(4k) = 35.5 e^4k = 35.5/53 = .6698... using ln 4k = ln .6693... = -.400759.. k = -.1001898 or k = -.1002 check you decimal check on mine: when t = 4 T(4) = 89.5 - 53 e^(4(-.1002)) = 54.001 , looks...
September 23, 2016

math
0.61m-1.51m=9 -0.9m = 9 m = -9/.9 m = -10
September 23, 2016

math
n-2= (10n+4)/2 n-2 = 5n + 2 -4 = 4n n = -1
September 23, 2016

Math
Easier to tell once we solve the inequation y-9>2y-2 y - 2y > -2 + 9 -y > 7 y < -7 so which numbers are less than -7 ?
September 23, 2016

math
discount = 275-220 = 55 percent of discount = 55/275 = .....
September 23, 2016

OOPS - GEOMETRY
let's back up a bit here. I set up a ratio of 1:3, thus splitting the line into 4 parts SHOULD HAVE BEEN RATION 1:2 let P(x,y) divide AB into 1:2 so for the y: (y+3)/(1-y) = 1/2 2y + 6 = 1 - y 3y = -5 y = -5/3 for the x: (x+6)/(3-x) = 1/2 2x + 12 = 3-x 3x = -9 x = - 3 , so...
September 23, 2016

GEOMETRY
let P(x,y) divide AB into 1:3 so for the y: (y+3)/(1-y) = 1/3 3y + 9 = 1 - y 4y = -8 y = -2 for the x: (x+6)/(3-x) = 1/3 3x + 18 = 3-x 4x = -15 x = -15/4 , so P is (-15/4, -2) check so far: http://www.wolframalpha.com/input/?i=plot+%7B+(-6,-3),+(3,1)+,+(-15%2F4,-2)%7D notice ...
September 23, 2016

Algebra 2
just divide both sides by pr s/(pr) = prt/(pr) s/(pr) = t
September 23, 2016

calculus help
find dy/dx 3y^2 dy/dx = 6x dy/dx + 6y - 3x^2 (dy/dx)(3y^2 - 6x) = 6y - 3x^2 dy/dx = (6y - 3x^2)/(3y^2 - 6x) = 0 for a max/min 6y - 3x^2 = 0 y = x^2/2 sub that back into the original: (x^2/2)^3 = 6x(x^2/2) - x^3 - 1 x^6/8 = 3x^3 - x^3 - 1 x^6/8 = 2x^3 - 1 x^6 = 16x^3 - 8 let x^...
September 23, 2016

Maths
well, if 2 cm ---> 5 km 1 cm ---> 2.5 km then 8 cm ----> .......
September 23, 2016

Math
f(4) = 200 e^(-.3(4)) = ... for 2nd part: half of 200 is 100 100 = 200 e^(-.3t) .5 = e^(-.3t) take ln of both sides ln .5 = -.3t lne , remember lne = 1 etc
September 23, 2016

Geometry and algebra
Don't understand your word salad, but it looks like you have a rectangle with a circle in it. No idea where the shaded region is, but ... find the area of the rectangle find the area of the circle Assuming the shaded region is the part outside the circle within the ...
September 23, 2016

Trigonometry
Assuming those directions are 75° and 165°. and ignoring the b) North , whatever that means you have a very simple problem. I made a sketch with O the port, P as its first position and Q as its final position. With some simple geometry you should see that angle P is a ...
September 23, 2016

Math
what is 2(50) - 40 ?? Btw, we mow lawns, not moe them we use a lawn-mower, not a lawn-moer
September 23, 2016

math
what is 2/3 of 60 ?
September 23, 2016

math
original fraction ----- (x-3)/x new fraction = (x-3 + 4)/(x+4) = (x+1)/(x+4) then (x+1)/(x+4) = 3/4 4x + 4 = 3x + 12 x = 8 the original fraction was .....
September 23, 2016

Math
You are choosing 3 of 4, which is C(4,3) = 4 or think of it this way: each choice you leave out a different colour, there are four colours to leave out. So four choices.
September 22, 2016

Thanks Steve - Algebra
Yup, my oops. Thanks
September 22, 2016

Algebra
how about multiply each term by 3, and look, no more fraction: -6x + y = 4 now replace your x with -3 -6(-3) + y = 4 18 + y = 4 y = 4 - 18 = -14
September 22, 2016

Math
look at a number line. The number farthest to the left is the smallest, so -8.2 <---- smallest etc
September 22, 2016

Finance
I will assume there will be 216 monthly deposits (18x12). The formula I will use assumes that the payment is made at the end of the month, but with that many payments and that trivial rate of interest it will be very little difference. i = .003/12 = .00025 p (1.00025^216 - 1...
September 22, 2016

math11
ezra's age in 2001 ----x lior's age in 2001 ----- 4x in 2003 ezra --- x+2 lior ----- 4x+2 4x+2 = 2(x+2) continue ....
September 22, 2016

mathematics
3/5 of 8 = 24/5 so what percent of 4 is 24/5 ---> 24/5 ÷ 4 = (24/5)(1/4) = 24/20 = 1.2 or 120 %
September 22, 2016

math
So the distance between them is changing at 64-53 or 11 mph time for that distance to reach 17.5 miles = 17.5/11 hrs = 1.59 hrs or appr 1 hour and 35 minutes.
September 22, 2016

math
x^3-(p+q-r)x^2+(pq-pr-qr)x+pqr If it factors, the p, or q, or r must be solutions to x^3-(p+q-r)x^2+(pq-pr-qr)x+pqr = 0 let f(x) = x^3-(p+q-r)x^2+(pq-pr-qr)x+pqr try x = p f(p) = p^3 -p^2(p+q-r) + (pq - pr - qr)(p) + pqr = p^3 - p^3 - qp^2 + rp^2 + qp^2 - rp^2 - prq + pqr = 0 ...
September 22, 2016

Math
if 1 gallon give you 15.1 miles 2 gallons will give you 2(15.1) or 30.2 miles 7 gallons will give you 7(15.1) miles .. 24 gallons will give you ....
September 22, 2016

honors algebra 1
correct, I was following that format in (3,1) , x = 3, y = 1 so in y = x - 4 I let LS = y = 1 RS = x - 4 = 3-4 = -1 so the point (3,1) does NOT lie on y = x-4
September 22, 2016

honors algebra 1
I can't see which choices you made. simply , sub each point into the equation to see if it works e.g. in #1 (3,1) into y = x - 4 LS(left side) = 1 RS = 3-4 = -1 , looks like that one didn't work.
September 22, 2016

math
I will assume you made monthly payments let that payment be p i = .08/12 = .00666... n = 36 PV = 10300 p( 1 - 1.00666..^-36)/.00666.. = 10300 solve for p (hint: it is around 320 ) take it from there
September 22, 2016

mathematics
Bob showed you that T = 7, then B = 11 there are 7 trikes and 11 bikes check: total is 18 vehicles 7(3) + 11(2) = 21 + 22 = 43 Bob's answer is correct
September 22, 2016

math
only true if you meant: tanA/(secA+1) + cotA/(cosecA+1)=cosecA+secA -secAtanA LS = (sinA/cosA)(cosA) + 1 + (cosA/sinA)(sinA) + 1 = sinA + cosA + 2 RS = 1/sinA +1/cosA + (1/cosA)(sinA/cos) = 1/sinA +1/cosA + (sinA/cos^2 A) = (cos^2 A + sinAcosA + sin^2 A)/(sinAcos^2 A) = (1 + ...
September 22, 2016

maths
term8 = a+7d term2 = a+d a+7d = 5(a+d) a + 7d = 5a + 5d 2d = 4a d = 2a term5 = a+4d = 8 a + 4(2a) = 8 9a = 8 a = 8/9 ---> d = 16/9 terms are: 8/9, 24/9, 40/9, 56/9, 72/9, 88,9, 104/9, 120/9, ... carry on check: 5 times the 2nd = 5(24/9) = 120/9 which is term 8
September 22, 2016

Math
Please restate in English using proper grammar and punctuation.
September 22, 2016

math 101
Writeacher, nice answer showing how mathematicians often assume what to them appears obvious, resulting in poor wording of the question. number of ways to choose 7 from 10 = C(10,7) = 10!/(3!7!) = 120
September 22, 2016

MATH HELP
I don't see your choices, so I can't check
September 22, 2016

MTH HELP
You did not indicate what your choices are, so how can I check your work?
September 22, 2016

Math
In what system do you get .5 marks for a wrong answer? Did you mean .5 marks are deducted for a wrong answer? then what is 2(42) - 35(.5) ?? This question makes no sense. If there are a total of 100 marks, and each correct answer is worth 2 marks, then there could only be a ...
September 22, 2016

math algebra
speed of current --- x mph distance ---- d miles time to go downstream = d/(20+x) time to go upstream = d/(20-x) d/(20+x) = (3/5)d /(20-x) divide both sides by d 1/(20+x) = 3/(5(20-x)) cross-multiply 60+3x = 100 - 5x 8x = 40 x = 5 the speed of the current is 5 mph check: ...
September 22, 2016

8th Grade Math-exponents
books have been know to be wrong, as do most teachers and students. from the way you typed it, the simplified answer is (x/2)^7 / (x/2)^6 = x/2 John1's explanation is correct
September 21, 2016

GOVT JUNIOR COLEGE
When your parrot has flown away
September 21, 2016

@ Steve - Math - check answer
Wow, simultaneous posting times. I wish there was a way to know if a fellow tutor is working on the same problem at the same time as another tutor. This would eliminate the unnecessary time that both spent on the solution. The only positive is that in most cases we end up with...
September 21, 2016

Math - check answer
To cut through the word salad of this question, we know: when t = 0 , f = 58000 when t = 2, f = 92800 , and our model is an exponential function the default base of an exponential equation is e, f = c e^kt , were c is the starting number so we can start with: f = 58000 e^kt ...
September 21, 2016

Math
true, sinx = 4 has no solution. Many equations have extraneous roots, so they don't become part of your solution set In this case the only factor that works is 3sinx + 1 = 0 sinx = -1/3 so x is in the third or fourth quadrant according to the CAST rule the angle in ...
September 21, 2016

Math
if you meant: (3/4)^3 , then = (3/4)(3/4)(3/4) = 27/64
September 21, 2016

Math
(3/4)(3) = 9/4 or 2 1/4 line up 3 sets of 3 quarters now count the quarters, you should see 9 quarters or $ 9/4, or $2 dollars and 1 quarter, or $2.25
September 21, 2016

ss
Reed, the tundra in my Canada north of Yellowknife has very little vegetation and is very cold for much of the year.
September 21, 2016

ss
The tundra would also fall within the categories stated in the question.
September 21, 2016

GOVT JUNIOR COLEGE MATHS
The exterior angles of a regular polygon are all equal, and for a polygon of n sides, they are 360/n ° each. So .....
September 21, 2016

Math
use your rules for powers recall: x^a × x^b = x^(a+b) (x^a)^b = x^(ab) x^-a = (1/x^a) ((4/x)^(n-m))×((2x^2)^m) = ((2^2 x^-1)^(n-m))×((2x^2)^m) = 2^(2n-2m) x^(m-n) × (2^m x^2m) = 2^(2n-m) x^(3m-n) check my arithmetic
September 21, 2016

Maths
You have in front of you the famous 1 - √3 - 2 right-angled triangle, with angles 30°, 60° and 90° respectively. You can easily find RP = 1 using Pythagoras. I strongly recommend that you memorize this for any future work in trig. (I always reminded my ...
September 21, 2016

Math
I don't know how Steve got those numbers, it comes out to appr 125.3 I made a sketch. I extended BC to E so the DE is an altitude and triangle DCE is right-angled. I let CE = x and DE = h x^2 + h^2 = 100, and (x+15)^2 + h^2 = 400 subtract them (x+5)^2 - x^2 = 300 30x + 225...
September 21, 2016

algebra
"y varies directly as x" ---> y = kx if x=24, y= 8 8 = 24k k = 8/24 = 1/3 <---- answer so y = (1/3)x "y varies inversely as x" ---> y = k(1/x) = k/x for x=4 and y=8 8 = k/4 k = 32 <---- the constant of variation y = 32/x Claire was right.
September 21, 2016

Math
volume = 12(12)(200) cm^3 = 28800 cm^3 or .12(.12)(2) m^3 = .0288 m^3
September 21, 2016

Algebra 1
g(X) = x^2 - X g(2) = 4 - 2 = 2 g(2)^2 -2 - (2)-2 = 4 - 2 - 2 - 2 = -2
September 20, 2016

Math
sketch a line making an angle of 27° with the horizontal. Label the length of the tree's shadow on that line as AB, with B the foot of the tree. Let the top of the tree be C (so we need BC) from A draw a horizontal and let CB extended hit that horizontal at D in the ...
September 20, 2016

math
your wording makes no sense. Did you mean 1/53 of Michael's age?
September 20, 2016

math
for both of your posts I got "file not found"
September 20, 2016

math
360 is the total of the trees number of oak trees --- 5x number of mapes ------ 7x 5x+7x = 360 12x = 360 x = 30 number of maples = 7x = 7(30) = 210 (oaks would be 150, for a total of 360 )
September 20, 2016

Mathematics
simple tangent ratio height/42 = tan36° solve for height
September 20, 2016

Maths Mensuration
first find the dimensions breath (width) ---- x length ----------- 2x 2x + 4x = 240 6x = 240 x = 40 so the park is 40 m by 80 m area of whole park = 3200 m^2 make a sketch to see that the area of the region inside the path is 36 m by 76 m area of that part = 2736 m^2 so area ...
September 20, 2016

Maths
looks quite simple, draw your Venn diagram, label the intersecting circles sw, s and f place 5 in the intersection of the 3 circles. Now look at the intersection of th sandwich and fruit, it says 7 but you already placed 5 into part of that region, so that leaves 2 for the ...
September 20, 2016

Maths Profit and Loss
solve for x, the production cost (1.06)(1.08)(1.1)x = 14741
September 20, 2016

Maths Congruence
It has to be the contained angle
September 20, 2016

math
rationals and integers
September 20, 2016

maths
10 men to build a 1 house in 6 months 10 men to build a 1/6 house in 1 months 10 men to build a 4/6 house in 4 months 1 man to build a 4/60 house in 4 months 60/4 men can build 1 house in 4 months 15 men can build 1 house in 4 months or more simply it takes 60 man-months to ...
September 20, 2016

Math
a = 5.4 v = 5.4t + c but v = 0 when t = 0 , so c = 0 v = 5.4t s = 2.7t^2 + k but s = 0, when t = 0 , so k=0 2.7t^2 = 145 t^2 = 145/2.7 t = ....
September 20, 2016

maths
NO first of all you are using x incorrectly (in the third last line x = 8,2584, and in the last line x = 41292, which is a contradiction) furthermore, we place a comma after groups of 3 digits for easier reading, not groups of 4 digits. furthermore #2, if the height is 6 cm, ...
September 20, 2016

algebra 1
find √7 and √3 on your calculator, change -7/4 to a decimal Now you should be able to tell their relative size
September 20, 2016

Math
to solve: 2x+c = 8-2x-x^2 x^2 + 4x + c-8 = 0 to have y = 2x+c to be a tangent, there can be only one real root of the quadratic so b^2 - 4ac = 0 16 - 4(1)(c-8) = 0 16 - 4c + 32 = 0 4c = 48 c = 48/4 = 12 check with Wolfram: http://www.wolframalpha.com/input/?i=y%3D2x%2B12,+y%...
September 20, 2016

Algebra
jorges ---- x years brother ---- 3x - 4 solve x + 3x-4 = 24 and sub back into my definitions.
September 20, 2016

Math
both are good examples
September 20, 2016

Math
what is .25(40) ?
September 20, 2016

correction - Math
actually I misread the question, Now I see that 12x = 48 x = 4 so we have 48 soccer balls and 60 baseballs (even easier than before)
September 20, 2016

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