Wednesday
July 30, 2014

Posts by steve


Total # Posts: 24,019

algebra/Steve or Damon help
f(3/2) = (3/2)^2 + 2 = 9/4 + 2 = 4.25 f(b) = b^2+2 how did you get zero?

math
r^3 = 3375 r = 15 Now just use S4 = 32.5 to find the cheapest price. I suspect a typo, since $32.5 is such a small number.

math
after each step, there is 0.9 as much alcohol as before. So, after 7 steps, the amount of alcohol is 10*0.9^7 = 4.78 liters.

Math
x+y=30 25x+30y=810

Algebra II
correct

math
S3 = 1(1-r^3)/(1-r) = 157 1+r+r^2 = 157 r^2+r-156 = 0 (r-12)(r+13) = 0 r = 12 or -13 So, the GPs are 1,12,144,... 1,-13,169,...

high school algrebra 1
for p people, the cost c is c = 25 + 18p the cost per person is 25/p + 18

math (cant figure it out)
a cube has 6 faces, so the theoretical probability is 1/6, not 1/30! (B) Why would you divide 120 by the number of spots that show? Would P(5) be 1/24?

math
h/75 = tan 62

Algebra 1
#1 ok #3 .701 = 0.7 to the nearest tenth. Your rounding doesn't have any tenths!

Algebra 1
#1 you cannot divide by zero. So, when the denominator is zero, that value of x must be excluded. So, what is x when 3x-6=0? #2 ok #3 use the quadratic formula for this one. #4 Nope. 4^0 = 1 2^-3 = 1/2^3 = 1/8 So, 1 - 1/8 = 7/8 You calculated 4^0 - 2^3 #5 correct. So why did y...

algebra 2
Starting from February, after m months, he has 40m dollars. So, when does 40m = 320? m=8 So, what's 8 months after February?

Math
20 cows 70 animals so, 20/70

Math - incomplete
Reiny went through this for you once. Now, maybe if you say which side of STU is b, we can make some headway.

Algebra 1
You did not factor correctly. x^2-4x+4 = (x-2)(x-2) If that's what you got, then you clearly don't understand what it means. x-2 = 0 when x=2, not -2.

averages
8(x+2) = 8x-24+y 8x+16 = 8x-24+y 40 = y It doesn't matter what the average age is. Replacing a 24-year-old by a 40-year-old adds 16 years to the total ages, raising the average by 2.

physics
72t + 1/2 at^2 = 70 72 + at = 54 so, a = -16.2 m/s^2 applied for t=10/9 seconds

maths
42

algebra
since g(3) = 2, g^-1(2) = 3 since h(-4) = 1, h^-1(1) = -4 (h*h^-1)(-7) = h(7)*h^-1(-7) = (-5)*(-8) = 40 If you meant (h◦h^-1)(-7) then that would be -7, since by definition (h◦h^-1)(x) = x.

Math
y = 2cos(3x+135) cos(kx) has period 2pi/k, so y has period 2pi/3. The 135 is just a phase shift, and does not affect the period.

check answer
correct.

Geometry
since area grows as r^2, the area grows by (1/2)^2 = 1/4

Goemetry
PQ has length √(2^2+15^2) = √229 P'Q' has length 4 times that.

math (check answer plz)
Repeating an experiment naturally gives rise to experimental probability. Since no experiment is described, the probability must be theoretical only. So, (C).

math
the clue is that (x+3) divides the volume. So, a little checking shows that the volume v = (x+3)(x-7)(x+9) so, if x+3=15, x=12 and the box is 15x5x21

math
surely you have the formula for the period of a pendulum of length L (and small amplitude): T = 2π √(L/g) Now just plug in your numbers.

Math
-.05t + 300 = 182 Now just solve for t.

Calculus
we just did one of these x(t) = 3t^2 - 18t + c Now just figure x(6)-x(0)

Maths
The max occurs when x = -b/2a = 5/4, and is indeed 65/8 wolframalpha.com confirms this: http://www.wolframalpha.com/input/?i=-2x^2%2B5x%2B5

Maths
done earlier, and you were correct.

Algebra
m = miles g = gallons m = 20g

math *check*
6 possible outcomes only 1 is a 5 So, theoretical P(5) = 1/6 You rolled 12 times, so that's B: experimentation. Evidently the die was heavily loaded.

Math
Correct. Reiny missed the -2x^2. Even experts trip over the details sometimes.

Calculus
Oops. Flipped a minus sign f(3) = 9-27+c = -18+c total change is thus -18

Algebra
just solve for x in 2771x/(100-x) = 36000 x = 92.85%

Math
Let the distance be d. If the kite is between the girls, d/sin75° = 20/sin40° But, if Kate is between the kite and Abigail, then d/sin25° = 20/sin40°

equation
after m months, you have 10*3^(m/2)

Algebra
0 < L <= 90 2L = 330-2W L = 115-W 0 < 115-W <= 90 90 >= W-115 > 0 205 >= W > 115

Algebra
(f-h)(4) = f(4)-h(4) = (2*4+5) - (7-4/3) = ?

math foundations 20
you want x such that P(Z<x) = 0.025 That means that x must be more than 1.96 std below the mean. In this case, that's 3.128 years.

math
C(12,2)*2 assuming the scoops must be different flavors. If duplicate scoops are allowed, then it's just 12^2 * 2

Math
You'll be covering rational functions, asymptotes, logarithms, inverse functions, and more. Go to your local used-book store, and buy a cheap text for Algebra II. Then, go for it -- with more tools at your disposal, the kinds of problems you can solve get much more interes...

Math 11
If the marker is at distance x away from the spot just below the balloon, we have h/x = tan 27.8 (h+345)/x = tan 46.2 Eliminate x to get h/tan 27.8 = (h+345)/tan 46.2 Now just solve for h.

math help plz2!!!!
from the vertex, we know that y = a(x+3)^2+5 Now plug in the values to get a: 1 = a(-6+3)^2 + 5 9a = -4 a = -4/9 y = -4/9 (x+3)^2 + 5 See http://www.wolframalpha.com/input/?i=y+%3D+-4%2F9+%28x%2B3%29^2+%2B+5

algebra
we breathlessly await further developments.

math
as with all parabolas, the vertex (in this case a maximum) is at p = -b/2a = 150/.006

Math
as with all parabolas, the vertex (in this case a maximum) is at x = -b/2a = 80/0.0002

MATH
the length is 270-x So, the area is length*width, or f(x) = x(270-x) As with all parabolas, the vertex is midway between the roots, so in this case, it's at x=135. Since the graph opens downward, the vertex represents the maximum possible area.

MATH
from the values of the roots, we know that the functions will be of the form y = ax(x+4) So, pick a positive to open upward, and a negative to open downward. Any nonzero value will do.

Calculus
hit the ground == drop 400 ft. So, 16t^2 = 400 Now just solve for t.

math
7 filled 8 unfilled Choose 6 of each. So, C(7,6) * C(8,6) = ?

Math
If two weigh 51, that's the minimum for two boys, leaving the maximum for the 3rd boy of 3*159-2*51 = 159-102 = 57

Calculus
dv/dt = 0.6t cos(0.08t^2-1) v = 3/8 sin(0.08t^2-1) + c Since v(0) = 14, c = 14+3/8 sin(1) = 14.3 v(t) = .375 sin(.08t^2-1)+14.3 Now just evaluate v(10)

Algebra/could show me how to work this problem
I suspect a typo. Why not just say 2x^2+1? At any rate, assuming things are correct as written, for any input, just substitute it for all the x's and evaluate for the output. input: -2, output (-2)^2+(-2)^2+1 = 4+4+1 = 9

Physics-can someone please check this
(b) The horizontal speed is unaffected by gravity, so it remains 24.5 m/s. In 3 seconds, John travels 3*24.5 = 73.5 meters. (a) we know that the vertical position, starting at y0 is y(t) = y0 - 4.9t^2 Since y(3)=0, we can get the initial height by solving y0 - 4.9*9 = 0 y0 = 4...

Math
wow. cubics are not generally easy to solve. Best bet is a graphical or numerical solution. wolframalpha gives http://www.wolframalpha.com/input/?i=4x^3-6.68E-7x^2%2B1.67E-8x-1.04E-10 The root is very close to zero, since the function is very nearly 4x^3=0 Blowing up the graph...

math
lose all the nonsense text. You have (x-1)^2 + (x-2)^2 + (x-3)^2 = 0 Now, you know that (x-1)^2 is a parabola, which is tangent to the x-axis at x=1, because of the double root. Similarly, the other two terms are never negative. So, since we are adding up three positive values...

math
you start out talking about two numbers, toss in some unknown quotient (maybe not even in lowest terms) then ask for "number"? The question is mighty unclear to me.

Math
just add .145258x to both sides and you have 1.145258x = .145258 now divide by 1.145258 and you get x = 0.126834

Doppler Effect
for non-relativistic speeds, we can use the approximation. c/520 = (1+v/c) * c/590 520(1+v/c) = 590 1+v/c = 59/52 v/c = 7/52 v = 7/52 c Is that relativistic? Generally, less than 0.1c is considered non-relativistic, so we may be a bit off, but if that matters, use the exact fo...

mathematics
The only possible choice assumes a typo where you meant to say that one quarter of x is 36. Then, x is 144. Hmm. Unless the question reads 4 quarters of x is 36. What is 1 quarter of x? Then the answer is 9.

science
Assuming you meant 0.400g/dm^3, that translates to 0.0004 g/cm^3 So, 500cm^3 of that means 0.2 g Or, in one step, that's 500 cm^3 * (1dm/10cm)^3 * 0.4 g/dm^3

physics
The orbital period is given by T = 2π√(r^3/GM) We want M, which is thus M = r^3/G * (2π/T)^2 Now just plug in your numbers.

Maths
Looks to me like they could all be 8. Are there any restrictions on the values allowed? 2014 is not a multiple of 5, so there is no cycle of 5 numbers which repeats.

Algebra/not sure what to do
f(x) = x-8 for whatever value x has. So, if x=p, f(p) = p-8 Just replace x with the desired value throughout the entire line.

math
I'd say yes. That's what Accounts Receivable are for -- waiting for cash flow to be realized. That's assuming the invoice is not generated until a purchase is confirmed. But, what do I know? I may be off base here.

Number Theory
Since the n numbers are divided up in pairs, I'd say n/2 copies. Hence the formula for the sum: n(n+1)/2 Technically, that's [n+1]/2 where [] is the greatest-integer function.

maths
If P is x meters from the base of the pole of height h, then h/x = tan 53° h/(x+20) = tan 28° eliminate x and you have h cot 53° = h cot 28° - 20 h = 20/(cot28°-cot53°)

math
10(q+7) + 25q = 280

Maths
If there are x children, then .6x = 18 x = 30 78? 1? You just throwing darts at numbers? If not, show you r work, so we can help you get it right.

math
If we add up terms n through n+10, then we get (n+10)/2 (2a + (n+9)45) - (n-1)/2 (2a+(n-2)45) = 891 11a+495n = -1089 a+45n = -99 If we are adding up the first 11 terms, then a = -144 and T28 = -144+27*45 = 1071 T45 = -144+44*45 = 1836 But, if we add up terms T5 through T15, th...

Calculus
Looks good to me.

Calculus
x(t) = -cos t + c now you know that x(0) = 3, so plug in t=0 to find c. Then you can use t=2 to get x(2)

Maths!
300 = 100 + 40*5 So, set things up as an arithmetic sequence, and find that S41 = 41/2 (100+300) = 8200

maths
simple: 10000(1+.12*5) compound: 10000(1+.10)^5 evaluate and compare.

calculus
c(x) = 350 + .20 x

Algebra
are there any pairs with the same 1st element? If not, it is a function.

math
or, using de Moivre's rule, 1+i = √2 cis π/4 so √(1+i) = ∜2 cis π/8 1-i = √2 cis -π/4 so √(1-i) = ∜2 cis -π/8 √(1+i)/√(1-i) = cis π/4 Now the angle doesn't matter, since cos^2+sin^2 = 1

math
√(1+i)/√(1-i) = √(1+i)√(1-i) / (1-i) = √(1-i^2) / (1-i) = √2/(1-i) = √2(1+i) / (1-i)(1+i) = √2(1+i)/2 = 1/√2 + 1/√2 i a = 1/√2 b = 1/√2 a^2+b^2 = 1/2 + 1/2 = 1

Math
since the slopes are the same, the lines are parallel. Or, in this case, they are the exact same line.

Math
Or, knowing that the general circle is (x-h)^2 + (y-k)^2 = r^2 plug in your points to get (-5-h)^2 + k^2 = r^2 h^2 + (4-k)^2 = r^2 (2-h)^2 + (4-k)^2 = r^2 h = 1 k = -19/8 r^2 = 2665/64 and we have the circle as derived above The brute-force way, of course, is to plug your poin...

Math
The center will lie at the intersection of the perpendicular bisectors of the line segments (chords) joining the points. If we label the points A,B,C, then The midpoint of AB is at (-5/2,2) The slope of the chord AB is 4/5 The line AB is y = 4/5 (x+5) The slope of the radius t...

math
-3 + i^2y = -3-y The conjugate of x^2+y + 4i is x^2+y -4i so, we want -3-y = x^2+y - 4i In no case is that ever true We can have -3-y = x^2+y, but there's no way to get the -4i I suspect a typo in the problem.

Math
#1. The kth odd number is 2k-1 Think about it : 1,3,5,... #2 It will be a multiple of 60. So, what's the biggest 3-digit multiple of 60? #3 There are 203 numbers from 101-303. Knock off one end, since both are odd, and half of the remaining 202 are even. #4 same thing #5 5...

math
2 3/4 = 2 + 3/4 1 1/4 = 1 + 1/4 add them up to get 2+1 + 3/4 + 1/4 = 3 4/4 = 4

Write each expression using a single exponent.
when dividing, just subtract exponents: 5^10 / 5^7 = 5^(10-7) = 5^3 because 5^10 = 5*5*5*5*5*5*5*5*5*5 5^7 = 5*5*5*5*5*5*5 divide, and seven of the 5's cancel, leaving only 3 in top: 5^3 76^11 / 76^5 = 76^(11-5) = 76^6

wdwd
csc(4θ+3) sin(5θ-6) = 1 That's surely an odd sort of expression. Still, since cscθ = 1/sinθ, we have sin(5θ-6) = sin(4θ+3) So, we want 5θ-6 = 4θ+3 θ = 9 That seems kind of big, so what if we consider that sin(π-x) = sin(x)....

maths
72000(1+.80n) = 87840 1+.80n = 1.22 and so on to get n

math
v = x^3, so dv/dt = 3x^2 dx/dt = 6(2t+1)^2

Math
since multiplication is commutative, 3 * 10^6 * 2 * 10^12 = 3*2 * 10^6 * 10^12 = 6 * 10^18 the other is analogous. Just recall that 30*10^13 is not scientific notation.

Math
3x^2+2x-x^2+3 3x^2-x^2+2x+3 (3-1)x^2 + 2x + 3 2x^2 + 2x + 3 not much to do -- just combine the x^2 terms. We used commutativity of addition and distributive property.

trig
cosA/(1-tanA) + sinA/(1-cotA) cosA/(1-tanA) + sinAtanA/(tanA-1) (cosA - sinAtanA)/(1-tanA) (cos^2A-sin^2A) / cosA(1-tanA) (cos^2A-sin^2A)/(cosA-sinA) cosA+sinA sure you don't have a typo somewhere?

trig
since cosA = 5/13, sinA = 12/13 Now just use those values in your double-angle formulas.

MATH
wolframalpha.com is your friend. For #26, see http://www.wolframalpha.com/input/?i=table+2x^2-4+for+x+%3D+-3+..+5

help needed with math
Was something wrong with the solution I posted here? http://www.jiskha.com/display.cgi?id=1401907573

math
4/52 * 4/51

MATH
#14. For each x, place a 3. f(3) = 4*3-4*3-7 = -7 Same way for #16 However, I suspect a typo, since 4x-4x-7 = -7 for any value of x.

algebra
clearly, 4y = (2/3)x - 8 so, 24y = 4x-48 -4x + 4x-48 = 32 -48 = -32 No solution exists

Can you help me find the answers?
#10 14-11*1 = 14-11 = 3 14-11*2 = 14-22 = -8 ... #12 23+1 = 24 23+2 = 25 ...

Find the common difference or ratio in each..?
6: r = 1/4 8: r = -2 That should do it.

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