Answers created by Cesareo R.
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Suppose that the cubic function f(x)=(x-a)(x-b)(x-c) has three distinct zeroes: a, b, c. Prove that a tangent line drawn at the average of the zeroes a and b intersect the graph of f at the third zero?
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How to do 4th question?
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How can I solve this differential equation? #(3+y+2 y^2 sin^2(x))dx+(x+2xy-y sin(2x))dy=0#
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A body initially at rest explodes into 2 pieces of mass 2M and 3M respectively having a total kinetic energy E. The kinetic energy of piece of mass 2M after the explosion is?
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How to solve the 31st question?
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What is the smallest integer which when divided by 3, 5, 7 & 11 leaves remainders of 2, 4, 6 & 1 respectively?
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objects A,B,C with masses m,2 m,and m are kept on a friction less horizontal surface. The object A move towards B with a speed of 9 m/s and makes an elastic collision with it . B makes completely inelastic collision with C. Then velocity of C is?
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Two forces #F_1# and #F_2# are applied on a spool of mass M and moment of inertia I about an axis passing through its center of mass. Find the ratio #F_1/F_2#, so that the force of friction is zero. Given that #I<2MR^2#?
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The topmost and bottommost velocities of a disk are #v_2# and #v_2# in the same direction. The radius is R. Find the angular velocity #omega#?
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Solve the following system?
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Mathematical Induction problem. ?
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How many complex roots does 6x^5 + x^4 - 3 = 0 have?
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How to solve the following system of equations for #C_0# in terms of #C#?
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Point #P(x, y)# is on the ellipse with equation #4(x-2)^2+y^2=4#. Find the largest possible value of #y/x#?
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How to evaluate this sum?
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How do you find the distance betweeen two parallel lines in #3# dimensional space?
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Point #P(x, y)# is on the ellipse with equation #4(x-2)^2+y^2=4#. Find the largest possible value of #y/x#?
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The solution of #sqrt(x)*y' + (1-2sqrt(x))*sqrt(y)= 0# is #(-2*sqrt(x)-1)*e^-sqrt(x)# ??
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Minimum frictional force when F=0??
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Please, help me solve it!
Or give me a method!?
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A stationary mass sudddenly explodes into two fragments, one heavy and another light. Which one has greater kinetic energy and why?
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Under what non-trivial circumstances does #(A+B)^2=A^2+B^2#?
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Find the angle?
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Vertices A(1,1),B(4,-2) and C(5,5) of a triangle are given.can you find the equation of the perpendicular dropped from C to the internal bisector of angle A?
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How can i solve this?
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Through the vertex S of a parabola the chord SP and SQ are drawn at right angles.Show that the straight line PQ intersects the axis at a fixed point?
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Painful vector problem (please see below - thank you!!). Can you find lambda?
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A particle undergoing S.H.M having its velocity (#v#) and displacement from mean position (#x#) relation plotted as a circle of equation #v^2 + x^2 =3#
Find,its angular velocity?
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How many ways? can 4 person is throwing a dice. Make a sum of 6
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How to integrate? Please help
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Hi !
How do you resolve #y'(t)=ty(t) + 1# and #y(0) =1# without using #erf(x)# please? Thanks!
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Find Limit of sqrt (8x^2 + 4x - 8) - sqrt (2x^2 - 3x+1) - sqrt (2x^2 + 4x-3) as x->infinity?
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How do I determine the parameter a of the following equation such that f(x, y) has an extremum at a point (x, y) with x = -3, and show that it is a minimum?
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The equation #x^4 -2x^3-3x^2+4x-1=0# has four distinct real roots #x_1,x_2,x_3,x_4# such that #x_1<x_2<x_3<x_4# and product of two roots is unity, then the value of #x_1x_2 + x_1x_3 + x_2x_4 + x_3x_4#?
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How to find the value of a?
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Determine the relation between the accelerations? Please provide your steps for finding the answer?
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Please solve this conservation of energy problem?
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Slider block A moves to the left with a constant velocity of #6m/s#. Determine?
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Do #x,y,z,t ∈ Q# exist so that #(x+y√2)^2+(z+t√2)^2 = 5+4√2#?
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Limit Value=?
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How would you show that the polar equation #r=(ed)/(1+ecos(theta))# represents an ellipse if e<1, a parabola if e=1, or a hyperbola if e>1?
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Prove that the number #sqrt(1+sqrt(2+...+sqrt(n)))# is not rational for any natural number #n# greater than #1#?
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When will the slope field for the differential equation #dy/dx=(yx^2+xy^2)/(3x+y)# have horizontal segments?
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#inte^(3x)sin(4x)dx#?
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The number #7^(1995)# when divided by 100 leaves remainder?( Solve using Binomial Theorem)
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(ll) Find a matrix A of 3 X 3 different from zero such that A = A ^ T?
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#lim_(n->oo)(Sin n+cos n)^n#
Find the value?
Thanks
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How to calculate the limit of #((1+x)^{x}-1)^x# when #x->+0# ?
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Prove that polynomial p(x)=ax^2+bx+c with integer coefficients that do not simultaneously equal zero does not exist, such that p(2^(1/3))=0?
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Expand 1/1+x² in ascending order of 1/x?
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The correct answer?
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How do I show that the sum of a convergent geometrical series 1+r+r^2+... > 1/2?
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How do you factor #x^4+2x^3y−3x^2y^2−4xy^3−y^4# without quadratic equation?
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How do you find the length of the line #x=At+B, y=Ct+D, a<=t<=b#?
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Can you write
#(a+b)^0.5 - (a-b)^0.5#
as the square root of a difference?
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How do you draw the slope field of the differential equation #y'=(y^2-y-2)(1-y^2)# ?
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Show that #3^(1/3)xx9^(1/9)xx27^(1/27)...# to infinity #=3^(3/4)#.how?
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Find the reading of the spring balance shown in fig. The elevator is going up with an acceleration g/10, the pulley and the string are light and the pulley is smooth?( The mass of the blocks are 1.5 Kg and 3.5 Kg)
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What is the correct answer ?
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-what is the magnitude of tension in the rope?
-find the horizontal and vertical components of the force exerted at A on the
lamina by the wall.
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What is #(dy)/(dx)# of #sqrt(y/x)+sqrt(x/y)=sqrta???#
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Can someone help me solve this?
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How to solve this limit #\lim_{x\to pi/4} (sin2x)^(tan^2(2x)) # ?
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Given: #x+y+z = 5# what is the value of #2^x+2^y+2^z# ?
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In the arrangement the coefficient of friction between the 2 blocks is#mu=1//2#What is the force of friction acting between the 2 blocks?
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The curve described parametrically by #x=t^2+t+1#, and #y=t^2-t+1# represents?
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A vertical rod A of mass m rests on the inclined surface of a wedge B of mass M?
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Projectile launcher problem?
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How do you find a and b?
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For what values of #m# does #z^3+(3+i)z^2-3z-(m+i) = 0# have at least one real root?
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Question is given below ?
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Question #9ae53
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How do you find the minimum of T = #sqrt(x^2+1)/3-(2-x)/5# (WITHOUT USING CALCULUS)?
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What is the general term of this suit #5/3, 7/8, 9/15, 11/24, 13/35# ?
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Prove that: (is true for any positive x,y):?
#x^x*y^y>=((x+y)/2)^(x+y)#
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#lim_(x->oo) sqrt(25x^2-9x-6)-5x+3# ?
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How do you solve this system of equations: #2x + 3y \geq 6;x - y \leq 3#?
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The value of λ+k=?
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Value f a=?
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Approximate #sum_(n=1)^oo(-1)^n/((3^n)(n!))# correct to four decimal places?
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#(x-y) dy/dx= (x+2y)# ?
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#sum_(n=1)^oo(n!)^2/((2n)!) # converges ?
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What is the inverse of #y=log_4( x-3) +2x?# ?
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A trough of mass 9 Kg is supported by 2 uniform discs that roll without sliding at all surfaces of contact. Mass of each disc is 6 Kg and radius 100 mm. A constant force of 135 N acts on the trough as shown?
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Q.3.find the integrating factor and solve the exact solution
consider the differential equation
(e^(x-y)cosy+cosx+2e^(2x-y)dx + (sinx-e^(x-y)siny+3y^2e^-y)dy
Q.5. Prove ?
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The number of real solutions #cos(e^x)=2^x + 2^-x# is ?
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Could you please prove the following equation from Arithmetic Progressions?
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Watering a garden?
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How can this be solved?
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Question #fa20c
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Question #89f79
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If #n# is a natural number, prove that the number #(sqrt(n) + sqrt(n+1))# is irrational?
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How do I solve this... L'Hopitals seems to go in an loop?
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How do you Rewrite 2sin(x)−2cos(x) as Asin(x+ϕ)? x=? ϕ=?
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Is the series #2+ 1 + 2/3 + 1/2+ 2/5+ 1/3 +2/7+ ...# convergent or divergent? Explain.
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How can i solve the matrix equation: 5Y - 2I₃ = Dt - (D+I₃)Y when D is a given 3x3 matrix?
Dt (transpose of D)
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Please solve this question of mechanics?
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Find a vector function, #r(t)#, that represents the curve of intersection of the two surfaces. The cylinder #x^2 + y^2 = 81# and the surface #z = xy#?
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Calculate:
#sum1/(n!+(n+1)!)#
; n from 0 to infinity?
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#f(x)=[2x]sin3pix# and #f'(k^+)=lamdakpi(-1)^k#, where [.] denoted greater integer function and #kinN#, then what is the value of #lambda# ?
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