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How to derive 1st of motion from second law of motion?

A parellel plate capacitor with plate speration d is charged with a battery so that energy stored is #"U"#. If a plate of dielectric #"K"# and thickness d is placed betweeen the plates of capacitor and battery remains connected. The work by battery is?

What are the range of initial values using the NewtonRaphson method for #(x9)/(x^2+1)=0# for it to converge to 9?

Show that the line integral #int_{1,2}^{3,1}(y^(2)+2xy)dx+(x^(2)+2xy)dy# is independent of path and evaluate it?

A circle touches two perpendicular lines
#2x3y=15#
and
#3x+2y=3#
at the points
#A(6,1)#, #B(1,0)#
respectively. Find the equation of the circle?

How do you evaluate the integral #int sqrtxsqrt(4x)#?

How do you solve #sin(x/2)1=0# between the interval #0<=x<8pi#?

A frequency of variation of kinetic energy of a simple harmonic motion of frequency n is?

How to integrate 1/(64x^2+100)?

Total resistance of the circuit ?

How many solutions are there to the following system of equations 4x – 8y = 0
and –3x + 8y = –7?

Find # i# for #t>0 # if the circuit is in steady state at # t=0# ?

Let #'f'# be an even periodic function with period '4' such that #f(x) = 2^x1#, #0<=x<=2#. The number of solutions of the equation #f(x) = 1# in #[10,20]# are?

An object moves along a curve has an acceleration of 5 m/s^2 at 30° with its velocity of 5 m/s at some instant . The radius of curvature of the path at that instant is ?
a) 10 m
b) 20 m
c) 5 m
d)15 m

What are the local extrema of #f(x)= xlnxxe^x#?

How to complete this electrical current table?

What is the antiderivative of # ln(x^2 + 2x + 2)#?

An amount Q of heat is added to a mono atomic ideal gas in a process in which the gas performs a work Q/2 on its surrounding .find equation of the process?

F(x)=e^0.5x when x<=0 and f(x)=(xh)2+k when x>0 find h and k such that f(x) is both continuous and smooth at x=0?

What is the derivative of #f(x)=sqrt(1+log_3(x)# ?

Find the required limit algebrically, if it exists.
lim (x+3)/(x3) if x approaches 4 ?

What is the area of the shaded segment?

What is the arclength of #(1/t^2,1/t)# on #t in [1,2]#?

How to find result ?

A particle of mass #m# moving with speed #v# hits elastically another stationary particle of mass #2m# inside a smooth horizontal circular tube of radius #r#. The time after which the second collision will happen?

Please solve with a detailed explanation?

The number of solution of the equation
3^(sin2x+2cos2x)+
3^(1sin2x+2sin2x)=28 in [0,2π]?

#intint_Asqrt(xyy^2)dxdyquadquadA={(x,y)inRR^2; 0<=y<=3, x/10<=y<=x}# Would anyone help me?

Find two numbers whose sum is 12 such that the sum of the square of one plus 4 times the other is a maximum?

I cut a triangle ABC out of a piece of paper. I found out that sinA+sinB+sinC=5/2 and a/sinA=16. What is the triangle’s perimeter?

How do you factor the expression #6 a^2  ab + 7 b^2#?

#psi_A(x,0) = sqrt(1/6)phi_0(x) + sqrt(1/3)phi_1(x) + sqrt(1/2)phi_2(x)#
Calculate the expectation value #<E># at any later time t=#t_1#, #phi_n# are energy eigenfunctions of the infinite potential well .Write the answer in terms of #E_0#?

A circular loop wire with current I1=I∘π and a V shaped wire with current I2 are arranged in a plane as shown in diagram. If magnetic field at O is zero, value of I2 is ?
(a)#(13aI_@)/35r#
(b)#(12aI_@)/17r#
(c)#(aI_@)/r#
(d)#(12aI_@)/35r#

#int sqrt(x^2+5/x)=#?

If the area under the curve of f(x) = 25 – x2 from x = –4 to x = 0 is estimated using four approximating rectangles and left endpoints, will the estimate be an underestimate or overestimate?

How do you solve for x given #\frac{2x}{7}+9  > frac{5}{7}#?

Integrate. What is the next step ?

Integral Lnx/(1+x)^2 dx Answer Guys ???

A projectile is shot from the ground at an angle of #( pi)/3 # and a speed of #9 m/s#. Factoring in both horizontal and vertical movement, what will the projectile's distance from the starting point be when it reaches its maximum height?

When #a1/a=1#, #a^51/a^5 =#?
how to solve....

A particle begins to move with a tangential acceleration of constant magnitude #0.6m/s^2# in a circular path. If it slips when it's total acceleration becomes #1m/s^2#, then the angle through which it has turned before slipping is?

#y=f(x)# is given. Graph, #y=f(3x)2# and #y=f(x1)#?

What is the solution to the integral of 2cosx + 3sinx / cosx + sinx? Thanks

How do you solve the inequality #x^2+3x28<0#?

Question #265f1

A town's January high temperatures average 36°F with a standard deviation of 10°, while in July the mean high temperature is 74° and the standard deviation is 8°. In which month is it more unusual to have a day with a high temperature of 55°?

Find the Taylor series expansion formula of #f(x)=\lnx# at #a=3#?

Three rods each of mass M and length L, are joined together to form an equilateral triangle. What is the moment of inertia of a system about an Axis passing through its centre of mass and perpendicular to the plane of the triangle?

Find the sum of the infinite series #ne^(1n)# from #n=1# to #oo#?

When a load is connected to a voltage divider, will the total resistance of the circuit increase or decrease?

How to define a, b, c, d, e that are integer between 19 so that matrix is a symmetry matrix?

How do you prove [(sinxcosx)/(secxcscx)]=[(sin2x)/2]?

A particle moves in the xy plane with velocity #v_x#=#8t2# and #v_y#=2.If it passes through the points #x=14# and #y#=4 at #t#=2,what is the equation of the path?

If the AM and GM for 10 observations are both 15 then the value of harmonic mean......?

Triangle A has an area of #15 # and two sides of lengths #4 # and #9 #. Triangle B is similar to triangle A and has a side of length #12 #. What are the maximum and minimum possible areas of triangle B?

The answer is?

What is the answer please?

In a garden a boy is swinging in the standing position how will the time period of the swing be affected if the boy sites down on the swing?

A radioactive isotope #""_Z^XA# decay and emits one alpha particle and two beta particles
consecutively. How to write the formula for the nuclides produced?

Integrate #x^3/sqrt((x^2+16))# dx using trig substitution?

17!/(5!*12!) ?

What is the integration of #(dx)/(x.sqrt(x^3+4))#??