Monday
August 31, 2015

Posts by steve


Total # Posts: 33,168

Algebra
if there are n jr high students, then we have n/(n+100) = 7/9 9n = 7(n+100) 2n = 700 n = 350
August 26, 2015

Ap algebra
since a function maps values in its domain to values in the range, if the y-value is undefined, the x-value cannot be in the domain. Surely the minimum value of a function is the least y-value in the range. For continuous functions, that is no problem. But, if there are point ...
August 26, 2015

precalc
y = -4x+1 has slope -4 so do all parallel lines perp. lines therefor have slope 1/4 Now use your point-slope form for the line: parallel line is y-3 = -4(x+2) change the slope to 1/4 for the perpendicular line.
August 26, 2015

Math
domain is all reals, but since x^2 >= 0 for all x, y >= 9 for all x. That is the range. D: (-∞,+∞) R: [9,∞)
August 26, 2015

Algebra 2
The angles are 2x,3x,3x. The sum is 180, so x=22.5 C-A = 3x-2x = x
August 26, 2015

Precalc
check the graph of x^3+1. No horizontal line crosses it more than once, so its inverse is a function. 4^x = (1/2)^(x-3) 4 = 2^2 = (1/2)^-2, so (1/2)^(-2x) = (1/2)^(x-3) -2x = x-3 x = 1
August 26, 2015

Algebra
15^3
August 26, 2015

AP Calculus
recall the definition of |u|. It is u for u>=0, and -u for u<0. So, your function f(x) = (x-2)/(x-2) for x >= 2 (x-2)/(-x-2) for x < 2 Now you can easily find the necessary limits. Then, peek at the graph below to verify your calculations.
August 26, 2015

Math
correct. you can also note that a constant function y(x)=k is the same as y=kx^0, and since 0 is an even power, kx^0 is an even function, and thus symmetric about the y-axis.
August 26, 2015

Precalc
5x^3 y^-1 z^-5 = 5x^3 / yz^5 take the -3 power of that and you have y^3z^15/125x^9 x^2 y^0 z^-6 = x^2/z^6 square that and you have x^4/z^12 Now just multiply the two fractions and you have y^3z^3 / 125x^5
August 26, 2015

Math
k is 1000, as in kg, km, etc. 2.0*10^3kcal/day * 1day/86400s * 1000cal/kcal = 23.15 cal/s
August 26, 2015

Math
.6carat * 200mg/carat * 1kg/10^6mg * 2.205lb/kg * 16oz/lb = 0.00423 oz
August 26, 2015

Geometry
well, you know that AC+CB=AB, so 3x+55+2x = 65 Now just solve for x and AC=3x
August 26, 2015

math
divide 36 into 4+5=9 parts. Each part is 4. so, the bikes are 16:20
August 26, 2015

Logs
well, it is easy enough with a calculator; there's an e^x button. can you use Taylor Series? e^x = 1 + x + 1/2 x^2 + 1/6 x^3 + ... 1 + (-.6) = 0.4 1 + (-.6) + (-.6)^2/2 = 0.58 ...+(-0.6)^3/3!+(-0.6)^4/4! = 0.5494 ...+(-0.6)^5/5!+(-0.6)^6/6! = 0.5488 what other ...
August 26, 2015

geometry
(-3+x)/2 = -3/2 -3+x = -3 x = 0 Think about it. Starting at -3, x grows by 3/2 to -3/2 at B. It grows by another 3/2 to be 0 at C. (4+y)/2 = 1 4+y = 2 y = -2 Had you plotted these points, you would have seen that your C point was way off. And what's with the "over&...
August 26, 2015

Algebra 1
I sense a question in there somewhere... x+y=50 20x+30y=1200 so, ...
August 26, 2015

vector
I see you are not about to do anything more than repost your question. IT'S 90 DEGREES!
August 26, 2015

Math
D=L D-26 = 2(L-38)
August 26, 2015

math
oh, come on. You can draw x- and y-axes, surely? They meet at a right angle. How many degrees is that? Just place a pencil pointing out the +x axis, and rotate it till it points upward along the y-axis. You must surely know how many degrees that is. If not, you are in for a ...
August 26, 2015

math
hint: 1 is on the +x-axis i is on the +y-axis. How far do you have to rotate the +x direction to point in the +y direction?
August 26, 2015

Algebra
list the x values in the domain, and apply the rule to get y x y=x+1 1 2 2 3 3 4 4 5 Now plot those points and draw a line through them.
August 26, 2015

math
just start filling in the blanks. Start with xxxxxx greater than 700,000. The choices are 7xxxxx 8xxxxx 9xxxxx my hundred thousands digit is twice my ones digit, my thousands digit,and my hundreds digit. So, the 1st digit must be even, leaving 8x44x4 my remaining digits are ...
August 26, 2015

science
conserve momentum 20*8 + 10*0 = (20+10)v
August 26, 2015

Geometry
the diameter of the circle is the distance between the points. That distance is 5. So, now you know the radius is 5/2, and you can take it from there.
August 26, 2015

Geometry
The endpoints of a diameter on a circle are a(2,1)and B(5,5). Find the area of the circle in terms of 3.14.
August 26, 2015

Geometry
thank you
August 26, 2015

Geometry
A garden is 5 ft by 6 ft has a walkway that is 2 ft wide around it. What is the amount of fencing needed to surround the walkway?
August 26, 2015

HELPPPP! ELECTRONICS
the hole is positive, so it is drawn to the negative pole: the cathode.
August 26, 2015

algebra, numerical operation
No idea at all? Multiplication comes before addition. Where is that rule violated?
August 26, 2015

Calculus
BZZT! But thanks for playing. Consider f(x) = 1/(x-a)^2 The limit from both sides is +∞
August 26, 2015

math
∜500/∜5 = ∜(500/5) = ∜100 = √10
August 26, 2015

math
11 - 5/(4x-5) There is no "both sides" -- it's a simple expression. Suppose you had 3 - 2/5 You put it all over the denominator: (3*5-2)/5 Same here: (11(4x-5)-5)/(4x-5) = (44x-60)/(4x-5)
August 26, 2015

Math
you need √((8-4)^2 + (y-3)^2) = 11 √(16+(y-3)^2) = 11 16+(y-3)^2 = 121 (y-3)^2 = 105 y-3 = ±√105 y = 3±√105 you can check this by noting that the locus of all points a distance of 11 from (4,3) is a circle: (x-4)^2 + (y-3)^2 = 121 Now pick...
August 26, 2015

math
1 radian is 180/π degrees, so ...
August 26, 2015

Trig
This kind of problem works very well when you draw the pertinent triangle. If cosθ = 12/13, you have a 5-12-13 triangle, so sinθ = 5/13 Similarly, sinθ = 3/5 gives you a 3-4-5 triangle, so tanθ = 3/4
August 26, 2015

mathematics
2x^2 - 5x - 2 = 0 x = [5±√(25+16)]/(2*2)
August 26, 2015

Math
We can without loss of generality assume a=1, so (1+4d)/(1+2d) = (1+16d)/(1+4d) d = -5/8 The AP is 1, 3/8, -2/8, -7/8, -12/8, -17/8, -22/8, ... -9 The GP is 1, -5/8, 25/64, ... (-12/8)/(-2/8) = 6 (-9)/(-12/8) = 6
August 26, 2015

Math
can you find x when x^2 = 4? x^2 = 9? Does 144 have two equal factors?
August 26, 2015

Math
well, each cm represents 5m, so 9cm --> 5m * 9 = 45m now do 7cm the same way.
August 26, 2015

Math - eh?
If you say so.
August 26, 2015

Math
The width grows by the same ratio as the height, so w/8 = 30/14
August 26, 2015

Calculus
x^2+y^2+6x-8y+9 = 0 rearrange things a bit to get ready to complete the squares: x^2+6x + y^2-8y = -9 x^2+6x+9 + y^2-8y+16 = -9+9+16 (x+3)^2 + (y-4)^2 = 16 so, the center is at (-3,4) with radius 4. Note that the center is 4 units above the x-axis, so C touches the x-axis at...
August 26, 2015

Math-Trigonometry
Assuming B is between A and the mountain, then the height h is found from h cot22° - h cot40° = 125
August 26, 2015

MATH
n^0 = 1 for all nonzero n. So, you just have x^3x^4 = x^7
August 26, 2015

MATH
well, just plug in the numbers: 2^5*2^8/1^5 = 2^13 = 8192
August 26, 2015

algebra
since there are two corners cut from each side, the volume is 3(x-6)(x-6)
August 26, 2015

Lccn acardamy
well, first off, mercury is a metal. A simple google search will provide a wealth of interesting explanations.
August 26, 2015

pre algebra
20-2*7+1+(3)+10 20-14+4+10 6+4+10 10+10 20 In order to get your answer, you'd need 20-(14+4+10) Also, online you should use * for multiplication, so you don't get things mixed up with decimal points, as in 2.7
August 26, 2015

maths
ok, I'll give you this one (5x-3)(2x^2+3x-3) = 5x(2x^2+3x-3)-3(2x^2+3x-3) = 10x^3+15x^2-15x -6x^2-9x+9 = 10x^3+9x^2-24x+9
August 26, 2015

AHOOOGAAH! HOMEWORK DUMP!
How about if you (a) post the complete problem (b) show some work of your own?
August 26, 2015

math
so, use the number line. Which hundred is closest to 153?
August 25, 2015

Precalculus
(2π*50ft/rev)(3rev/min) = 300π ft/min
August 25, 2015

Math
How so? The first item was: The greatest place value is hundred thousand. So why do you put 7 first? I'd start with a 9.
August 25, 2015

math
clearly, they will begin with the 3 smallest digits first: 203xxxx 204xxxx 205xxxx in each case, fill in the x's with the remaining digits, from least to most.
August 25, 2015

maths
I'm having a hard time parsing your text. Is it all one expression? What is the significance of the spaces? Or are there three separate expressions? 2(x+2)^2-(2x-1)(x+2) 2x(x-2)+5x(x/3)-x(3x-1) (5x-3)(2x^2+3x-3) As for the other one, I think it's (x-2)^2+3x-2 = (x+3)^2...
August 25, 2015

Calc
points equidistant from a point in 3D are the surface of a sphere. So, your two constraints will be the intersection of two spheres, which is a circle. Naturally, the intersection will lie in the x-y plane, since the centers of the spheres are both on the z-axis. Your circle ...
August 25, 2015

math
We are told that S12 = 135 S20-S12 = 210 S20 - 135 = 210 S20 = 345 Now, we know that S20 = 20/2 (2a+19d) S12 = 12/2 (2a+11d) So, we have 10(2a+19d) = 345 6(2a+11d) = 135 Solve that for d.
August 25, 2015

Math
when multiplying roots, take the root of the product. You then have 7throot( (11x/y^6) * (y^6/11x^8) ) = 7throot(1/x^7) = 1/x It would help if you showed your work...
August 25, 2015

Math
You did the right thing to get the numerator. Now just put it all over the common denominator: (3a+3b) / ab when you're solving equations, the cross-multiplying affects both sides of the equation. When just evaluating an expression, you need to remember why you are cross-...
August 25, 2015

math
get rid of the parentheses and rearrange things a bit: (y-2) + (z+3) + (x-3) y-2+z+3+x-3 x+y+z-2+3-3 But, you know that x+y+z = 26, so that gives you 26-2+3-3 24
August 25, 2015

maths
distance = speed * time = 5*90 = 450 km/hr speed = distance/time = 450/4 = 112.5 km/hr Or, you can reason like this: 4/5 the time means 5/4 the speed. 5/4 * 90 = 112.5
August 25, 2015

Red House Primary School
x/y = 2/3 (x-1)/(y+2) = 1/2 The original ratio was 8/12
August 25, 2015

TC
Assuming that the two parts share no common volume, then just add up the volumes, using the normal formulas: Clearly, the radius of the hemisphere (and the base of the cone) is 49-35=14cm So, the volume is just (1/2)(4/3)(pi)(14^3) + (1/3)(pi)(14^2)(35) = 4116 pi
August 25, 2015

math please help 9th grade
#1 (B) since 19 is not a perfect square, √19 is irrational. 18/3 is just 6, and 11/10000 is just a rational number. #2 (A) any repeating decimal is rational. #3 (B) ok. I can't say I like your syntax. Even if you can't figure out how to copy/paste special symbols...
August 25, 2015

Maths
1800 + 11*1500
August 25, 2015

Math
57/99 is 0.5757575757...
August 25, 2015

TC
If there are n means, then the common difference is (31-1)/(n+1) = 30/(n+1) The kth mean is 1+k*30/n So, you want [1+7*30/(n+1)]/[1+(n-1)*30/(n+1)] = 5/9 n = 14 Check: 1,3,5,7,9,11,13,15,17,19,21,23,25,27,29,31
August 25, 2015

Math
you are correct
August 25, 2015

math
-12 ÷ 3 x ( -8 + (-4)^2 - 6 ) + 2 -12 ÷ 3 x ( -8 + 16 - 6 ) + 2 -12 ÷ 3 x 2 + 2 -4 x 2 + 2 -8 + 2 -6
August 25, 2015

Maths
S8 = 5S4 r^8-1 = 5(r^4-1) r^8 - 5r^4 + 4 = 0 r^4 = 1 or 4 r = ±1 or ±√2 Clearly r=±1 does not work. For r=√2, we have 1,√2,2,2√2,4,4√2,8,8√2 S4 = 3+3√2 S8 = 15+15√2 and similarly for -√2
August 25, 2015

math
y = 75.00x
August 25, 2015

Bytco College
30.8g = 0.251 moles KClO3 You can see from the reaction 2KClO3 = 2KCl + 3O2 that 1.5 moles of O2 are released for every mole of KClO3. So, you have 0.377 moles of O2. You know that at STP 22.4 moles of a gas occupy 22.4L of volume. You can finish it off, right?
August 25, 2015

math
100 cos60°
August 25, 2015

math
total possible results: 36 ways to make 5: 14,23,32,41 So, p(5) = 4/36
August 25, 2015

Math
If the dimensions are x,y,z then we have x+y+z = 80 x = 2(y+z)-10 2y = z+6 Now just solve for z.
August 25, 2015

maths
So, did you draw the tree? Can't show you mine on this site.
August 25, 2015

Calculus
the distance z is found using z^2 = 1^2 + x^2 at x=5, z^2 = 26 z dz/dt = x dx/dt so at the moment in question √26 dz/dt = 5*400 note that z will be in mi/hr
August 25, 2015

MATH
(a+6)/a = 15/12 12(a+6) = 15a 12a+72 = 15a 3a = 72 a = 24 a/j = 12/9, so 24/j = 12/9 j = 18 So, if Andy gave Joe 9, he'd have 27
August 25, 2015

Physics
(8.5 m/s) / (3.6 m/s^2) = 2.36 s
August 25, 2015

Physics
constant speed means zero acceleration
August 25, 2015

oblique triangle trigonometry
you should be able to convince yourself that the area of a parallelogram with sides a and b, and angle θ is ab sinθ
August 25, 2015

oblique triangle trigonometry
as usual, draw a diagram and review your basic trig functions. sinθ = 5.45/58.36
August 25, 2015

Algebra
|t-68| <= 3.5 68-3.5 <= t <= 68+3.5 64.5 <= t <= 71.5
August 24, 2015

BHEKISISA
Probably not an English translator or transcriber ... I suggest you talk to your school counselor, rather than a bunch of strangers half a world away.
August 24, 2015

math
Assuming the usual carelessness with parentheses, I'll go with (34-5^2) / (5 * 2^2) (34-25) / (5*4) = 9/20
August 24, 2015

calculus
x+y = 10, so y = 10-x. p = xy^3 = x(10-x)^3 dp/dx = -2(10-x)^2(2x-5) p is max when x = 5/2
August 24, 2015

Science
yes
August 24, 2015

Science
if you're breathing the atmosphere, then it must.
August 24, 2015

trigonometric oblique triangle
assuming you meant 20°50' and not 20"50', draw the diagram, filling in the angles. Use the law of sines to find h: 40/sin61°10' = h/sin20°50'
August 24, 2015

trigonometric oblique triangle
Draw a diagram. T = top of pole B = bottom of pole S = tip of shadow Draw a horizontal line from S to intersect the pole at P. The height of the pole is BP+PT BP = 16 sin14° PS = 16 cos14° PT = PS tan20°
August 24, 2015

Math
because 1 is the multiplicative identity. 1*n = n for any value of n. Since the number is the same on both sides, the ? is 1. Or, you can do it the hard way: n * 6.273 = 6.273 Now divide everywhere by 6.273 n = 6.273/6.273 = 1
August 24, 2015

Trigonometry
You can see that the altitude of the planes makes no difference. If the earth is considered a sphere with a polar radius of 6357 km, then an arc of 3000 km subtends an angle of 3000/(2pi*6357) radians
August 24, 2015

Algebra
2m - nx = x + 4 2m - 4 = nx + x 2(m-2) = x(n+1) x = 2(m-2)/(n+1)
August 24, 2015

Algebra
why bother wit LaTex? Just type it in: Suppose A and B are digits for which the product of the two-digit numbers 2A and AB is 1971. Find A+B. 2A*AB = (20+A)(10A+B) = 1971 1971 = 3^3*73 So, its only two-digit factors are 27 and 73 A+B=10
August 24, 2015

geometry
area = 4 pi r^2 volume = 4/3 pi r^3 So, for any sphere, the area:volume ratio is 3/r However, I suspect that you garbled the question. Since area varies as the square of the diameter, if the diameters are in the ratio 3/4, area is in the ratio (3/4)^2 volume is in the ratio (3...
August 24, 2015

Math
If he invested $x in B, then just add up the interest: .04(x-8000) + .08x = 1360
August 24, 2015

math
just write the words in symbols. Ben ran 2 times as many laps as Ray. B = 2R Lee ran 3 laps L = 3 which is one-half of the number of laps that Ray ran. 3 = R/2 That leaves us with the equations B = 2R L = 3 L = R/2, so R = 2L B = 2R = 2(2L) = 2(2*3) = 12
August 24, 2015

Math accelerated
Assuming a single blue tile between red tiles, we have the following table, for a single row of red tiles: R B 1 12 2 20 3 28 4 36 ... If the red tiles are laid out in a rectangular grid, then we have R B 1 12 2 20 4 34 ... So, decide on the layout of the red squares before ...
August 24, 2015

Maths
heading, not bearing. From Y, Z is on a bearing of S60E, so that is the plane's heading. 200 @ N45E = <141.42,141.42> z @ S60E = <.866z,-.50z> Since Z is directly east of X, you need 141.42 - 0.50z = 0 So, evaluate the distance z, and then the distance XZ will ...
August 24, 2015

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