# Let a, b, and c be positive real numbers. Prove that sqrt(a^2 - ab + b^2) + sqrt(a^2 - ac + c^2) is greater or equal to sqrt(b^2 + bc + c^2). Under what conditions does equality occur?

44,221 results

1. ### Real Analysis (Math)

Prove: [1/sqrt(2)] [sqrt(a) + sqrt(b)] <= sqrt(a + b) <= sqrt(a) + sqrt(b) for all non-negative real numbers a and b.
2. ### Math:)

A person is on the outer edge of a carousel with a radius of 20 feet that is rotating counterclockwise around a point that is centered at the origin. What is the exact value of the position of the rider after the carousel rotates 5pi/12 radians? a. {5[sqrt(2)-sqrt(6)], 5[sqrt(...

Could someone show me how to solve these problems step by step.... I am confused on how to fully break this down to simpliest terms sqrt 3 * sqrt 15= sqrt 6 * sqrt 8 = sqrt 20 * sqrt 5 = since both terms are sqrt , you can combine them. sqrt 3* sqrt 15= sqrt (15*3)= sqrt 45 ...
4. ### Math

How do you find a square root of a number that's not a perfect square? I'm very confused. The book doesn't explain it too well. You can approximate it or simplify it in terms of (products of) square roots of smaller numbers. E.g. consider sqrt[117] The number 177 can be ...
5. ### Trigonometry/Geometry - Inequalities

Let a, b, and c be positive real numbers. Prove that sqrt(a^2 - ab + b^2) + sqrt(a^2 - ac + c^2) is greater or equal to sqrt(b^2 + bc + c^2). Under what conditions does equality occur? That is, for what values of a, b, and c are the two sides equal? This looks like a geometry...
6. ### algebra,math,help

Use Property 2 to simplify each of the following radical expressions. sqrt (10)/ sqrt(49) My answer: sqrt (10) / (7) THis next one i need help: Use the properties for radicals to simplify each of the following expressions. Assume that all variables represent positive real ...
7. ### Mathematics

sqrt 6 * sqrt 8 also sqrt 7 * sqrt 5 6.92820323 and 5.916079783 So you can see the steps — sqrt 6 * sqrt 8 = sqrt 48 sqrt 7 * sqrt 5 = sqrt 35 I hope this helps a little more. Thanks for asking.
8. ### Math(Roots)

sqrt(24) *I don't really get this stuff.Can somebody please help me? The square root of 24 is 4.898979485566356 I know that..lol,but it says not to use decimals.Here is an example they gave me. Ex.sqrt(18)=sqrt(2*3*3)=3sqrt(2) sqrt[24] = sqrt[4*2*3] = sqrt[4]*sqrt[2]*sqrt[3]= ...
9. ### Algebra

Evaluate sqrt7x (sqrt x-7 sqrt7) Show your work. sqrt(7)*sqrt(x)-sqrt(7)*7*sqrt(7) sqrt(7*x)-7*sqrt(7*7) sqrt(7x)-7*sqrt(7^2) x*sqrt 7x-49*x ^^^ would this be my final answer?
10. ### Inequality

When I solve the inquality 2x^2 - 6 < 0, I get x < + or - sqrt(3) So how do I write the solution? Is it (+sqrt(3),-sqrt(3)) or (-infinity, sqrt(3))? Why? Thanks. So would this work? abs x < ( sqrt 3 ) or - sqrt 3<x<sqrt 3 The answer is given (+sqrt(3),-sqrt(3)) ...
11. ### math,algebra,help

Directions are simplify by combining like terms. x radiacal 18 -3 radical 8x^2 can someone show me how to do these types of problems. thanks I cant determine the second term. For the first, I think you meant x sqrt(18) which reduces to x sqrt (9*3) or 3x sqrt 3 First remove ...

l = lim as x approaches 0 of x/(the square root of (1+x) - the square root of (1-x) decide whether: l=-1 or l=0 or l=1 Let me make sure I understand the question. Do we have lim x->0 x/[sqrt(1+x) - sqrt(1-x)] ? If so then multiply the expression by [sqrt(1+x) + sqrt(1-x)]/[...
13. ### math,correction

the problem reads: evaluate sqrt (-4) if possible. my answer: sqrt (-4)<0 therefore this is not a real number looks correct you cannot take the square root of a negative number in the real number set. Have you learned the imaginary number i = sqrt(-1) ?? if so you can do: ...
14. ### Math/Calculus

Solve the initial-value problem. Am I using the wrong value for beta here, 2sqrt(2) or am I making a mistake somewhere else? Thanks. y''+4y'+6y=0, y(0)=2, y'(0)=4 r^2+4r+6=0, r=(-4 +/- sqrt(16-4(1)(6))/2 r=-2 +/- sqrt(2)*i , alpha = -2, beta = 2(sqrt(2)) y=e^-2x*(c1*cos(sqrt(2...
15. ### Calculus

Please look at my work below: Solve the initial-value problem. y'' + 4y' + 6y = 0 , y(0) = 2 , y'(0) = 4 r^2+4r+6=0, r=(16 +/- Sqrt(4^2-4(1)(6)))/2(1) r=(16 +/- Sqrt(-8)) r=8 +/- Sqrt(2)*i, alpha=8, Beta=Sqrt(2) y(0)=2, e^(8*0)*(c1*cos(0)+c2*sin(0))=c2=2 y'(0)=4, c2=4 y(x)=e^(...
16. ### Math

f(x)= 4-x^2 and g(x)= sqrt (x) find the implied domain of fg(x) fg(x)= f(sqrt(x)) fg(x)= 4-(sqrt(x))^2 fg(x)=4-(sqrt x)(sqrt x) fg(x)=4-x domain= (x:x=all real numbers) Am I correct?
17. ### trig2

given real numbers x, a, b with x>= a>= b>= 0, show that sqrt x+b - sqrt x-a >= sqrt x+a - sqrt x-b
18. ### TRIGONOMETRY

given real numbers x, a, b with x>= a>= b>= 0, show that sqrt x+b - sqrt x-a >= sqrt x+a - sqrt x-b
19. ### Math sequence

Let {An} be the sequence defined recursively by A1=sqr(2) and A(n+1) = sqr(2+An) for n is bigger and equal to 1. Show that An < 2. What is An? and how do I find it? Thank you for your time. An is the nth number in the sequence, and is defined by the recursion rule A(n+1) = ...
20. ### Calculus

Evaluate the indefinite integral: 8x-x^2. I got this but I the homework system says its wrong:sqrt((-x-8)x)/(2*sqrt(x-8)*sqrt(x))*(((sqrt(x-8)*(x-4)*sqrt(x))-32*log(sqrt(x-8)+sqrt(x))
21. ### algebra

am I right? 1. Simplify radical expression sqrt 50 5 sqrt ^2*** 2 sqrt ^5 5 sqrt ^10 5 2. Simplify the radical expression sqrt 56x^2 28x 2x sqrt 14*** 2x sqrt 7 sqrt 14x2 3. Simplify the radical expression. sqrt 490y^5w^6 2 sqrt 135y^2 2y sqrt 135*** 27 sqrt 15y^2 27y sqrt 15 ...
22. ### math;)

Find the unit vector in the direction of u=(-3,2). Write your answer as a linear combination of the standard unit vectors i and j. a. u=-3[sqrt(13)/13]i+2[sqrt(13)/13]j b. u=-3[sqrt(5)/5]i+2[sqrt(5)/5]j c. u=3[sqrt(5)/5]i-2[sqrt(5)/5]j d. u=3[sqrt(13)/13]i+2[sqrt(13)/13]j I do...
23. ### math help

15sqrt8x^15/5sqrt2x^4 remember that sqrt(a)/sqrt(b) = sqrt(a/b) simplify the inside. also notice that sqrt(x^11) = sqrt(x^10) * sqrt(x) = x^5 * sqrt(x)
24. ### Calculus check

Given f(x)=x^4(2x^2-15). On what interval(s) is the graph of f concave upwards? A. (0, sqrt(3)) B. (-sqrt(3), 0) C. (-sqrt(3), 0) and (0, sqrt(3)) D. (-sqrt(3), sqrt(3)) E. (Negative infinity, -sqrt(3)) and (sqrt(3), infinity) I got E
25. ### MATH

I need to simply this equation, but I got stuck. h/(4-sqrt(16+h)) = y First, I multiplied (4+sqrt(16+h)/(4+sqrt(16+h) to both sides, and I ended up with h(4+sqrt(16+h)/-h. Is this correct? (I tried to graph both equations to see if I would get the same graph, but I didn't, ...
26. ### algebra

Simplify: 2 sqrt (3) + 6 sqrt(2) - 4 sqrt(3) + sqrt (2) a) 8 sqrt(2) - 3 sqrt(3) b) 6 sqrt(2) - 8 sqrt(3) c) 5 sqrt(6) d) 7 sqrt(2) - 2 sqrt(3) the answer i picked was d
27. ### algebra

Simplify: sqrt (21) (sqrt(7) + sqrt(3)) a) 7 sqrt (3) + 3 sqrt(7) b) 7 sqrt(3) + sqrt (3) c) sqrt (210) d) sqrt (147) + sqrt (63)''. a
28. ### linear algebra check

Use the Gram-Schmidt process to transform the basis [1 1 1] , [0 1 1] , [2 4 3] for the Euclidean space R3 into an orthonormal basis for R3. (Enter each vector in the form [x1, x2, ...]. Enter your answers as a comma-separated list.) so i went through the process and got [1/...
29. ### algebra

simplify: square root of 5 + square root of 20 - square root of 27 + square root of 147. simplify: 6/4square root of 2 sqrt 5 + sqrt 20 - sqrt 27 + sqrt 147 = sqrt 5 + sqrt (4*5) - sqrt (3*9) + sqrt (49*3) = 3 sqrt 5 - 3 sqrt 3 + 7 sqrt 3 = 3 sqrt 5 + 4 sqrt 3 Your second ...
30. ### calculus

prove that d/dx 4x .√(x + √x) = 6x+5 (x)1/2/√(x + √x) solution is d/dx 4x.[x+(x)1/2]1/2 = d/dx 4x.[x+(x)^1/2]^1/2 d/dx 4x.[x+(x)^1/2]^1/2 Product Rule = 4x[1/2(x+(x)^1/2)^-1/2 * (1+1/2x^-1/2) +[x+(x)^1/2]^1/2*4 d/dx(4 x sqrt(x+sqrt(x))) = (2 (1/(2 sqrt(...
31. ### Surds

Solve in the exact form. (sqrt of 4x+1)+(sqrt of x+1)=2 Someone showed me to do this next: Square both sides..so.. 4x+1+2((sqrt of 4x+1)•(sqrt of x+1))=4 I do not understand where the 2 come from ..and why do we need to multiply the sqrt of 4x+1 and sqrt of x+1 together to ...
32. ### math

how would you simplify this equation: y = (x+3)/[(4-sqrt(16+h))] please help me! you have three variables. I am not certain "simplify" is an appropriate term here. ohhhh it was my mistake. I meant: y = h/[(4-sqrt(16+h))] y = h/[(4-sqrt(16+h))] rationalize the denominator.. y...
33. ### Algebra 2

Operations with Complex Numbers Simplify. 1. sqrt(-144) 2. sqrt(-64x^4) 3. sqrt(-13)*sqrt(-26) 4. (-2i)(-6i)(4i) 5. i13 6. i38 7. (5 – 2i) + (4 + 4i) 8. (3 – 4i) – (1 – 4i) 9. (3 + 4i)(3 – 4i) 10. (6 – 2i)(1 + i) 11. (4i)/(3+i) 12. (10+i)/(4-i) 13. (-5 + 2i)(6 – ...
34. ### Math

Simplify each expression. All variables represent positive numbers. Sqrt of 75p^3q^2 divide by sqrt of p^5q^4 My answer: 5q sqrt of 3 / p^2q^2 Is this right?
35. ### pre-cal

Find the roots of the function f(x)= x^2+2x+2 Determine f(x) a) (x+1-i)(x+1+i) b)(x+1-i sqrt of 2)(x+1+i sqrt of 2) c)x-1+i)(x-1-i) d)x-1+i sqrt of 2) (x-1-i sqrt of 2) Please Help! For all of these, use the rule [f(x) + ai]*[(f(x) - ai} = [f(x)]^2 + a^2 where a is a real ...
36. ### algebra

simplify by combining like terms: x sqrt(18) - 3 sqrt(8x)sqrd If <sqrt(8x)sqrd> means [sqrt(8x)]^2, then that also equals 8x. So x sqrt(18) - 3 sqrt(8x)sqrd = x[sqrt(9*2)-3*8] = 3x(sqrt 2 -3
37. ### Algebra

Multiplying sq rts sqrt18a^7b times sqrt27a^8b^6 Jake 1214- 18 = 9 * 2 then sqrt 18 = 3sqrt2 sqrt a^7 = a^3 * sqrt a 27 = 9 * 3 then sqrt 27 = 3 sqrt3 sqrt a^8 = a^4 sqrt b^6 = b^3 Now just multiply the like-terms together. 3sqrt6 and sqrt2a^4?
38. ### 9th grade algebra (completing square)

Can you check the following? A1. (2x + 3)^2 = 25 sqrt(2x + 3)^2 = +-sqrt(25) 2x + 3 = +- 5 2x + 3 = 5, 2x + 3 = -5 2x = 2, 2x = -8 x = 1, x = -4 {-4, 1} A2. x^2 + 14x + 45 = 0 x^2 + 14x + __ = -45 + __ x^2 + 14x + 49 = -45 + 49 (x +7)^2 = 4 sqrt(x+7)^2 = +- sqrt(4) x + 7 = +- ...
39. ### Math

So I am supposed to solve this without using a calculator: Sqrt[20]/10 - Sqrt[10]/Sqrt[32] - Sqrt[0.3125] + Sqrt[3 + 1/5] You can put this into WolframAlpha as is to make it prettier. Answer given is 1/2 * SQRT(5) I really don't know where to start here. I have 5 sqrt rules in...
40. ### Math

Which is the exact value of the expression sqrt 32- sqrt 50 + sqrt 128 2 sqrt 7 7 sqrt 2 22 sqrt 2 2 sqrt 55
41. ### Algebra

Which of these expressions is in simplified form? A. a ^3 sqrt 4 - b ^3 sqrt 2 / 2 B. sqrt 1/2x + sqrt 1/2z C. x^2 - 3x sqrt y / sqrt 3 D. sqrt 125x - x^2
42. ### math,correction

simplify: sqrt ((7)/(100)) my work: 7 = 1sqrt (7) 100= 10 sqrt (1) (1)/(10) sqrt (7) my answer: (sqrt (7))/(10) Your answer is right but your statements: 7 = 1sqrt (7) 100= 10 sqrt (1) make no sense. how can sqrt(7)=7 ? you are saying 2.6457..=7 and 10sqrt(1) = 100 ---> 10 ...
43. ### algebra

Rationalize the denominator, assume that all expressions under radicals represent postive numbers. sqrt:a - sqrt:b/sqrt:a + sqrt:b
44. ### Algebra

SIMPLIFY: ROOT 0F 7 * ROOT OF 14 SIMPLIFY: ROOT OF 1/5 EVALUATE, IF POSSIBLE: ROOT OF 9/16 (I GOT 3/4 BUT I WAS NOT SURE IF THAT WAS CORRECT OR NOT) SIMPLIFY. ASSUME X REPRESENTS A POSITIVE NUMBER: ROOT OF 45X^4 ROOT 0F 7 * ROOT OF 14 = sqrt 7 * sqrt 7 * sqrt 2 = 7 sqrt 2 ROOT...
45. ### rationalizing

sqrt(18) - sqrt(17) How does this expression equal 1/(sqrt(18) + sqrt(17)) ? How would you change it like that? And why is this good to use when not using a calculator?
46. ### algebra

I asked a question and it was answered by Steve. He had the numbers wrong. The problem should be sqrt of 18 over (sqrt of 8)-3. not sqrt of 18 -3. I got 2+sqrt of 8. Is it correct?
47. ### Algebra 2: Radicals URGENT!!

Could some kind, saintly soul help me solve this problem? Simplify: 8w sqrt(48w^5) - x^2 sqrt(3xw^2) . . =8w(√16)(√3)(√w^4)(√w) - x^2(√3)(√x)(√w^2) =32w^3(√3w) - wx^2(√3x) not much of a "simplification" really 8w sqrt(16*3w...
48. ### Calculus - Second Order Differential Equations

Posted by COFFEE on Monday, July 9, 2007 at 9:10pm. download mp3 free instrumental remix Solve the initial-value problem. y'' + 4y' + 6y = 0 , y(0) = 2 , y'(0) = 4 r^2+4r+6=0, r=(16 +/- Sqrt(4^2-4(1)(6)))/2(1) r=(16 +/- Sqrt(-8)) r=8 +/- Sqrt(2)*i, alpha=8, Beta=Sqrt(2) y(0)=2...
49. ### Algebra

1 last square root : Rationalize the denominator 5/sqrt[3]+sqrt[5]= 5*sqrt[3]-sqrt[5]/ sqrt[3]sqrt5[5]*sqrt[3]-sqrt[5]= 5sqrt[3]-5sqrt[5]/sqrt[9]-sqrt[15]+sqrt[15]- sqrt[25]= 5sqrt[3]-5sqrt[5]/-16 = 5sqrt[3]-5sqrt[5]/ -2
50. ### math

solve 2x^2+3x+8=0 and express the solutions in a+bi form. Let's use the quadratic formula to solve for x and express those solutions in a+bi form. x = [-b + or - sqrt(b^2 - 4ac)]/2a Note: sqrt = square root. a = 2, b = 3, and c = 8 from your problem. Therefore: x = [-3 + or - ...
51. ### Math

Find of g(f(x)) when f(x)=sqrt(x+3) and g(x)=(x^2+2)/x. a. g(f(x))=(x^2+2)(sqrt(x+3))/x b. g(f(x))=(x+5)/(sqrt(x+3)) c. g(f(x))=(x^2+6x+11)/(sqrt(x+3)) d. g(f(x))=(sqrt(((x^2+2)/x)+3) Every time I work this problem, I get some crazy answer. Can someone please help me?
52. ### algebra

Simplify -11 sqrt 112. -44 sqrt 7******** -176 sqrt 7 -27 sqrt 7 4 sqrt 7 Is this right? and I need to show my work, idk the steps
53. ### ap calculus

Which of the following definite integrals gives the length of y = e^(e^x) between x=0 and x=1? All the answers are preceded by the integral sign from 0 to 1. (a) sqrt[1 + e^(2*(x+e^x))] dx (b) sqrt[1 + e^(4x)] dx (c) sqrt[1 + e^(x+e^x)] dx (d) sqrt[1 + e^(2e^x)] dx (e) sqrt[e...
54. ### Algebra

I have a question if someone could help, please explain it. Given b = -1 and h = -1, what is the equation of the graph if the parent function is y = sqrt (x) Answers: a.y = sqrt(x-1) b.y = sqrt (-x+1) c.y = - sqrt (-x-1) d.y = sqrt(-x-1) I think it is "b"
55. ### algebra

simplify: sqrt (28) a) 4 sqrt (7) b) 7 sqrt (2) c) 2 sqrt (7) d) sqrt (7) c im just making show that they are correct sorry for posting up so many
56. ### Algebra 1

sqrt r - sqrt s/ sqrt r + sqrt s =r sqrt r- sqrt rs +sqrt s/ r can someone check this for me please.
57. ### Calculus

show lim x->3 (sqrt(x)) = (sqrt(c)) hint: 0< |sqrt(x)-sqrt(c)|= (|x-c|)/(sqrt(x)+sqrt(c))<(1/(sqrt(c))*|x-c|
58. ### Calculus

show lim x->3 (sqrt(x)) = (sqrt(c)) hint: 0< |sqrt(x)-sqrt(c)|= (|x-c|)/(sqrt(x)+sqrt(c))<(1/(sqrt(c))*|x-c|
59. ### is this correct?- math

find the domain of the real valued function; f(x) = sqrt(5 - (sqrtx)) my solution: 5 - (sqrt x) >=0 -(sqrt x) >= -5 (sqrt x) <= 5 x <= 25 (-infinity, 25] is this correct?
60. ### Cody

Write the following with rational, positive exponents. a. sqrt of 8 = 8^1/2 b. seventh root of 5^2 = 5^2/7 c. sqrt sqrt 6 = ??? d. fourth root of sqrt of 5^3 = ??? Can someone please check my work and help with "c and d"? Thanks.
61. ### Calculus

In these complex exponential problems, solve for x: 1)e^(i*pi) + 2e^(i*pi/4)=? 2)3+3=3i*sqrt(3)=xe^(i*pi/3) MY attempt: I'm not really sure of what they are asking. For the 1st one I used the e^ix=cos(x)+i*sin(x) and got -1+sqrt(2) +sqrt(2)i 2) I solved for x and fot (3+3i*...
62. ### algebra

Simplify: ( sqrt (2) + sqrt (3) ) ( sqrt (2) - sqrt (3) )? a) 2 - 2 sqrt (6) - 3 b) -1 c) 2 + 2 sqrt (6) - 3 d) 5 i just need to know if my answer or right or wrong. i think the answer is b thanks
63. ### Calculus 3

I need help writing the series 4 + 1/5 + .3 + 1/(3 + sqrt 2) + 1/(9+ sqrt 3) + 1/(27 + sqrt 4) + 1/(81 + sqrt 5 .... I have played with using irrational numbers, natural log and a vast variety of exponential arrangements. Any help to get me going in the right direction would ...
64. ### Math

How would I do: sqrt32a^8b + sqrt50a^16b Are the exponents 8b and 16b or 8 and 16? I'll assume they are 8a and 16a sqrt 32 = sqrt (16*2) = 4 sqrt 2 sqrt 50 = sqrt (25*2) = 5 sqrt 2 sqrt32 a^(3b) + sqrt50a^(2b) = sqrt2*a^(8b)[4 + 5(a^8b)] There are many ways to write it, but ...
65. ### math problem

I'm trying to get a handle on what square roots are (I think that's what they are called). Here is an example. 4(almost like a division sign but it is more like a check mark)3. I don't understand what it is, its a square root? and How do I deal with these things? A square root...
66. ### Algebra 2

Simplify the number using the imaginary unit i. (sqrt)of -28 •2(sqrt)-7 •-2 (sqrt)-7 •i (sqrt)28 •2i (sqrt)7
67. ### some algebra help (radicals)

I hope I am writing this down right.. I am trying to do some practice questions to learn 10^5 (sqrt)2y - 4^5 (sqrt)2y I am trying to figure out how to solve this They gave us some answers to choose from, but I am clueless on how to solve this 6y ^5 (sqrt)2 6y ^5 (sqrt)2y - 6y...
68. ### math

d/dx x(1+y)^(1/2) + y(1+x)^(1/2)=0. Can some1 show me the calculation because i didn't get like the answer. [ans=-1/(1+x)^2 but my calculation=-(sqrt(y+1) (2 sqrt(x+1) sqrt(y+1)+y)/(sqrt(x+1) (2 sqrt(x+1) sqrt(y+1)+x)]
69. ### math

d/dx x(1+y)^(1/2) + y(1+x)^(1/2)=0. Can some1 show me the calculation because i didn't get like the answer. [ans=-1/(1+x)^2 but my calculation=-(sqrt(y+1) (2 sqrt(x+1) sqrt(y+1)+y)/(sqrt(x+1) (2 sqrt(x+1) sqrt(y+1)+x)]
70. ### Calculus

Graph the curve and find its exact length. x = e^t + e^-t, y = 5 - 2t, from 0 to 3 Length = Integral from 0 to 3 of: Sqrt[(dx/dt)^2 + (dy/dt)^2] dx/dt = e^t - e^-t, correct? dy/dt = -t^2 - 5t, correct? So: Integral from 0 to 3 of Sqrt[(e^t - e^-t)^2 + (-t^2 - 5t)^2] Then what ...
71. ### Calculus - Second Order Differential Equations

Solve the initial-value problem. y'' + 4y' + 6y = 0 , y(0) = 2 , y'(0) = 4 r^2+4r+6=0, r=(16 +/- Sqrt(4^2-4(1)(6)))/2(1) r=(16 +/- Sqrt(-8)) r=8 +/- Sqrt(2)*i, alpha=8, Beta=Sqrt(2) y(0)=2, e^(8*0)*(c1*cos(0)+c2*sin(0))=c2=2 y'(0)=4, c2=4 y(x)=e^(8x)*(2*cos(Sqrt(2)x)+4*sin(...
72. ### math

determine the area of triangle abc when side ab= square root of x, side bc= square root of x, and side ca= the square root of the square root of x. So how do I solve it. How do I add the square root of x + the square root of x + the square root of the square root of x? what is...
73. ### Calculus - Integrating

Question: ∫(x^2)/sqrt(x^2+1) u=x^2+1 , x^2= u-1, du=2xdx ∫(u-1)/sqrt(u) , expand ∫u/sqrt(u) - 1/sqrt(u) Integrate: 2/3(u^(3/2)) - 2u^(1/2) + c My answer: [ 2/3(x^2+1)^(3/2) - 2(x^2+1) + c ] When I took the derivative of this to check my answer, it was not (x^2)/sqrt(x^2+...
74. ### Complex numbers

Prove algebraically that |w+z| is less than or equal to |w|+|z| for any complex numbers w and z, where || is the magnitude. After letting w = a+bi and z = c + di and doing some plugging in etc. I got that ac-bd <= b^2 + sqrt (a^2+b^2)(c^2+d^2) + d^2 But is my proof complete...
75. ### Math

For f(x) = 2sinx + (sinx)^3 + tanx find f'(pi/3). Ok, so what I tried was... f'(x) = 2cosx + cosx(3(sinx)^2) + (sinx/cosx) pi/3 = (1/2, sqrt(3)/2) therefore, 2(1/2) + 1/2(3(sqrt(3)/2)(sqrt(3)/2) + (sqrt(3)/2 (2/1)) 1 + .5(3 (3/4)) + sqrt(3) 1 + .5(9/4) + sqrt(3) = 4.982... but...

2^x+20=15+3^x A)1 B)16 C)-5 D)25 I chose c but i got it wrong i am having a problem understanding it. Let me rewrite the question in a more standard format. 2* sqrt(x)+20=15 + 3*sqrt(x) where * means multiply, and sqrt means the square root. Your use of ^ for square root is ...
77. ### Algebra

Solve for s: h=(square root of 3)times s/2 and solve for h V= (pi)r squared h / 3 Solve for s: h=(square root of 3)times s/2 Multiply both sides by 2. 2h = (sqrt 3)*s*2/2 which cancels the 2 on the right. 2h = (sqrt 3)*s Now divide the right side by everything except what you ...
78. ### Algebra 1

sqrt r - sqrt s/ sqrt r + sqrt s =r sqrt r- sqrt rs +sqrt s/ r Can see if I did this right.
79. ### physics

Objects of equal mass are oscillating up and down in simple harmonic motion on two different vertical springs. The spring constant of spring 1 is 186 N/m. The motion of the object on spring 1 has 3 times the amplitude as the motion of the object on spring 2. The magnitude of ...

Posted by Megan on Tuesday, October 12, 2010 at 3:44pm. I have a question if someone could help, please explain it. Given b = -1 and h = -1, what is the equation of the graph if the parent function is y = sqrt (x) Answers: a.y = sqrt(x-1) b.y = sqrt (-x+1) c.y = - sqrt (-x-1) ...
81. ### Math - Complex Numbers

Could someone show me how to get the work for: 3/4 (sqrt)-16/25 ? The answer says 3/5i. Could anybody tell me how to get there and work with complex fractions and simplify them? Thanks! 3/4 SQRT(-16/25) 3/4 SQRT( 16/25*-1) 3/4 *4/5 *SQRT( -1) but the sqrt of -1 is defined as i...
82. ### algebra

sqrt(45)+ sqrt(20)+ sqrt(5)-sqrt(125)=?? I came up with 6sqrt5 I know it's wrong. I think I messed up the breakdown of the sqrt of 125
83. ### Class 12th : Calculus

If y = sqrt(x-1)+sqrt(x+1),prove that sqrt(x^2-1)dy/dx=1y/2
84. ### linear algebra urgent

For the orthogonal matrix A = 1/sqrt(2) -1/sqrt(2) -1/(sqrt(2)) -1/sqrt(2) verify that (Ax,Ay)=(x,y) for any vectors x and y in R2. Can someone please explain this
85. ### math,correction

i am really trying is this correct. solve: 5(x-2)^2 = 3 MY ANSWER THAT I GOT IS: X = 2 +- (SQRT (3) )/(5) no. 5(x-2)^2 = 3 (x-2)^2 = 3/5 x-2 = +- sqrt (3/5) x= 2 +- sqrt (3/5) so the whole fraction of 3/5 is inside the sqrt yes

Find the Avrage value of the function i=15(1-e to the power of -1/2 t) from t=0 and t=4? A.7.5 sqrt 1+4e^-2 -e^-4 <<<<not sure though B.7.5 sqrt 4-2e^-2 + e^-4 C.7.5 sqrt 4+4e^-2 - e^-4 D.7.5 sqrt 5-2e^-2 + e^-4
87. ### Math

Simplify the product. -9 sqrt 28a^2 * 1/3 sqrt 63a I came until -3 sqrt 49a^2 * sqrt 36a, but then I got confused...
88. ### calculus

the point (1,9) lies on the graph of an equation y=f(x) for which dy/dx=4x(sqrt(y)) where x is greater than or equal to 0 and y is greater than or equal to 0 a)6 b)4 c)2 d)sqrt(2) e)0
89. ### calc

Verify that the function satisfies the three hypotheses of Rolle's Therorem on the given interval. Then find all numbers c that satisfy the conclusiton of Rolle's Theorem. f(x)= x*sqrt(x+6) [-6,0] f is continuous and differential f(-6) =-6*sqrt(-6+6) =0 f(0)=0 f(x) = x (x+6^1/...
90. ### math-Inverse functions

f(x)=-4x-2 & g(x)=5x-6. Find (f*g) and state domain. f(x)-x^2-1 what is the equation for f^-1(x)? f(x)=3x+2, find f(f^-1(14)). f(x)=4x+7 and g(x)=3x-5 find (f*g)(-4) f(x)=sqrt x+3 what is equation for f^-1(x)? Graph y=sqrt x-2 +5 which point lies on graph? A(7,6) B(0,5) C(-2,5...
91. ### algebra

can someone tell me if i did the problem correct (solve by completing the square) 4x^2+2x-3=0 x^2+(1/2)=3/4 x^2+(1/2)+(1/4)^2=3/4+(1/4)^2 (x+1/4)^2=13/16 x+1/4=+-sqrt 13/16 x+1/4=+-sqrt 13/4 x=-1/4+-sqrt 13/4 x=-1+-sqrt 13/4
92. ### Math

1. The length of the hypotenuse of a 30-60-90 triangle is 7. Find the perimeter. A) 7/2+21/2 sqrt 3 B) 21+7 sqrt 3 C) 7+21 sqrt 3 D) 21/2 + 7/2 sqrt 3 Could someone please help me, I don't know how to do this. Thank you!
93. ### Algebra 1

Combine the following into a single expression of the form a x sqrt b. Sqrt 6 + Sqrt 54 + Sqrt 150
94. ### Math/Calculus #2

Integrate: 1/(x-sqrt(x+2) dx I came up with: (2/3)(2*ln((sqrt(x+2))-2)+ln((sqrt(x+2))-1)) but it keeps coming back the wrong answer even though I integrated correctly. Is there a way to simplify this answer, and if so, how? I found: Ln[x-sqrt(x+2)] + 1/3Ln[(sqrt(x+2)-2)/(sqrt(...
95. ### algebra

simplify: sqrt (121/9) a) 11/3 b) sqrt (11/3) c) sqrt(11 / sqrt 3) d)3 sqrt (11) a is the answer

1)f(x) = -x + sqrt 4 - x^2 Find f(-2) -(-2) + sqrt 4 - (-2)^2 = 2 + sqrt 4 + 4 2 + sqrt 8 = 4.828 Is this correct?
97. ### geometric mean

The geometric mean of two postitive numbers a and b is sqrt(ab). Show that for f(x) = 1/x on any interval [a,b] of positive numbers, the value of c in the conclusion of the mean value theorem is c = sqrt(ab) I have no idea how to do this! If the mean of a and b is sqrt(ab), ...
98. ### calculus

A) How do you prove that if 0(<or=)x(<or=)10, then 0(<or=)sqrt(x+1)(<or=)10? B) So once that is found, then how can you prove that if 0(<or=)u(<or=)v(<or=)10, then 0(<or=)sqrt(u+1)(<or=)sqrt(v+1)(<or=)10? * calculus - Damon, Saturday, April 3, ...
99. ### math

Find the product and enter the real and imaginary parts below. Note that you do not need to type in the since it is already given to you. Simplify your square roots as much as possible. sqrt-27((sqrt-5)-(sqrt-11))
100. ### calculus

A) How do you prove that if 0(<or=)x(<or=)10, then 0(<or=)sqrt(x+1)(<or=)10? B) So once that is found, then how can you prove that if 0(<or=)u(<or=)v(<or=)10, then 0(<or=)sqrt(u+1)(<or=)sqrt(v+1)(<or=)10?