# Posts by Steve

Total # Posts: 52,251

Math
factor out the ?27 and you have ?27^2 (6 - 1/4)^2 = 27 (23/4)^2 = ...

finite math
well, it is certainly not (a) 30. Note that you can choose any of 6 appetizers. For each of those 6, you can pick any of 8 salads. and so on. So, what do you think?

Math - typo
I hope you caught my top. The total area is (c+d)^3

Math Division polynomials
Note that (c^2+2cd+d^2) = (c+d)^2 That means the area is (c+d)^2 * (c+d) = (c^2)^3 Now, divide the total area by the area covered by one can to get the number of cans needed.

geometry
relative to C=(-1,4), P = (-1,-1) Q = (5,-3) So, scaling those coordinates by 2, P -> (-2,-2) Q -> (10,-6) making P' = (-3,2) Q' = (9,-2) That is, P' = C+2(P-C) Q' = C+2(Q-C)

Computer programming
sum=0 for i = 1..4 {sum += cat[i]} for i = 1..4 {pct[i] = cat[i]/sum * 100}

Math
Too bad you didn't show your work... -16(5^2)+430 = -16 * 25 + 430 = -400 + 430 = 30 How ever did you get 270? 5^2 is not 10

Math
just plug in 5 for t and evaluate it.

Maths
30% = 30/100 = 3/10 = 0.3

Maths
just plug and chug: (4/7+5/21)÷(4/7-5/21) = (12/21+5/21)÷(12/21-5/21) = (12+5)/(12-5) ...

Optional mathematics
(3-4sin^2x) (1-3tan^2x) = (3-4sin^2x) * (cos^2x-3sin^2x)/cos^2x = (3-4sin^2x)/cos^2x * (cos^2x-3sin^2x) = (3sec^2x-4tan^2x)(cos^2x-3sin^2x) = (3+3tan^2x-4tan^2x)(cos^2x-3sin^2x) = (3-tan^2x)(cos^2x-3sin^2x) see if you can finish up from here

math
the product of weight and distance must be equal on both sides, so 60*8 = 80x

geometry
of which lines? I don't mind helping to find answers, but I hate having to provide the questions as well ...

geometry
so, where is P?

Maths
1.20 * 0.90 * 0.95 = 1.026 so he gets 2.6% profit

math
4526.5/4050 = 1.1176 or 11.76% in two years. That means it gets 5.88% each year so, 1 lakh grows by 0.0588 each year ...

math
If all 30 heads are chickens, then there are 60 legs. But we have 86 legs, so there are 26 extra legs. If we replace a chicken with a cow, we get 2 more legs. We need 26 more legs, requiring 13 cows. So, there are 13 cows and only 17 chickens.

geometry
you only show one line.

Math
3*33 + 2*35 + x = 6*34 or, if you notice that 34 is midway between 33 and 35, the extra day had to be a 35, to balance them out.

math
234 = 2m m = 117 so, 117 mangoes, 234 apples ...

Calculus
(a) Apparently you are supposed to find the slopes over the various intervals [a,b]. As always, that is [f(b)-f(a)]/(b-a) Just plug in the numbers. (b) By looking at the way the results approach a single value, that is the estimate of the speed. It should be 50.28

calculus 3
see related questions below

calculus 3
Draw a diagram of the velocities. If the plane's heading is ?, we need the final x- and y-components to be N45W. So, 180sin? - 32cos60 = v sin135 180cos? - 32sin60 = v cos135 ? = 20° v^2 = 180^2+32^2-2*180*32 cos40° v = 157 mph

College Physics
Assuming it was thrown horizontally, the height h = 4.9*2.33^2 = 26.60 meters The vertical speed vy = 9.8*2.33 = 22.83 m/s The horizontal speed vx is just 17.3/2.33 = 7.42 m/s The final speed is of course ?(vx^2+vy^2) = 24.00 m/s

Math
you want dy/dt = 2 dx/dt x^2+4 = y 2x dx/dt = dy/dt So, you want 2x dx/dt = 2 dx/dt 2x = 2 x = 1 So, at (1,5) dy/dt = 2 dx/dt or, you want dy/dx = 2 y = x^2+4 dy/dx = 2x = 2 x = 1

math
I assume that by "five times less" you mean "1/5 as much" -- if so, then we have, using the scarf as the basic measure, x + x+5 + 5(x+5) = 555 7x = 525 ...

Math
there are 4 numbers, so add 'em up and divide the sum by 4.

Calculus - 7?
am I missing something here?

Math
r/d = 3/4 (r/2)/(d+r/2) = r/(2d+r) = 1/((2d+r)/r) = 1/(2d/r + 1) = 1/(2(4/3)+1) = 1/(11/3) = 3/11

maths
see related questions below.

Geometry
you're kidding, right? Just solve the equation I showed you. Don't forget your Algebra I now that you're taking geometry! subtract x from both sides, subtract 2 from both sides.

Geometry
since P and Q are congruent, their measures are equal. So, x + 7 = 2x + 2 find x, then you have something to work with.

Algebra
you haven't eliminated anything. Adding the equations does no good unless x or y disappears. Try writing them as x + 2y = 1 8x + 2y = 22 Now if you subtract them, y is eliminated...

Math
ok. now what? I know. Why not write them as 22x ? y = -23 22x + 24y = 2 guess what comes next?

CAlculus
the line 4x ? 2y = 3 has slope = 2 so, you want a line with slope = -1/2. Now you have a point (2,9) and a slope (-1/2), so your line is g-9 = -1/2 (x-2)

Math
.88p = 704

Linear equations
2k+50 = 500 Looks like a lot of unsupervised kids!

math
That ?(mn) is a problem. Try setting n = secx-tanx and see where that takes you.

Maths
there is a common difference, so log_y(x) - 1 = log_z(y)-log_y(x) log_z(y)-log_y(x) = -15log_x(z) - log_z(y) Not sure just where you want to go with this, since you only have two equations in three unknowns, but if you play around a bit, you should arrive at the fact that both...

trigonometry
sec(A) = r/x, so r = 4 x = 3 y = -?7 so, cot(A) = x/y = -3/?7

maths
(26*8)cm^2 / 2cm = 104 cm or 4*26 = 13*8 = 104

Number theory
take a look at the powers of 2 and their remainders: 2^1: 2 2^2: 4 2^3: 1 The remainders repeat like this, with a period of 3. Since 50 (mod 3) = 2, 2^50 (mod 7) = 4

physics
g = -9.8 m/s^2 So, if it loses 9.8 m/s every second, it had to start out at 3*9.8 m/s to drop to zero in 3 seconds. algebraically, v(t) = vi - 9.8t so, vi-9.8*3 = 0 vi = 3*9.8

math
BC has slope -2/5 AC has slope 6 Those two lines are not perpendicular, so there is a misprint somewhere. Now, if you just want a parallelogram, you want AD to have slope -2/5, and BD to have slope 6. That means you want the intersection of the lines y+4 = -2/5 (x-3) y-4 = 6(x...

physics
(100/s)÷(6/s^2) = 100/6 s It starts with a speed of 100, and loses 6 every second...

surface area
I'll assume that the surfaces lying on the ground are not counted. They are all 1x1 anyway, for an additional 3 u^2 area. The 1/6 block has its top and 3 faces exposed: 1+3*(1/6) = 3/2 The 1/3 block has its top, two sides, and half of another side exposed: 1+2*(1/3)+(1/6...

Science
That is Avogadro's number -- the number of atoms or molecules in a mole of matter. There are that many electrons in a mole of hydrogen atoms.

trigonometry - maths

trigonometry - maths
well, the two angles add to pi/2, so if x is the smaller angle, x + (x+2pi/5) = pi/2 2x = pi/10 x = pi/20 So, the two angles are pi/20 and 9pi/20

College linear word equation
42000 + 0.10 * 800000 However, if you are looking for a linear equation, pay = 42000 + 0.10 * sales

Maths
or, how about this? (a^2-b^2)sin? + 2abcos? = (a^2+b^2) sin? + 2ab/(a^2-b^2)cos? = (a^2+b^2)/(a^2-b^2) Multiply the the fractions top and bottom by 1/a^2, and we have sin? + 2(b/a)/(1-(b/a)^2)cos? = (1+(b/a)^2)/(1-(b/a)^2) Now let tanx = b/a sin? + tan(2x)cos? = (1+tan^2x)/(1-...

Maths
(a^2-b^2)sin? + 2abcos? = (a^2+b^2) (a^2-b^2)tan? + 2ab = (a^2+b^2)sec? (a^2-b^2)^2 tan^2? = ((a^2+b^2)sec?-2ab)^2 (a^2-b^2)^2(sec^2?-1) = (a^2+b^2)^2sec^2? - 4ab(a^2+b^2)sec? + 4a^2b^2 ((a^2-b^2)^2-(a^2+b^2)^2)sec^2? + 4ab(a^2+b^2)sec? + 4a^2b^2 = 0 -4a^2b^2sec^2? + 4ab(a^2+b...

Math
suppose they were all chickens. That would require 35*2 = 70 legs You have 8 extra legs. Each chicken you replace with a cow requires 2 extra legs. So, it looks like 4 of the 35 animals are cows.

Geometry
at least in the case of an equilateral triangle, a little diagramming should convince you that the small circles have 1/2 the radius of the larger circle. So, the sum of their areas is the same as the area of the large circle. Not sure about other triangles, though ...

math trigonometry
the shortest distance from a point to a line is along a direction perpendicular to that line. So, you want a right triangle, and the desired distance x can be found by x/1000 = sin 75°

ftcc
well, it has 8/3 that many atoms of hydrogen ...

Math 50
(x-6)^2 + x^2 = (x+6)^2 or, consider that a 3-4-5 triangle has sides which differ by 1. You have a triangle whose sides differ by 6.

math
surely you can see that the probability of three consonants is 21/26 * 20/25 * 19/24

math

Geometry
since the area of ABE is 100, and the altitude is 20, the length of AB is 10. Since the area of ABCD is 3/4 the area of ABE, CDE has 1/4 the area. So, CDE~ABE, with a scale factor of 1/2. So, CD = AB/2 = 5 check: the altitude of ABCD is 1/2 * 20 = 10 the area of ABCD is thus (...

Math
note that the 2nd difference is a constant, so we expect a quadratic rule. Using the method of your choice, you should be able to arrive at y = (x^2+x+6)/2

Calc
not quite. The 1st derivative is (-2x^2+4)/?(4-x^2) The 2nd derivative is (2x^3-12x)/(4-x^2)3/2

Mensuration maths
why are B and C the same? v = ?r^2h = 6468? cm^3 a = ?r^2 + 2?rh = 1120? cm^2 As for the distance, the most obvious answer is to go right across the bottom and straight up, for a distance of 28+33=61 cm. To figure minimum distance, you have to find the length of 1/2 of a turn ...

Math
20-8 = 12 so, how many small dogs will it take to make up the other 12 lbs?

physics
I'll assume he's lying on the ground... The arrow's height is y = tan? x - 4.9/(v cos?)^2 x^2 so, we need 400?3 - 19.6*400^2/v^2 = 40 v = 69.309 m/s y = ?3 x - 4.9/(69.309/2)^2 x^2 see the graph at http://www.wolframalpha.com/input/?i=plot+y%3D%E2%88%9A3+x+-+4.9%2F...

Math
12...x...17 so each row has 30 seats Now do the same idea to get the number of rows.

calc
#2 Let the rectangle extend from -x to +x, with height y. Then the area a = 2xy = 2x?(25-x^2) now find x such that da/dx = 0 #3 If the square cross-section has side x, and the package has length y, then the girth is 4x, and the volume is v = x^2y = x^2(108-4x)

math
surely you know that "at least" means "greater than or equal" at least 8 means 8 or more.

I am in class7
I don't see a formula, but to get the average, just add them up and divide by 7.

Maths
120(20-x) - 10x = 1880

Maths (!!)
surely you are joking! sin/cos + sin/1 is certainly NOT 2sin/(cos+1) any more than 4/3 + 4/1 = 2*4/(3+1) = 2 It just happens that your mistakes eliminated each other. sin = tan*cos, so tan+sin = tan(1+cos) tan-sin = tan(1-cos) divide and you get (1+cos)/(1-cos) divide top and ...

Math
no. |6| = 6 |-6| = 6 > -6 it is always equal unless the integer is negative. Then it is greater.

math
no. It is greater than all the negative integers.

Maths
well, you probably know that the sum of the 1st n odd numbers is n^2 ... if not, just work in from the ends. You have 6 pairs of numbers that each add to 24. (1+23, 3+21, ...)

Math
If you multiply the 2nd by 3, then you have 5a+6b = 1 9a-6b = 15 Now just add the two equations ... you sure it's not -1?

Math - and ... ?
Is there a question somewhere?

Maths
I'm sure you know how to find the volume of a rectangular tank, and a cylinder. Just divide one by the other.

math
455-464 or 465, depending on which rules you follow for rounding 5's.

Grammar
should be things also, in agreement with the other gerunds, living well would be better.

Calc
The page has a print area with width x and height y. Since xy=30, y = 30/x The page dimensions including borders are x+2 and y+2. You want minimal page area. So, a = (x+2)(y+2) = (x+2)(30/x + 2) = 2x + 34 + 60/x now just find x where da/dx = 0 The fencing problem is similar. ...

Statistics
you can play around with Z table stuff here: http://davidmlane.com/hyperstat/z_table.html

Chem 111
how many moles of Ca and O2 do you have? Each mole of O2 uses 2 moles of Ca, so check to see which will run out first. Then change the moles of CaO back to grams.

Science - see @Damon's solution
Big OOOPS! I used a speed of 1 km/hr, not 40. See Damon's "physics" solution below.

Science
40 km/h = 0.278 m/s If it accelerated at a m/s^2, then it took t=0.278/a seconds to achieve that speed. The distance covered while accelerating/decelerating is thus 1/2 at^2 + 0.278(3t) - 1/2 (a/3)(3t)^2 = 1/2 a(0.278/a)^2 + 0.278(3(0.278/a))-1/2 (a/3)(3(0.278/a))^2 = 0.155/a ...

Calculus
we know that sin(u) = u - u^3/3! + u^5/5! - ... so, sin(x^4) = x^4 - x^12/3! + x^20/5! - ... so, f(x) = 4x^7 - 4x^15/3! + 4x^23/5! - ... it is certainly obvious that d/dx -cos(x^4) = 4x^3 sin(x^4). Using series, -cos(x^4) = -1 + x^8/2! - x^16/4! + x^24/6! + ... so, its ...

URGENT - Vectors
consider the vectors as sides of a parallelogram. When are the two diagonals equal?

math
224000(1+.02)^17

math
what, no calculator handy? Still, you could do it like this: 119^2 - 111^2 = (119-111)(119+111) = 8*230 = ?

Chemistry
well, 1 mole occupies 22.4L so, how many moles do you have?

science
PE = mgh so, m*9.8*1.5 = 44.1 now just crank it out...

geometry
48/x = tan 15°

geometry
First is always draw a diagram. Then review your basic trig functions. It should be clear that the distance between the boats is 150 cot 12.5° - 150 15.3° You will also see this problem where you want to find the height, given the distance between two points on the ...

math
A?B = {(1,3),(2,2),(3,1),(3,2)...(3,6),(2,3)...(6,3)} A?B = {(1,3),(3,1)}

Math
https://www.jiskha.com/display.cgi?id=1499370105

math
every multiple of a 3-4-5 triangle would lie on the grid.

math
clearly, x must be a multiple of 5*42 = 210 I get 101010 = 42*2405 = 210*481

Math
(?3-?2)^2 = 3-2?6+2 = 5-2?6 so that means you have 5-2?6 - 3?3 + 3?2) + 4 = 9 + 3?2 - 3?3 - 2?6

Math
If a+2b=60 that is just like the problem of finding the maximum area enclosed on three sides by 60 ft of fencing. That is when a=30 and 2b=30. So, maximum ab = 30*15 = 450 f(x) = x^2 - 3x + 4 f(?3-?2) = (?3-?2)^2 - 3(?3-?2) + 4 The mean is (90+x)/5 = 18 + 0.2x arranged in ...

@oops
4-3/8 = 29/8, not 31/8

Math, algebra
If I read this right, x<>y = ?(xy)/|x-y| so, 9<>1 = ?(9*1)/|9-1| = 3/8 4<>(3/8) = ?(4*3/8)/|4-3/8| = ?(3/2)/(31/8) = 4/31 ?6 f(-1) = 3*1-5 = -2 f(-2) = 3*4-5 = 7 so, f(f(-1)) = 7