Thursday
May 5, 2016

Posts by STEVE

Total # Posts: 40,202

Math
for the quadratic, note that f(-1) = f(1) = 4 That means the vertex lies on the line x=0. y = a(x-0)^2 + c or, y = ax^2+5 Now use one other point to get a: 1 = 4a+5 a = -1 y = -x^2+5
April 13, 2016

Calculus
f(x) increases where f'(x) > 0. f(x) is concave up when f"(x) > 0.
April 13, 2016

Math
brute force way: n + n+2 + n+4 + n+6 = 296 using progressions: 4/2 (2n+3*2) = 296 In either case solve for n, and the next number is n+2
April 13, 2016

Maths
looks good to me, if all the cricket players also play football.
April 13, 2016

Maths
A set of n elements has 2^n subsets, including the empty set. So, if you have 4 fillings, and want at least one, that will allow for 2^4-1 = 15 different combinations, using 1 to 4 items. add in the totally plain one, and that gives 16 ways to make the sandwich. (not sand which!)
April 13, 2016

math
remember that the terms have a constant ratio, so (2k-28)/(k-6) = (k-6)/k Now just solve for k. You will get two answers, only one of which makes all the terms positive.
April 13, 2016

Integers
or, using what you know about arithmetic progressions, 6/2 (2a+5*1) = 171 a = 26 so the numbers are as shown above.
April 12, 2016

Math
Medi* comes off before taxes, so 22.48 + 52.72 + 0.23(1625.35-22.48-52.72) = 431.73
April 12, 2016

Math
just divide the deposit by the total: 175/625 = 0.28 = 28%
April 12, 2016

Math
well, g(1) = int{1,1} f(t)dt if the integral is done over an interval of zero width, its value is zero.
April 12, 2016

Math
just subtract the field from the total: (8x)(12x) - (3x)(6x) = 96x^2 - 18x^2 = 78x^2
April 12, 2016

Please HELP! Calculus (Implicit functions)
or, using implicit, 16x^2 - 8xy - x + y^2 = 0 32x - 8y - 8xy' + 2yy' = 0 (2y-8x)y' = 8y-32x dy/dx = (4-16x)/(y-8x) dx/dy = (√x+4x-8x)/(4-16x) = (1/4)(√x-4x)/(1-4x) Check my math and see whether these agree.
April 12, 2016

Please HELP! Calculus (Implicit functions)
switch variables and solve for y, and you get (after squaring) 16y^2 - (8x+1)y + x^2 = 0 y = [(8x+1)±√(16x+1)]/32 Pick the branch you want and take the derivative. Using the + branch, y' = 1/4 (1 + 1/√(16x+1))
April 12, 2016

Math
some kind of exponential would do it. So, with t as time since 1998, f(0) = 72000 f(2) = 70379 f(∞) = 60000 f(t) = 60000 + 12000 e^-kt now we need k so that f(2) = 70379 60000 + 12000 e^-2k = 10379 k = 0.073 So, f(t) = 60000 + 12000 e^(-.073t)
April 12, 2016

try,check,and revise
If Carly had c, the Rob had c-4. So, c + c-4 = 42 2c = 46 c = 23 So, Carly had 23 and Rob had 19
April 12, 2016

Calculus Help Stuck Part 2?
or, consider x-64 as the sum of cubes: x-64 = (∛x)^3 - 4^3 so it factors into (∛x-4)(∛x^2+4∛x+16) Now the fraction is just 1/(∛x^2+4∛x+16) = 1/(16+16+16) = 1/48
April 12, 2016

Calculus Help Stuck Part 2?
(∛x-4)/(x-64) -> 0/0 so try L'Hospital's rule. Then the limit is (1/(3∛x^2) / (1) = 1/(3*16) = 1/48
April 12, 2016

try,check,and revise
27+3x
April 12, 2016

math
(1-2i)(1+2i) = 1^2+2^2 = 5 (1-i)(1+i) = 1^2+1^2 = 2 5*2 = 10
April 12, 2016

algebra/math
surely you have learned how to solve a quadratic equation, or you'd not have been given this exercise. x^2+6x + 9 = 24 x^2+6x-15 = 0 x = (-6±√96)/2 = -3±2√6 clearly, -3-2√6 is less than -3+2√6
April 12, 2016

algebra
since (a-bi)(a+bi) = a^2+b^2, we have (15-20i)(1+2i) ------------------ (1-2i)(1+2i) = (15-20i+30i-40i^2)/(1^2+2^2) = (55+10i)/5 = 11+2i
April 12, 2016

Math
well, solve the equation and pick the smaller value. I hope you are not expecting integers.
April 12, 2016

math
well, (x + 7/2)^2 = x^2 + 7x + 49/4
April 12, 2016

Trigonometry
draw a diagram. Then it will be clear that your distance x can be found by 1200/x = sin32°
April 12, 2016

Graphs
The points on f(2x) are half as far from the y-axis as those of f(x)
April 12, 2016

Math
depends on the shape of the volume, eh?
April 12, 2016

math
see whether you get what wolframalpha does: https://www.wolframalpha.com/input/?i=solve+%28x-2%29^2+%2B+%28y-7%29^2+%3D+169,+x-2y%3D10
April 12, 2016

math
all points (x,y) that are 13 units away from the point (2,7) defines a circle: (x-2)^2 + (y-7)^2 = 169 so, the line x-2y=10 may intersect the circle in 0,1, or 2 points. So, plug x=2y+10 into the equation of the circle and see where the two graphs intersect.
April 12, 2016

math
well, they intersect where f(x) = g(x). x^3-x^2+x+1 = x^3+x^2+x+1 -x^2 = x^2 x = 0 to check, see https://www.wolframalpha.com/input/?i=x^3-x^2%2Bx%2B1+%3D+x^3%2Bx^2%2Bx%2B1
April 12, 2016

Math 142 (Pre-Cal) (Circles)
the circumference is 2pi*10 = 62.83cm So, multiply that by the number of times the wheel turns in 15 seconds.
April 12, 2016

Math/geometry
since the angles x and y are complementary, x+y = 90 y = 3x+6 now just solve for x and y.
April 12, 2016

Geometry
since the circle has area πr^2, and the sphere has surface area 4πr^2, what do you think?
April 12, 2016

Algebra
A linear equation is y=mx+b where x is the sales, b is the base pay, and m is the percentage used to find the commission. We have 560 = m*800 + b 460 = m*460 + b 540 = m*540 + b 600 = m*1000 + b Those points do not fit any linear equation. Check for typos.
April 12, 2016

Maths Ms sue
300+10+16+22+... = 310 + 19/2 (2*16 + 18*6) = 1640
April 12, 2016

math
can you not check your answers? (-4,8) works (5,35) works
April 12, 2016

Geometry - incomplete
No idea where CDE are in relation to BGF. All you have said is that the two squares share corner A. However, you do know that the smaller square has sides 1/2 as long as the larger one, so its area is 1/4 as big. I suspect you can use that to determine the shaded area. Also, a...
April 12, 2016

Algebra 1
Who needs a teacher? Just think a bit. Where is the ball to start with? At the top of the cliff. That's when t=0. So, plug in 0 for t and evaluate.
April 12, 2016

math
they all express a ratio, but I'd guess C is least likely to be used.
April 12, 2016

Math
can't quite parse your text. It's probably one of 976 + 2n or 9762n
April 12, 2016

Math
if the angle is x, then it is opposite the shortest side. tan(x) = 5/8
April 12, 2016

Math
P(blue) = 3/12 * 2/11 P(>= 1 blue) = 1-P(no blue) = 1 - (9/12 * 8/11)
April 12, 2016

algebra. someone please explain to me please!
since time = distance/speed, d/12 + d/6 = 6
April 12, 2016

Pre calculus
what about the uphill anchor point? I assume the antenna is vertical. Anyway, if the uphill anchor point is x feet from the base, then we have uphill cable length is u, where u^2 = x^2+100^2 - 2*100x cos 78° downhill cable length d is d^2 = 95^2 + 100^2 - 2*95*100 cos102°
April 12, 2016

algebra
900 + .07(x-1000) = 2900
April 12, 2016

Basic math
5ml/4hr * 14days * 24 hr/day * 1floz/29.57ml = 14.20 floz
April 12, 2016

Math Check my Answers please ?
good work. both correct.
April 12, 2016

Math
I like C, but it rises 3 ft for every 4 ft of horizontal travel. Double-check the table and the questions. If D says it rises 3/4 ft or 9 inches, then D is your choice.
April 12, 2016

Math
4^4 * 4^6 = 4^(4+6) = 4^10 you add exponents, since what you are really doing is just short for 4x4x4x4 x 4x4x4x4x4x4 = 4x4x4x4x4x4x4x4x4x4 just as multiplication is short for 4x4 + 4x6 = 4x(4+6) 4+4+4+4 + 4+4+4+4+4+4 = 4+4+4+4+4+4+4+4+4+4
April 12, 2016

math
a = l*w a = (w+3)(w) = w^2+3w
April 12, 2016

math
25,10,10,5,5,1
April 12, 2016

math
(n+3)^2 = 25 n+3 = -5 n = -8
April 12, 2016

Algebra
Just use the quadratic formula, which you learned in Algebra I: t = -233±√(233^2 - 4(-16)(48)) --------------------------------       2(-16) t = (233±√57361)/32 or, t = -0.20 or 14.76 We don't allow negative time, so ...
April 12, 2016

Algebra
it hits the ground, naturally, when h=0. So, just find t when -16t^2 + 233t + 48 = 0
April 12, 2016

Math
If you bisect the first chord with a radius, you will have a right triangle with sides 15 and 20. So, the hypotenuse (another radius) is 25. Now, draw the second chord, and its triangle is 7-24-25, so the full chord is 14 cm long.
April 12, 2016

Algebra
x^2-9x+14 = 0 x^2 - 9x + (9/2)^2 = -14 + (9/2)^2 (x - 9/2)^2 = 25/4 x - 9/2 = ±5/2 x = 9/2 ± 5/2 x = 2 or 7
April 12, 2016

science
if 1/4 remains, that means 2 half-lives have passed.
April 12, 2016

Math
2x-4 = 2(x-2) 12x-24 = 12(x-2) So, the LCD is 12(x-2), not 24(x-2) (6x+5x) / 12(x-2) 11x/12(x-2) This is the same as your answer, if you cancel a factor of 2 which you did not need in the LCD.
April 12, 2016

word problems
naturally, when cost = revenue: 32x = 22x+1830 10x = 1830 x = 183
April 12, 2016

math
since time = distance/speed, d/12 + d/6 = 12
April 12, 2016

Algebra
you can get an idea of how these things work here: http://davidmlane.com/hyperstat/z_table.html try using your numbers, and you will see shaded areas.
April 12, 2016

Physics
nove height?
April 12, 2016

math
70 + 28n <= 1800
April 11, 2016

math investment problem
.05*4400 + .09x = 697.00
April 11, 2016

Math
clearly that would be 72/134
April 11, 2016

Business math - question help
400*1.1^14 + ... + 400*1.1^1 = 400(1.1^15-1)/(1.1-1) = 12709
April 11, 2016

science
recall that F = ma now plug in your numbers.
April 11, 2016

Math
mr and mrs smith, their 2 children and fog want to cross a river in a boat that would hold only 80 kg and both mr. amd Mrs Smith have a mass of 80 kg and both the children have a mass of 40 kg and the dog has a mass of 5 kg explain how they can cross the river in the fewest ...
April 11, 2016

Math
f' = 1 - 3/x^(2/3) = (x^(2/3)-3)/x^(2/3) f'=0 when x^(2/3) = 3 x^2 = 27 x = ±√27 the tangent is vertical at x=0. f increases where f' > 0: (-∞,√27)U(√27,∞) f decreases where f' < 0: (-√27,√27) The graph ...
April 11, 2016

Geometry
perimeter grows by a factor of 2, area by 4. So, find the existing values and then scale them up.
April 11, 2016

Math
well, the width is 7 and the height is 1.
April 11, 2016

Math
clearly the width is 7, since JK is a horizontal line. so the height is 1.
April 11, 2016

Geometry
I assume you can find the perimeter and area of the original pyramid. if the sides double, so does the perimeter. But the area, since it is the product of two sides, grows by a factor of 2^2, so it is 4 times as big.
April 11, 2016

Math
If CD=h and BC=x, then h/x = tan24° h/(x+7600) = tan16° or, h = 0.4452x h = 0.2867x + 2179.2649 0.4452x = 0.2867x + 2179.2649 BC = x = 13750 CD = h = 6121
April 11, 2016

Math
two distinct solutions means that the discriminant is positive. So, we need k^2 - 64 > 0 also, we need (k±√(k^2-64))/4 to be an integer. So, k±√(k^2-64) must be a multiple of 4. and k^2-64 must be an integer. so, what pythagorean triples do you ...
April 11, 2016

Math
the ball hits the ground when y=0. If you want a fraction, then let's get rid of the decimals: y = 1/10 (-49t^2 + 35t + 50) = 1/10 (7t+5)(10-7t) y=0 when t = 10/7
April 11, 2016

Pre algebra
6n-8 = 13 + 4(n+3) 6n-8 = 13+4n+12 2n = 33 n = 33/2
April 11, 2016

maths help!??
since time = distance/speed, 4/9 + x/2 = 1 That will tell you the rest of the distance. I suspect you have garbled your question, since they told you his speed for the first 4km was 9km/hr.
April 11, 2016

Math
translate up 3 means add 3 to all the y-values. left 3 and up 2 means subtract3 from x and add 2 to y. just think of the axes, and which directions are positive and negative. (4+2 , 3-5)
April 11, 2016

Algebra 2
tan^4 - sec^4 = (tan^2-sec^2)(tan^2+sec^2) = (tan^2-(1+tan^2))(tan^2+(1+tan^2)) = (-1)(1+2tan^2) = -2tan^2-1 Reiny, imagine the missing x's are present!
April 11, 2016

Math
the first digit must be 3,5,7 the other digits can be 1,3,5,7,9 since the 1st digit cannot be repeated, that means the last 3 digits must be formed using only 4 of the available choices, giving 4*3*2 choices. So, since the 1st digit can be chosen 3 ways, there are 3*4*3*2 ways...
April 11, 2016

Math
using the sum of tangents formula, tan(arctan x + arctan y) = tan(arctanx)+tan(arctany) ----------------------------- = tan(pi/4) 1 - tan(arctanx)-tan(arctany) (x+y)/(1-xy) = 1 x+y = 1-xy x+xy+y = 1
April 11, 2016

Factor out the Greatest Common Factor (GCF)
well, take a look 45d^3 = 9d^2 * 5d 18d^2 = 9d^2 * 2 so, what do you think?
April 11, 2016

maths
length = w+2
April 11, 2016

Calculus
check the related questions below. for extrema as described above, you need f' = 3ax^2+2cx = 0 at x=0 and -4, so x(3ax+2c) = 0 -12a+2c = 0 You also have two points, so -64a+16c+d = 9 0a+0c+d = 6 a = 3/32 c = 9/16 d = 6 so, that means that f(x) = 3/32 x^3 + 9/16 x^2 + 6 the...
April 11, 2016

Math
Remember your Algebra I. The max height is represented by the vertex of the parabola. As with all quadratics, the vertex is at t = -b/2a. So, for #1: t = -122/-32 = 3.8125 seconds use the same logic on #2.
April 11, 2016

Vectors, Math
Since |B| = 4, B = <4/√2,-4/√2> = <2√2,-2√2> AB = B-A = (2√2-3,-2√2-2)
April 11, 2016

math
b/a = tan 60° = √3 The ratio of the volumes is thus πb^2a/πa^2b = b/a = √3
April 11, 2016

calculus 2
What, you don't have any work to show? You can verify your results using the handy calculator at http://keisan.casio.com/exec/system/1392171850
April 11, 2016

fds
all of them
April 11, 2016

math
you might show your work, so we could check your method. each dogs eats 3.5/7 = 0.5 kg/day 16 dogs eat 8 kg/day That's 720 kg for 90 days Or, 1584 lbs. That's 63.36 bags I guess it depends on how many days you use for 3 months. 91 days gives 64.06 bags
April 10, 2016

Math geometry
w/146 = cot 50°
April 10, 2016

Geometry
you are correct if the "thickness" means the height of the material on the ground.
April 10, 2016

Calculus derivatives
well does that not mean that dy/dx = -1? Using implicit differentiation, 2x + y + xy' + 2yy' = 0 y' = -(2x+y)/(x+2y) so, you want (2x+y)/(x+2y) = 1 2x+y = x+2y y = x plug that into the original equation and you get x^2 + x^2 + x^2 = 1 x^2 = 1/3 so, at (1/√3,1...
April 10, 2016

Math
If there are x wheat and y oats, x <= 200 y <= 300 x+y <= 250
April 10, 2016

Math :)
I'd say high volume, since that minimizes the surface area, making the cube last longer. High surface area (lower volume) means faster cooling, but the cube does not last as long.
April 10, 2016

Calculus
nope 4x/(x-5) -> 20/0 this is just algebra. Recall your rational functions work? Vertical asymptote at x=5.
April 10, 2016

Math
If Owen has x and Charley has y, then we are told that x-50 = y+50 (x+100) = 4(y-100) Now just find x.
April 10, 2016

Calculus
This is just ∫∫∫ dz dy dx using the appropriate limits Unfortunately, the plane 2x+z=3 is a vertical plane, and does not bound a region of the paraboloid.
April 10, 2016

math
8914*1.0136^t = 15000 t = 38.53 Better check your math.
April 10, 2016

Math
these are headings, not bearings. I do not get a right triangle. I get an angle of 27+90+27= 144 at the turning point. To get the final location, convert each side to its x- and y-components. Add them up, and you can then get the angle θ using tanθ = y/x and then the...
April 10, 2016

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