Monday

January 16, 2017
Total # Posts: 37,289

**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*

**Math**

soccer balls --- 12x baseballs ------ 15x solve 12x+15x=48 x = 16/9 soccer balls ---- 12(16/9) = 64/3 ???? bogus question! both soccer balls and baseballs must be whole numbers.

*September 20, 2016*

**Math**

Since the ball is returned, these are independent events prob(not white) = 12/17 we want this 4 times in a row, so prob(your event) = (12/17)^4

*September 20, 2016*

**maths**

Did you sketch your Venn diagram? The missing part is the intersection of all 3, label it x Now look at the intersection of A and C, it must be 34. But you already have x accounted for in the intersection of all 3. So label the part in A and C, but not B as 34-x 36 study A and...

*September 20, 2016*

**Math**

It takes 1 team 5 minutes to clean 200 yards It takes 2 teams 5 minutes to clean 400 yards (assuming they don't get in each other's way) 1760/400 = 22/5 It takes 2 teams 5(22/5) minutes to clean 1760 yards <b<It takes 2 teams 22 minutes to clean 1 mile (DonHo'...

*September 20, 2016*

**Math**

What she is referring to is this: 337 = 300 + 30 + 7 so the value of the 3 in the tens place is 1/10 the value of the 3 in the hundreds place

*September 19, 2016*

**Math**

what does x4x mean? did you mean x^(4x) ?

*September 19, 2016*

**Math 6th grade**

numbers which when divided by 4 leave 3: 7 11 15 19 23 27 31 35 39 43 ... numbers which when divided by 5 leave 3: 8 13 18 23 28 33 38 43 48 ... numbers which when divided by 6 leave 1: 7 13 19 25 31 37 43 ... ahh, 43 is in all 3 lists, so ....

*September 19, 2016*

**math**

P = I^2 R plug in your given 40 = I^2 (3) 40/3 = I^2 I = √(40/3) = ...

*September 19, 2016*