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Posts by Steve

Total # Posts: 52,084

Algebra
google is your friend: https://math.stackexchange.com/questions/1967491/suppose-we-have-the-following-identity-px-1-py2-ax2-bxy-cy2-f

Algebra
xf(x) + f(1-x) = x(x-1)(x+1) (1-x)f(1-x) + f(1-(1-x)) = (1-x)((1-x)-1)(1-x+1) multiply the first by (1-x): x(1-x)f(x) + (1-x)f(1-x) = x(x-1)(x+1)(1-x) f(x) + (1-x)f(1-x) = (1-x)(-x)(2-x) subtract to get (x(1-x)-1)f(x) = (x(x-1)(x+1)(1-x))-((1-x)(-x)(2-x)) f(x) = -x(1-x)(x^2-x+...

Algebra
If y=f(x) maps a value of x to a value of y, then look at the first line. It says f(4) = -2 f(4) = 2 it cannot be both. So, (A) is not a function.

Algebra
if a value of x maps to two different y's, it is not a function. So, look for a line with a repeated 1st element.

Algebra
ya think? 3f(1/x)+(2f(x)/x)=x^2 now, if x = -2, 3f(-1/2) + 2f(-2)/-2 = 4 3f(-1/2) - f(-2) = 4 if x = -1/2, 3f(-2)+2f(-1/2)/(-1/2) = 1/4 -4f(-1/2) + 3f(-2) = 1/4 f(-2) = 67/20 ------------------------ or, we have ------------------------ 3f(1/x)+2(1/x)f(x) = x^2 3f(x) + 2xf(1/x...

physics
conserve momentum: 3*5 + 4*0 = 3*0 + 4v

Math
The number of fish in a tank decreases by x% each year. Given that the number of fish halves in 8 years, (1-x/100)^t = (1/2)^(t/8) t log(1-x/100) = t/8 log(1/2) log(1-x/100) = log(2^(-1/8)) 1 - x/100 = 2^(-1/8) x/100 = 1 - 2^(-1/8) x = 100(1 - 2^(-1/8)) = 8.3

Math Help TIMED!
but yes, it is A.

Algebra 2
not quite... 5?8^(4x) = 376 8^(4x) = 75.2 4x log8 = log75.2 x = log75.2/(4log8) or, since 4log8 = log4096, x = log409675.2

math
you are correct. The question is, why did you use that value? Just think it through, and you should see why it is correct.

Chemistry
start by recalling that 1 mole occupies 22.4L (dm^3) at STP Then use the fact that PV=kT since all the items are given in the same units, the formula works just fine. Just find the one which matches the standard values.

trigonometry
is the building uphill or downhill from the post? If the building is downhill from the post, at a horizontal distance of x, then let a = vertical distance from the base of the building to the base of the post x = horizontal distance between building and post h = height of post...

trigonometry
Draw a diagram. Let a = distance from A to the base of the tower b = distance from B to the base of the tower h = height of the tower Then we have b^2 = a^2+50^2 h/b = tan18° h/a = tan30° Now you can find a,b and thus h.

Science
google is your friend: https://socratic.org/questions/write-a-balanced-ionic-equation-to-represent-the-reaction-between-sulfur-dioxide

Maths
clearly, (7 1/4)*(1 3/5) = 29/4 * 8/5 = ?

Math
42%

Math
no idea what "M<mon" means

Trigonometry
yes

Trigonometry
just so.

Trigonometry
just recall the definition of the trig functions, in terms of a standard triangle. sin = y/r cos = x/r tan = y/x since r is always positive, you just need to ask yourself where are x and y both positive? do you feel lucky? . . . well, do ya?

calc
in either case, apply the chain rule. If u is a function of x, then if y is a function of u, we have dy/dx = dy/du * du/dx so, what do you get?

math
they will be in QII and QIII. cos 53.3° = 0.5982 Use that for your reference angle.

Maths - Polar coordinates
you can also do the rotation simply by adjusting the angle. Rotate (?13,30) by 30, and you end up at (?13,60). Now just convert that back to rectangular coordinates.

physics
Draw right triangle ABC with right angle at A. As sides of the triangle, a^2 = b^2+c^2 a^2 = 12^2 + (18-a)^2 a = 13 You have a 5-12-13 triangle.

Maths
you really need to proofread your posts ... The cross-section is a trapezoid with area A = (3/2 + 3)/2 * 15 m^2 So, the volume of the pool is A*40 m^3 now just convert that figure to "lotelres"

MATH
how many of the 6 numbers are greater than 3?

Physics
Draw the velocity vector v, pointing kind of northwest, with length 100. At its end, add a vector pointing eastward, of length 45. You want to figure the angle of the velocity vector so that when you add the two, the east-west component is zero. That is, the resultant velocity...

Math
h/7.5 = sin32°

Algebra 2
x chose option 2 x+45 chose option 1 the rest (475-x-(x+45)) chose neither now add up all the money 35(x+45)+25x+15(430-2x) = 13275 solve for x and then you're on your way.

Math
(c) two line with different slopes intersect in a single point, so ...

math
since the curved part is a semi-circle of radius 4, (8*6 + ?/2 * 4^2)*15 = 720+120? in^3

Algebra 2
x = (g-5)^2 g-5 = ±?x g = 5±?x picking one branch, g = 5+?x Hard to say what all your weird syntax means.

Math
the plane z = k is parallel to the x-y plane at a distance |k| The x-y plane is the plane z=0 (which, or course, does pass through the origin)

cms
y+x = 116 y-x = 24 Now just solve for x,y and 180-(x+y)

Maths
area grows by a factor of 1.2^2 = 1.44 resistance decreases by that factor. (Not a decrease of 44% !!)

math
217 = 7*31 310 = 10*31 713 = 23*31 It appears that dividing any of the original numbers by 31 will leave a remainder of 3.

Maths
sides

math
just add the two numbers. That's what "increase" means.

physics
(90-27)g / 50ml = 63/50 g/cm^3 now just convert that to kg/m^3

Math
7m + (m/2)(d-7)

Algebra
your equations are correct your solution is correct D is of course, not a solution. Not only does 5*180+8(-30)?900, but -30 is not a valid number of tickets.

fractions
7600(3/8)(2/3)

geometry
? * 0.5^2 * 3 (1+8+27) = 27? in^3

Math
#1 ok #2 not so much what is -3-4 ?

Algebra 2 quick check
except for the typos, looks good. Online you should use parens or spaces so we can tell whether 3/4x means 3/(4x) or 3/4 x = (3/4)x

Algebra 2
I disagree: 4600*0.983^7 = 4080

Algebra
you seriously need to work on your formatting... http://www.jiskha.com/display.cgi?id=1496332774

Math
just as with the others, the sum is a1/(1-r) just plug in your numbers.

Math A Calculus
this is calculus. Surely you can work with fractions... (a) a+b = (2/3)+(-1/4) = 8/12-3/12 = 5/12 (b) what do you think? recall that the length of ai+bj+ck = ?(a^2+b^2+c^2)

Math
so, what are the even multiples of 13? 26 52 78 so, what do you think?

Math
convert each displacement to rectangular form, and then just add them up. Then if the final position is (x,y), the displacement is ?(x^2+y^2)

Math
no diagrams here.

maths
well, 100% is all of the students. what is 100-54? no idea what the "strength" of a class is. Size? If so, then 23 = (1-.54)x

geometry
so, using the formulas, what do you get?

Math (Sorta dumb question)
Your final answer is correct.

Math
a1=243 r = 2/3 an = 243(2/3)^(n-1) a5 = 48 s = a/(1-r) = 5/(5/4) = 4

Math
hard to say, with no figure to compare ...

Math
recall that sin(90-?) = cos? cos(90-?) = sin? now see what you have.

Algebra 1b
(d) not (a) if n is negative

Math
huh? You surely must see from Scott's lines of text that 792 = 12C5

Math
oops tan(?) = y/x

Math
well, let's try to take this step by step. Let's call the two lower vertices L and R. Suppose we have L = (h,-k) Then the line LC has slope mLC = k/(1-h) and its equation (using point A) is y = k/(1-h) (x-1) Since LRC is equilateral, its angles are all ?/3. So, the ...

Math
well, let's try to take this step by step. Let's call the two lower vertices L and R. Suppose we have L = (h,-k) Then the line LC has slope mLC = k/(1-h) and its equation (using point A) is y = k/(1-h) (x-1) Since LRC is equilateral, its angles are all ?/3. So, the ...

Math
well, let's try to take this step by step. Let's call the two lower vertices L and R. Suppose we have ?/3 L = (h,-k) Then the line LC has slope mLC = k/(1-h) y+k = k/(1-h) (x-h) Since LRC is equilateral, its angles are all ?/3. So, the slope of LR is mLR = tan(arctan(...

Calculus
clearly, the series converges, since |sin(4n/?)+3|/4^n < |1+3|/4^n which converges to 16/3 But I can't come up with the actual limit value.

Math: Trigonometry
not quite -- 4/?7 is csc? did you draw the triangle?

Math
just set up equations to fit the facts. For example, #1 m/k = 5/6 m = k-12 so, (k-12)/k = 5/6 #2 7/15 = f/75 d = 75-f what do you get for the others?

Math
(c) because multiplying or dividing by a negative value changes the direction of the inequality 6 > 3 6(-4) = -24 < -12 = 3(-4)

Math
You know that Pn = 5+7n so, replace n with 4, and you get P4 = 5+7*4 = 33

Math
actual increase: 9.68-9.57 = 0.11 % increase: 0.11/9.57 = 0.01149 = 1.15%

algebra
15. yes 16. f(6) = 11*6+15 = 81 g(81) = -11*81^3 - 15*81^2 + 12*81 - 13 = -5,943,307 17. f(9) = 15*9^3 + 13*9^2 - 15*9 + 15 = 11,868 g(11868) = 15*11868 + 11 = 178,031 see? nothing to it! Although all the big numbers are annoying. The arithmetic just gets in the way of the ...

algebra
g(7) = -15*7^2 + 14*7 - 10 = -647 g(g(7)) = g(-647) = -15(-647)^2 + 14(-647) - 10 = -6,288,203 Not hard - just be careful with the arithmetic.

help me maths anyone
Draw a diagram. If we let T be the top of the mast O be the base of the mast P,Q be attachment points of two wires (PQ forms one side of the base of the triangle on the ground) M be the midpoint of PQ OV = 1 PV = 2 so, OP = ?3 triangle MOP is a 30-60-90 right triangle, so OP...

@Dang
Reiny is correct.

sir steve damon reiny steve help maths
Draw a diagram. Using similar triangles, if x = the distance from the lamp post s = length of shadow s/1.5 = (x+s)/6 s = x/3 so, ds/dt = 1/3 dx/dt ... Extra credit: how fast is the tip of the shadow moving?

Algebra 2
plus, since they are inverses, (b) is also correct.

Algebra 2
your answer is correct if you meant y = 2x y = log2x

Algebra
Who says it has to be simplified at all? However, since 97 is prime, 97x is a perfect square if x is 97. Or, if x is 97 times any perfect square.

Math check my answer
I agree... I think.

Math~Algebra
just plug in the numbers to the formula. Clearly you get (C).

algebra help
if the proper branch is taken, then (5,2) would be on the inverse. As it stands, the function has no inverse function, since it fails the horizontal-line test.

Calculus
at time t hours after the observation, the distance z between the ships is z^2 = (15-12t)^2 + (9t)^2 2z dz/dt = 90(5t-4) dz/dt=0 when t = 4/5 z(4/5) = 81

Calculus
(a) there is a local extreme every time sinx = cosx: x = ?/4 + k? (b) since the maxima occur when sinx=1, the envelope of these maxima is the curve y=e^-x.

Math
#1 ok #2 h(t) = 3(t-1)^2+2 is apparently a typo, but your solution is correct as written #3 ok if you ignore 3.00-0.5(2)=$11.5 good work

Math
I read it as meaning that 2/5 of the original amount was spent on fruits, giving: 50 on chocolate 180 on fruit then subtract all that from the original 450.

Algebra
Midway between 14 and 26 is 20. |x-20| <= 6

Algebra
A is right. Although, it could just as easily be 57 <= t <= 73 On the number line plot the points 57 and 73, and shade the line between them. Then make sure the two points are either open or closed circles, depending on whether the endpoints are to be included.

Algebra 2
If you want rational coefficients, then that ?6 has to go, just like the i terms. So, you need f(x) = (x-2)(x-2i)(x+2i)(x-(4-?6))(x-(4+?6)) = (x-2)(x^2+4)((x-4)+?6)((x-4)-?6) = (x-2)(x^2+4)(x^2-8x+10)

algebra 1
for all the details of long division, you can verify your results by entering your polynomials at http://calc101.com/webMathematica/long-divide.jsp

GPA
there's a lot not being said, but if all the classes are weighted equally, they would indeed "cancel out." You don't say what an A means as far as percentages, so it's hard to say just what the effect is. If you have all those A's, including math, you...

math
1:2:3 = 7:14:21

math test help
that covers a lot of ground. Don't expect an online course here. That's what your text was for. Any general explanations we can provide will look a lot like your text, dontcha think? Or, you can google topics of interest.

math test help
but if you have a particular problem that is vexing you, we can help get to the solution. If you haven't studied the topic by now, it may be too late...

math
The sum of their ages 2 years ago was 8*20 = 160 So, if the new child's age is x, 160 + 8*2 + x = 9*20 x = 4

math
Hmmm. I'm not sure I agree. Since A&B can fill the tank so fast, and it takes about 9 times as long to fill it with the leak, the leak must be pretty fast in relation to the fill speeds. You sure that 5 minutes is right?

math
A&B together take 1/(1/5 + 1/20) = 4 minutes to fill the tank. So, if the leak takes x minutes to empty the tank, 1/4 - 1/x = 1/(30+4) x = 68/15 = 4 8/15 minutes

calculus
use product rule

calculus
these are all just powers of x. Use the power rule: d/dx x^n = n x^(n-1)

math
If his speed was x, then since time = distance/speed, 30/15 + 16/x = 10/3

Math
If the two legs are x, then x^2/2 = 25/2 x = 5 so now you can get the hypotenuse. Or, since a = s^2/2 h = s?2 h^2 = 2s^2 = 4a h = 2?a

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