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Posts by STEVE

Total # Posts: 50,428

Advanced Functions
by definition, f(f^-1(x)) = f^-1(f(x)) = x

Geometry
so the scale factor is 1 in : (12+4 in) = 1:16

Math
2.50a + 1.00(1300-a) = 1951 a = 434

physics
clearly the force is attractive, pointing toward the proton. F = kqq/r^2 = (8.99*10^9)(1.60*10^-19)^2/(4.30*10^-11)^2 = 1.24*10^-7 N

physics
? = 15rev/5sec = 3rev/s = 6? rad/s v = 20*2? cm/rev * 3rev/s = 120? cm/s

physics
since F = qq/r^2, changing r to 5r means you now have qq/(5r)^2 = qq/25r^2 = 1/25 * qq/r^2 = 1/25 F

Math
No value for x is needed. This is an exercise in recognizing the distributive property. 5(x+3) = 5*x + 5*3 = 5x+15 Now see what you can do.

Science
yes, but the sand is not part of it.

Math
how about some diagrams? Not available here. Interactive web sites don't translate well to a text-only site such as Jiskha. You would do well to remember that for circles, area = pi r^2 circumference = 2pi r

math
Since the ratios between terms is nowhere near constant, it is not exponential. If you look at the differences, they are always 2 or 3, so it is approximately linear.

algebra invers mathod
I have no idea what that weird double equation is, unless you might possibly mean to solve the system of equations 4x+y = 8 2x+3 = -1 that is clearly x = -2, y = 16 But that does not involve any "invers" method, so ...

Math
You think it is 3? Did you actually solve the equation to determine what it really is? Better yet, does the value 3 work in the equation? 2(1+3) ? 3+3 Bzzzt. Now it's time to do the math: 2(1 + x) = x + 3 2+2x = x+3 ... Now what do you think?

Math
in what context? It's just a number. Compared to a billion, it's not much. Compared to 1.5, it's pretty significant.

Precalculus
I'm sure your text includes the derivation of the formula that the rate of change of fg is ?(fg)/?t = f * ?g/?t + g * ?f/?t In this case, the rate of change of fg is thus 8*5 + 5*3 = 55 units/sec

calculus
The temperature T is the ambient temperature plus a steadily decreasing difference. In this case, T(t) = 15 + (23-15)e^(-kt) You can see that T(0) = 15 + (23-15)*1 = 23 that is the starting temperature. Now we are told that T(1) = 20: 15+8e^-k = 20 k = 0.47 So, T(t) = 15+8e^(-...

math
(32/13)*350 = 862

math
96*12^3 = 165888 cm^3

Trigonometry
Draw the base AX of the triangle, with AX nice and long. Draw angle A, making the other side nice and long. Mark C and drop an altitude to D on AB. Label the height CD=9 Now draw an arc of radius 15 centered at C, and you will see that it intersects AX at two points. Either of...

Math
1/2 of 1/2 = 1/2 * 1/2 = 1/4

Algebra
surely you know the radical indicates the "root": ?14 -- square root ?14 -- cube root ?14 -- fourth root etc.

Maths
well, how many hours passed? 2 degree drop every hour, starting at 10

Maths
A*0.08*7.5 = 1770

calculus
The way this is done is to express everything in terms of sin or cos: sin^3(?)cos^5(?) d? = sin^3? cos^4? cos? d? = sin^3? (1-sin^2?)^2 cos? d? Now let u=sin? du = cos? d? and you have u^3 (1-u^2)^2 du and it's a cinch...

Algebra
I don't know why you can't get it either, especially since you didn't show your work ... (26000-x)2813.95 + x(314.73)=26000(640.2) 73162700 - 2813.95x + 314.73x = 16645200 73162700 - 2499.22x = 16645200 2499.22x = 56517500 x = 22614.05559

please help
Don't let all those decimals scare you. Just do things as normal: -9.4(z-8)-4.1=5(z+2.5)-5.9 -9.4z + 75.2 - 4.1 = 5z + 12.5 - 5.9 -9.4z + 71.1 = 5z + 6.6 14.4z = 64.5 z = 64.5/14.4 ? 4.47917

Math - Mean Value Theorem
see the related questions below.

Calculus
Always draw a diagram for these problems. You will see that if the plane is x feet away from Maude's position, then tan? = 4500/x so, sec^2? d?/dt = -4500/x^2 dx/dt When ?=60°, that gives x = 2250, so 4 d?/dt = -4500/2250^2 * 22600 d?/dt = -226/45 ? -5.02 Of course, ...

Math ASAP
If by 33/ you mean ?33, then that is the irrational one, since 33 is not a perfect square. ?25 = 5, so that is rational.

Math - calculus
f'(x) = p x^(p-1) f(0)=0 and f(1)=1 So, you want c such that p*c^(p-1) = 1 Now just solve for c. For example, if p=2, f'(x) = 2x 2c = 1 c = 1/2 For p=3, 3c^2 = 1, c = 1/?3 so, the tangent line at x = 1/?3 is y = (1/?3)^3 = 1(x - 1/?3) or, y = x - 1/?3 + 1/3^(3/2) See ...

algebra
this would have been easy if you had used the proper units. The resistivity is ?-m So, you have (130m * 14.2?-m)/(A m^2) = 4.30? A = 429.3 m^2 That seems unlikely, so I looked up the resistivity of copper, and it is really 1.7*10^-8 ?-m Using that, we get A = 5.139*10^-7 m^2...

Math
There's nothing missing here. To solve for x, just follow the usual steps: e^(x+6) + 5 = 1 e^(x+6) = -4 No real solutions exist. Powers of e are never negative.

Math
you want t such that e^-.05t = 0.5 -.05t = ln(0.5) t = ln(0.5)/(-.05) = 13.86

Algebra
(-2t^2k)^2 = (-2)^2 (t^2)^2 (k)^2 = 4t^4k^2 Now you can see how to do the cube, right?

Algebra
Well, just factor it to see the zeroes: (m+3)(m-3)(3m+4)^2

Algebra 2
It's a parabola. Just google conic sections for various discussions. Wikipedia might be a good place to start: https://en.wikipedia.org/wiki/Conic_section

Algebra
the length is 6 more than the width, so w(w+6) = 216

Calculus
The distance z from (2,1/2) to (x,x^2) is z = ?[(x-2)^2 + (x^2 - 1/2)^2] = 1/2 ?(4x^4-16x+17) dz/dx = 4(x^3-1)/?(4x^4-16x+17) dz/dx=0 at x=1 z(1) = ?5/2 Or, consider the line through (x,x^2) and (2,1/2). It has slope (1/2 - x^2)/(2-x) The tangent line to y=x^2 has slope 2x. So...

Geometry
?(78/128) ? 0.78 It is an odd scale factor, but that's life.

math - algebra
?(1/81) = ?(1/3^4) = 1/3

Mat222
(s-t) = (x-3)-(3x+1) = -2x-4 (s.t) = (x-3)(3x+1) (s+t)(-2) = s(-2)+t(-2) = -5 + -5 = -10 or, (s+t)(x) = (x-3)+(3x+1) = 4x-2 so (s+2)(-2) = 4(-2)-2 = -10

Algebra
(b*(b-4))/2 = 86

Algerba
from 2^(x-1) = 2^(4x+8) you get x-1 = 4x+8 Your sloppiness with parentheses makes it hard to parse the math correctly. The other answers are correct. But I have no way to check the graph.

Percentage
S = 11/10 R so, R = 10/11 S = .9090S So, R is 9.1% less than S

MATH
If the low score was x and the high score was y, then x+4*93 = 5*90 4*87.75 + y = 5*90 x+y = 5*90-4*93 + 5*90-4*87.75 = 177

Algebra
just cube all the numbers and multiply the exponents by 3. For example (-5xy^2)^2 = (-5)^2 (x)^2 (y2)^2 = 25x^2y^4 (-5xy^2)^3 = -125x^3y^6

Math
700/1000 That's some big bus!

Math
well, each pound is 16 oz, so ...

calculus
when does it hit the ground? -t^2+8t+1 = 0 Now use that in Vy(t) = -2t+8 to get the vertical speed. The horizontal speed is constant at Vx(t) = 8cos(arctan 8) ? 1 m/s The final speed is ?(Vx^2 + Vy^2)

Math Answer Check
#2 I'd say B is wrong, since 7-10 ? 1 #3 The slope is (-5+10)/(-2+9) ? -7/5 #10 correct

differential equation
If w is proportional to u and v, then w = kuv. So, we are told that dx/dt = kx(1000-x) I have set it up so that "the rate at which the disease spreads is proportional to the number of students who have the flu and the number of students who do not yet have it. I have no ...

Math- Graphing (check answer)
-5(3)+10 = -15+10 = -5 ? 25 No joy there, either.

Math- Graphing (check answer)
well is it true that -5(-15) + 10 = 5? Bzzt. Try again.

Trigonometry
See the related questions below for one just like this.

Pre-Cal/Trigonometry
Let the base of the triangle be side AB, with the altitude h from C meeting AB at point D. Since side a is greater than h, there are two triangles possible, one with B between A and D, and one with D between A and B. Note that if a > h/sinA then there is only one triangle.

math
sorry we cannot see your diagram. No idea what <8 is.

Geometry
If you did problem 1, then just subtract that from the area of the whole circle. If not, let's do it now. Recall that the area of the smaller segment is a = 1/2 r^2 (?-sin?) So, what's ?? Draw your diagram, and you can easily see that sin(?/2) = 4/8 = 1/2 ? = ?/3 Plug ...

calculus
see your posting from last night in the related questions below.

Trig Identities
Oops -- my bad! secx - sinx tanx = 1/cosx - sin^2x/cosx = (1-sin^2x)/cosx = cos^2x/cosx = cosx

Trig Identities
1/cosx - sinx/cosx = (1-sinx)/cosx I guess you could go further, recalling that sin and cos are complementary functions, and get (1-sinx)/cosx = (1-cos(90-x))/sin(90-x) = tan((90-x)/2) = tan(45 - x/2)

math
(-5+10)/(-2+9) = 5/7 Did you try plotting the points? It would be easy to see that the slope must be positive.

Maths
u = t+1 10t+u = 1+5(t+u) Solving for t and u, we get 34

Math
There are only 3 colors. So, 4 socks must have two matching.

Math
well, 1/4 of 1200 is 300 So, how about 3 times that?

Alex
(x^3-4)/(x^2(x+2)) = 1 + 1/x - 2/x^2 - 3/(x+2)

Math
Assuming 182 days in 6 months, we have 1637/182 = 0.003x

algebra
Use your terms carefully. Consider that growth of 50% give a result 1.5 as big as the starting value. So, growth of 174% gives a result 2.74 times as big. 51 * 2.74 = 139.74 cm Make sure that's how you intended to phrase the question.

Math
The short side is 4/5 as long as the long sides. So, they are 5/4 as long as the short side. 2 * 5/4 x + x = 15.4

maths
multiply top and bottom by the conjugate, and you get (3+?5)(2+?5) ------------------ (2-?5)(2+?5) = (11+5?5)/(4-5) = -11-5?5

maths
To avoid writing all the powers of 1, let's agree that they are all just 1. So, (1+x)^(1/4) = 1 + (1/4)x^1 + (1/4)(-3/4)/2! x^2 + (1/4)(-3/4)(-7/4)/3! x^3 + ... = 1 + x/4 - 3x^2/32 + 7x^3/128 - ...

word problem
6800-6400 = 400 So, the population rises by 200 each year. Go with that...

Math
Assuming the three groups are disjoint, then there are 545 total students. So the central angle you want is (190/545) * 360°

calculus
Since ?y/?t is the slope of the line approximating the curve, the ?y is just the slope times ?t So, if dy/dt = f(t) yk+1 = yk + f(t)*?t

Algebra 2
17 ? 3+7k k=0 S18 = 18/2 (2*3+17*7)

Precalculus
Assuming the usual sloppiness with parentheses, I'll assume that f(x) = (3x-4)/(x+2) = -10/(x+2) + 3 so you appear to be correct, with the caveat that the stretch is done before the upward shift.

pre calc
So, are you Ruth or Beth? You don't say whether the observers are shining lights in the same direction or opposite directions. I'll assume the same direction (the 2nd observer is behind the 1st one). In that case, h cot45° - h cot75° = 600 If the lights are ...

Pre calc
the tower's height can be considered in two pieces: above the window, and below the window. So, it is 375*tan39° + 375*tan25° = 303.669 + 174.865 = 478.534 or, 479 You only calculated the height above the window. They gave you the second angle for a reason, but you...

precal
swap values, and you need (2,?),(4,?),(8,?) where the ?'s must match the 1st numbers

Algebra
I don't know about "simplify" bu to expand it, try this: You know that (a-b)(a+b) = a^2-b^2 (a-bi)(a+bi) = a^2+b^2 So, (x+1)(x(-4-5i))(x-(4+5i)) = (x+1)((x-4)-5i)((x-4)+5i) = (x+1)((x-4)^2 - (5i)^2) = (x+1)(x^2-8x+16 + 25) = (x+1)(x^2-8x+41) = x^3-7x^2+33x+41 =

math
P(navy) = 1/2 how many total sizes? How many 10 or larger? P(navy & >=10) = P(navy)*P(>=10)

math 8
yes. That is how binary numbers are formed.

Math
?r^2 = 120 so, solve for r.

precalc
(a) 3-hr factor is 0.41 m^3 = 0.41 (b)m = 0.743 (c) m^6 = 0.41^2 = 0.168 (d) 15min = 1/4 hr, so that is m^(1/4) = 0.928

Math 120
Of the 6 outcomes, 2 are not greater than 2. So, the odds are 2:4 = 1:2

Science
(75*9.8)(5.12*0.2)/5

Precalculus
a little synthetic division yields factors of (x-2)(x+6) so, divide that out and you are left with (x^2+2)

Math
well, at 3:00 they form a right angle...

Pre-cal
as always, draw a diagram. Then it should be clear that the distance is 500 cot32° + 500 cot23°

Math
I assume your two equations are y = 4x+8 y = x^2+7x-20 So, just set them equal: x^2+7x-20 = 4x+8 x^2+3x-28 = 0 (x+7)(x-4) = 0 x = -7 or 4 See http://www.wolframalpha.com/input/?i=x%5E2%2B7x-20+%3D+4x%2B8

math
2 cups = 8/4 cups That is 11/4 = 11/8 * 2 So, you will need 11/8 as much milk. 11/8 * 3/4 = 33/32 cups milk. Or, 1 cup + 1/2 tbsp.

Math - typo
rate. make that 6^2 + 4*(6*4)/2 = 84

Math
well, it sounds like the triangles have two sides of length 5, and an altitude of 4. That means, each triangle consists of adjoining 3-4-5 right triangles, making a base of 6, which is also the side of the square. So, the area of the pyramid is 4^2 + 4*(6*4)/2 = 64

Math
A net is an unfolding of a line drawing of the pyramid. Each line represents an edge of the original figure. So, they will give a way to determine the dimensions and thus the area and volume of the pyramid. If you google "square pyramid net" you will see lots of ...

Math
well, what do the lines on the net represent? The surface area is the area of the square base, plus 4 isosceles triangles.

Trigonometry
see your previous post, in related questions below. Also, recall that tanA = sinA/cosA

math please help me out fam
#1,#2 use any online grapher, such as wolframalpha.com #3 well, what do you have to add to 4 to get to -4? (4,-4) + (-8,?) = (-4,7) #4. Put the words into algebra: T: (x,y) -> (x-4,y+1) ... #5 no figure available #6 to reflect in the x-axis, change the signs of the y-...

physics help
Knowing the radius of the circle is not enough. Is it a full semi-circle, or a smaller section? A speed bump 1cm high will not do much.

calculus
if the NS sides have length x and the EW sides have length y, then if he spends the entire $500, 2*4x + 2*8y = 500 or, 2x+4y=125 A = xy = x(125-2x)/4 This is just a parabola, with its vertex (maximum area) at (125/4, 15625/32) For #b, y=1878/x, so the cost c is 8x+16y = 8x+16(...

Trigonometry
cosA = -3/5 so A is ins QIII sinA = -4/5 now the rest is easy...

math help? burnet help.
1/(4x) takes 1/4 as long to get to the same y, so the graph is compressed by a factor of 4 horizontally. the rest is easy ...

Algebra 1
how is 3^5^2 a radical? Looks like exponents to me. 3^5^2 = 3^(5^2) = 3^25 no idea where a enters the picture ...

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