# Posts by STEVE

Total # Posts: 51,184

Math
you want t such that 1550 * .9465^t = 825

math
three times as much But, lots of people use them the same way. If you are working on a problem, be sure to find out what was intended. "times" indicates multiplication "more than" indicates addition using them together always causes trouble.

math
huh? If you let u=cos(1/2x) then you just have 2u-u=0 clearly u=0 when is cos(1/2x)=0?

math
if the zeros are p,q,r then pqr=c

math
j/s = 30/40 j/d = 20/25 d/s = d/j * j/s = (25/20)(30/40) = 15/16 15/16 * 36 = \$33.75

Math
ln(1/2) = -0.69314718 So, -.0001216 = 0.00017543ln(1/2) = ln2/5700 e^(-.0001216t) = e^(ln(1/2)*t/5700) = (1/2)^(t/5700) So, the half-life is 5700 years

Math
just using the first two data points, then in year t since 1990, you have y = 353 e^(kt), so 353e^(10k) = 375 That gives you k, so then you need to find when e^(kt) = 2

math
440/? + 28

Math
360/20 = ?

math
Note that 48^2+55^2=73^2 So, you have a right triangle...

math
f(x) = x^2 g(x) = ?(x+4) f(g) = g^2 = x+4 g^-1(x) = x^2-4 g^-1(f) = f^2-4 = x^4-4 g(f) = ?(f+4) = ?(x^2+4) g(f(x))+g^-1(f(x)) = ?(x^2+4)+x^4-4 for domain, just recall that ?u is defined only for u>=0 Then determine the range as usual.

Math Help
distance = speed * time

Science unit 9
Fill a jar with water. Submerge the ball and measure how much water spilled out.

(a) just plug and chug: 100(1+x/2)^20 = 300 (1+x/2)^20 = 3 1+x/2 = 3^(1/20) x = 2(3^(1/20)-1) = 0.1129 or 11.3% (b) See http://www.wolframalpha.com/input/?i=plot+y%3D100(1%2Bx%2F2)%5E20,+y%3D300+for+0%3C%3Dx%3C%3D0.12

Geometry
Draw an altitude from D to AB. It has length h. Let AB = x, AK=KD=y, BD=z since m?A = 60º, h=y?3 Now you have 4 equations in x,y,z,h: 2x+4y=24 x^2 = y^2+z^2 hx=2yz (area=base*height) h=?3 y Solve those and you will see that the parallelogram is a rhombus of side 6, with ...

Designing Specialty Areas
planes? Those babies are sharp, and easy to slice your hand with

math
Oops. I guess that is maybe ???

math
???

math
yes. The key is "more than 4"

Calc
Assuming you mean y = .2(9-x^2) Clearly, y(-4) ? -2 So, let's work with something like y' = .2(9-x^2) Then there will be families of arrows following trajectories of parabolas. You can find a nice online site at https://www.desmos.com/calculator/p7vd3cdmei Just type in...

Math
ever hear of google? Try looking for pentagon area

Math
can't read you attempts at fractions. Try something like 11 1/4 or 10 1/2 Consider using a regular pentagon with an apothem of 7", or the radius of the pizza. Look online to find the area of such a figure. It will be the smallest 5-sided box that will hold the pizza. ...

Math
Technically true, given the very poor wording of the question. But I think we can agree that we're looking for and answer of 20/4 = 5

Math (Calculus II) (Graph approximation)
(a) the graph is f', which is the slope of f. So, the slope at x=4 is on the graph, and appears to be -1 (b) sure it's possible. f(x) = ?f'(x) dx = "f(x)" + C where "f(x)" is the antiderivative of f'(x) So, f(2) can be anything you want, ...

Maths
rate of flow = volume/time

Maths
just substitute, since x=2y+3: (2y+3)^2 + y^2 = 18 Solve that for y, and then x=2y+3

Maths
an odd number is of the form 2k+1 where k is any integer. So, subtracting 2m+1 from 2n+1 you get (2n+1)-(2m+1) = 2n+1-2m-1 = 2n+2m = 2(n+m) any multiple of 2 is even

Math
Since we have no image, we cannot help. Why don't you try cutting out a triangle of the appropriate size, and see what you have to do to get it to line up with the other. If there's a scaling factor, make sure that you don't move the center of the triangle, and ...

Algebra
I don't mind answering the questions, but I don't like having to figure out what the question is, as well. I assume those three numbers are zeroes of the polynomial. So, by the Factor Theorem, the factors are y = (x+1)(x-2)(x+8)

math
figure out how many scores lie below 59 Turn that into a percent, and that gives the percentile. For example, if 42% of the scores lie below 59, 59 is in the 42nd %-ile.

Math
x/5 = 2/400 First, reduce 2/400 to 1/200 x/5 = 1/200 Now multiply both sides by 200 to get 40x = 1 x = 1/40

science
I hope some time in the last 6-7 hours you decided to spend 10 seconds with google, and found ... the term used to describe a species that influences the survival of many others in an ecosystem? The answer is Keystone Species

Math
#1,#2: the lines have different slopes, so they will intersect in one point #3 The lines are parallel, so they will not intersect at all. You should try graphing the lines to see what happens. If you don't have any graph paper, there are lots of online graphing sites.

Math (Algebra 2)
7/11 = 0.6363 77 is no kind of probability, as probabilities are always between 0 and 1. What were you thinking??

Math
think carefully. The next step is to subtract 8 from both sides.

Physics

Science
Sorry. I just get annoyed when I see someone just guessing, with no apparent thought involved. Of all the possible answers, D is the most absurd, since the sun does not orbit the earth.

Science
NO - Try B The earth spins around completely every day, making the sun (in the sky) appear to go around from east to west! Geez.

Science
the orbit around the sun takes a long time. The sun's rise-fall happens every day.

Physics
(120m^3/min) * (1000kg/m^3 * 9.8) * 35m * (1min/60s) = ? W

method of teaching maths
google these topics, or look at existing texts.

math
I would parse it as the product of x and y: xy decreased by 2: -2 so, xy-2 The language is ambiguous. I guess a purist would say that the lack of a comma makes it mean x(y-2) and that the product of x and y, decreased by 2 would mean xy-2 Aren't you glad we use algebra ...

maths parabola
what's the trouble? The vertex is at (0,0), and tan(?/6) = 1/?3 so the line of the chord is y=x/?3 Now, see where the chord intersects the parabola: (x/?3)^2 = 4ax x^2/3 = 4ax x = 12a So, the length of the chord is ?((12a)^2 + 64a^2) = 4a?13

MATH
6^(3n) = 2^(3n) * 3^(3n) = 8^n * 27^n 9^(n+1) = 3^(2n+2) so you have 8^n * 3^(5n+2) = 8^n 3^(5n+2) = 1 = 3^0 5n+2 = 0 n = -2/5

MATH
FIND N: (6^(3n)*9^(n+1))/8^n=1

Maths
.80 = .15x

Linear algebra
z^3 = 27i z = 3?i i = 1 cis(?/2) ?i = cis((1/3)*(?/2 + 2k?)) for k=0,1,2 = cis ?/6, 5?/6, 9?/6 See http://www.wolframalpha.com/input/?i=z%5E3+%3D+27i

Trigonometry
This is the third time you've posted this question. See the related questions below. What seems to be the trouble?

maths
worst case: all 8 \$1 coins drawn first. Then the 9th coin must be a \$2 coin.

physic
(a) use the law of cosines: v^2 = 200^2 + 60^2 - 2*100*60*cos(80°) v = 198.6 km/hr at 2.7° N of E Now use that to break it into components.

physic
draw a diagram. (a) Ever hear of a 3-4-5 right triangle? (b) for this one, use the law of cosines to find the distance d: d^2 = 3^2 + 4^2 - 2*3*4*cos(120°)

math
not sure which face is the front, but clearly the point (3,6,4) lies on the plane x=3, and similarly for y and z.

MATH
think of a scaled-up 3-4-5 right triangle.

Math
(a) you have asked no question, but it appears you want to know when the height is 10 meters. (b) leaving your answer in the form shown, with no regard for operator precedence, is poor form.

Decroly
7 more, 2 less, 4 times, half of

Math
If you write them in the same form, you have x-2y = -3 x-2y = -3 so they are the same line.

mushi
To find c, use the law of cosines. cosc = cosa cosb + sina sinb cosC cosc = cos70° cos60° + sin70° sin60° cos89° c = 79° Now you can use the law of sines to find A,B.

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

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

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