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Suppose that the cubic function f(x)=(xa)(xb)(xc) 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?

How to do 4th question?

How can I solve this differential equation? #(3+y+2 y^2 sin^2(x))dx+(x+2xyy sin(2x))dy=0#

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?

How to solve the 31st question?

What is the smallest integer which when divided by 3, 5, 7 & 11 leaves remainders of 2, 4, 6 & 1 respectively?

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?

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#?

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#?

Solve the following system?

Mathematical Induction problem. ?

How many complex roots does 6x^5 + x^4  3 = 0 have?

How to solve the following system of equations for #C_0# in terms of #C#?

Point #P(x, y)# is on the ellipse with equation #4(x2)^2+y^2=4#. Find the largest possible value of #y/x#?

How to evaluate this sum?

How do you find the distance betweeen two parallel lines in #3# dimensional space?

Point #P(x, y)# is on the ellipse with equation #4(x2)^2+y^2=4#. Find the largest possible value of #y/x#?

The solution of #sqrt(x)*y' + (12sqrt(x))*sqrt(y)= 0# is #(2*sqrt(x)1)*e^sqrt(x)# ??

Minimum frictional force when F=0??

Please, help me solve it!
Or give me a method!?

A stationary mass sudddenly explodes into two fragments, one heavy and another light. Which one has greater kinetic energy and why?

Under what nontrivial circumstances does #(A+B)^2=A^2+B^2#?

Find the angle?

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?

How can i solve this?

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?

Painful vector problem (please see below  thank you!!). Can you find lambda?

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?

How many ways? can 4 person is throwing a dice. Make a sum of 6

How to integrate? Please help

Hi !
How do you resolve #y'(t)=ty(t) + 1# and #y(0) =1# without using #erf(x)# please? Thanks!

Find Limit of sqrt (8x^2 + 4x  8)  sqrt (2x^2  3x+1)  sqrt (2x^2 + 4x3) as x>infinity?

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?

The equation #x^4 2x^33x^2+4x1=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#?

How to find the value of a?

Determine the relation between the accelerations? Please provide your steps for finding the answer?

Please solve this conservation of energy problem?

Slider block A moves to the left with a constant velocity of #6m/s#. Determine?

Do #x,y,z,t ∈ Q# exist so that #(x+y√2)^2+(z+t√2)^2 = 5+4√2#?

Limit Value=?

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?

Prove that the number #sqrt(1+sqrt(2+...+sqrt(n)))# is not rational for any natural number #n# greater than #1#?

When will the slope field for the differential equation #dy/dx=(yx^2+xy^2)/(3x+y)# have horizontal segments?

#inte^(3x)sin(4x)dx#?

The number #7^(1995)# when divided by 100 leaves remainder?( Solve using Binomial Theorem)

(ll) Find a matrix A of 3 X 3 different from zero such that A = A ^ T?

#lim_(n>oo)(Sin n+cos n)^n#
Find the value?
Thanks

How to calculate the limit of #((1+x)^{x}1)^x# when #x>+0# ?

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?

Expand 1/1+x² in ascending order of 1/x?

The correct answer?

How do I show that the sum of a convergent geometrical series 1+r+r^2+... > 1/2?

How do you factor #x^4+2x^3y−3x^2y^2−4xy^3−y^4# without quadratic equation?

How do you find the length of the line #x=At+B, y=Ct+D, a<=t<=b#?

Can you write
#(a+b)^0.5  (ab)^0.5#
as the square root of a difference?

How do you draw the slope field of the differential equation #y'=(y^2y2)(1y^2)# ?

Show that #3^(1/3)xx9^(1/9)xx27^(1/27)...# to infinity #=3^(3/4)#.how?

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)

What is the correct answer ?

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.

What is #(dy)/(dx)# of #sqrt(y/x)+sqrt(x/y)=sqrta???#

Can someone help me solve this?

How to solve this limit #\lim_{x\to pi/4} (sin2x)^(tan^2(2x)) # ?

Given: #x+y+z = 5# what is the value of #2^x+2^y+2^z# ?

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?

The curve described parametrically by #x=t^2+t+1#, and #y=t^2t+1# represents?

A vertical rod A of mass m rests on the inclined surface of a wedge B of mass M?

Projectile launcher problem?

How do you find a and b?

For what values of #m# does #z^3+(3+i)z^23z(m+i) = 0# have at least one real root?

Question is given below ?

Question #9ae53

How do you find the minimum of T = #sqrt(x^2+1)/3(2x)/5# (WITHOUT USING CALCULUS)?

What is the general term of this suit #5/3, 7/8, 9/15, 11/24, 13/35# ?

Prove that: (is true for any positive x,y):?
#x^x*y^y>=((x+y)/2)^(x+y)#

#lim_(x>oo) sqrt(25x^29x6)5x+3# ?

How do you solve this system of equations: #2x + 3y \geq 6;x  y \leq 3#?

The value of λ+k=?

Value f a=?

Approximate #sum_(n=1)^oo(1)^n/((3^n)(n!))# correct to four decimal places?

#(xy) dy/dx= (x+2y)# ?

#sum_(n=1)^oo(n!)^2/((2n)!) # converges ?

What is the inverse of #y=log_4( x3) +2x?# ?

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?

Q.3.find the integrating factor and solve the exact solution
consider the differential equation
(e^(xy)cosy+cosx+2e^(2xy)dx + (sinxe^(xy)siny+3y^2e^y)dy
Q.5. Prove ?

The number of real solutions #cos(e^x)=2^x + 2^x# is ?

Could you please prove the following equation from Arithmetic Progressions?

Watering a garden?

How can this be solved?

Question #fa20c

Question #89f79

If #n# is a natural number, prove that the number #(sqrt(n) + sqrt(n+1))# is irrational?

How do I solve this... L'Hopitals seems to go in an loop?

How do you Rewrite 2sin(x)−2cos(x) as Asin(x+ϕ)? x=? ϕ=?

Is the series #2+ 1 + 2/3 + 1/2+ 2/5+ 1/3 +2/7+ ...# convergent or divergent? Explain.

How can i solve the matrix equation: 5Y  2I₃ = Dt  (D+I₃)Y when D is a given 3x3 matrix?
Dt (transpose of D)

Please solve this question of mechanics?

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#?

Calculate:
#sum1/(n!+(n+1)!)#
; n from 0 to infinity?

#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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