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A 0.75kg block is tied at one end of a rope, 1.5m in length. The block is swung around a vertical circle and rotates four times each minute.
(A)what is the centripetal acceleration of the block?

Find (f+g)(x) , (fg)(x) , (f/g)(x) and (g/f)(x) for the following f and g . State the domain for f(x)=(√2x+3) ; g(x)=x²2?

Solve (3x+y)/8 = (xy)/5 = (x²y²)/5.
What is the values for x and y?

A wheel has a radius of 4.1m. How far(path length) does a point on the circumference travel if the wheel is rotated through angles of 30° , 30 rad, and 30 rev, respectively?

A race car starts from rest on a circular track of radius 400m . The car's speed increases at the constant rate of 0.500m/s^2 . At the point where the magnitudes of the centripetal and tangential accelerations are equal , determine the speed of the car ?

During a solar eclipse , the moon , earth , and and sun all lie on the same line,with the moon between earth and sun. what force is exerted by the sun on the moon? what force is exerted by earth on the moon? what force is exerted by the sun on earth

What is the mass of electron if the charge of electron and the ratio of charge to mass are #1.6*10^(19)"C"# and #1.76*10^8"C/g"# , respectively?

A transition of an electron between two different energy levels produced a series of line spectrum . calculate the wavelength of (β) line in Paschen series. wavelength in nanometer?

Solve (z+3)(2z)(12z)>0?

How to solve (x^2  4x +3)(x^2 3)<0?

(f○g)(x)=√(13x²)/(2x8) and (g○f)(x)=(13x²)/(32x²) . How to find f(g(4))?

How to determine whether f(x)3sin2x +5 is onetoone function. How to find the inverse of the function?

How to determine whether f(x)= 2x²4x 1 is one to one function given that x is more than or equal to 1?

Two masses are connected by a light string running over a light pulley of negligible friction. One mass(m1=3kg) is on a frictionless 20° inclined plane and the other (m2=1kg) is freely suspended. What is the acceleration of the masses?

The velocity of a particle is #5.8*10^5 "m/s"# . Calculate the uncertainty in its position. (Mass of particle=#9.1x10^(28)"g"# , #h=6.63*10^(34)#)?

What is the carbon skeleton for purine and pyrimidine?

A bicycle wheel has a moment of inertia of 0.25 kg m² about ots axle. The wheel rotates at 120 rpm . Calculate the angular momentum of the wheel and the rotational kinetic energy of the wheel?

Solve x²3<3 . This looks simple but i could not get the right answer. The answer is (√5,1)U(1,√5). How to solve this inequality?

A girl 60kg stands at centre of a playground meryground rotating about frictionles axle at 1 rad/s.treat mground as a uniform disc(m=100kg radius=3m). If the girls jumps to a position 1m from the centre, what will be their angular v after she landed?

For butane,write condensed structural formula for an isomer which has only primary and secondary carbon atoms and another isomer which has one tertiary carbon atom?

Write structural formula(condensed) for all the primary , secondary and tertiary haloalkanes with formula of C4H9Br and all the carboxylic acids and esters with molecular formula C4H8O2 and also all secondary alcohols with molecular formula C5H120?

Two cylinders of the same mass and shape, one hollow and one solid, are set on incline and allowed to roll down. Which cylinder will reach the bottom of the incline first? Why?

An alcohol has the molecular formula C4H10O write the structural formulae of the isomers to show chain isomerism?

Write the structural formulae of the two isomers with the molecular formula #C_4H_8O# to illustrate functional group isomerism?

A ketone has the molecular formula C5H10O. Write the structural formulae of the isomers to show positional isomerism?

A worker pushes a wheelbarrow with a force 40N over a level distance 6m. Frictional force 24N acts on the wheelbarrow in opposite direction to that of the worker, find the net work done on wheelbarrow?

F(x)=√(1x) and g(x)=ln x (x2). TRUE OR FALSE.explain. (i)none algebraic operation between f and g. (ii)g(f(x)) exists but not f(g(x)) ?

Considering only the formal charge , determine the major contributor among the canonical resonance structures of the following speciea. Explain. Nitrite ion(NO2) and SCN^?

A 20 N crate starting at rest slides down a rough 5m long raml ,inclined at 25° with the horizontal. 20 j of energt is lost to friction. What will be the speed of the crate at the bottom of the incline?

A force of 100N is applied to a 50kg mass in direction of motio for a distance of 6m and then the force is increased to 150N for the next 4m. For the 10m of travel , how much work is doneby the varying force?

8m, 200N uniform ladder rests against a smooth wall. μs beetween the ladder and the ground is 0.6 and the ladder makes a 50° angle with the ground.how far up the ladder can an 80N person climb before the ladder begins to slip?

How to find first derivative of f(x)=2 sin (3x) + x?

A(40kg) and B(46kg). They went to a playground and wanted to play on centrally pivoted seesaw. "A" sat on the left of the seesaw at 2m from the pivot. If the 4.4m long board must be balanced horizontally,where must "B" sit?

How to know covalent bond with highest polarity?

Poiseuille's law is about factors that control the flow rate of fluid through pipe. Explain all the factors involved?

A 1kg lead(density=11200kg/m^3) block floats in mercury(13600kg/m^3). Determine the submerged volume of the block,the % of the block submerged and whether the object will submerge fully in water(1k kg/m^3)?

Write an expression indicating the Bernoulli equation, define all the symbols used and state all the conservation of energy involved?

A hydraulic system has small and large pistons with crosssectional area of 3x10^4 m^2 and 6x10^3m^2 respectively. When a firce of 30N is applied to small piston, it pushes down the piston by 30cm. Determine pressure transmitted in the fluid?

How to differentiate #y= ln^3(cos^2 √(1x)#?

(i)CH3CH3 + Cl2→CH3CH2Cl+HCl (ii)CH3CH(OH)CH→CH3CH=CH2+H2O (iii)CH3CHO+HCN→CH3CH(OH)CN (iv)CH3CH=CH2+HBr→CH3CHBrCH3 (v)CH3CH2C(OH)=CH2→CH3CH2COCH3
State the reaction type?

Cot theta+tan theta=k, where theta is an acute angle and k is a constant, has real value of tan theta, show that k«2 or k»2?

A 0.45kg object attached to a hotizontal spring oscillates in simple harmonic motion with frequency 2Hz. If the object is released from rest at x=0.05m,find velocity and acceleration at x=0.05m,0.00,and 0.005m?

Write the products of homolysis or heterolysis of each bond (a) H3CCH3 (b) O2NN2O(c) CH3OH (d) H3CH2CMgBr organic chemistry?

Tge equation of motion of 0.5kg object which is attached to a spring oscillates on a frictionless horizontal surface started t=0s given by x=10SiN t ,what is the amplitude,frequency,max velocity ,max acceleration ,total energy of the system?

A 0.10kg object connected to a light spring oscillates with frequency 5Hz on a frictionless horizontal surface.what is the total energy and speed of the object at x=8cm if the amplitude of the motion is 20cm?

A simple pendulum has length 20cm.it was displaced at an angle 15° and then released to execute simple harmonic motion. How much time is required for the pendulum to reach maximum speed?

How solve this equation where 0.8=0.2 cos (31.4 t) where 31.4 is the unit in radian per second and we want to find t (time)value, the answer is t=0.037 seconds, how to solve it algebraically?

Oxygen reacts with fluorine to form only #OF_2#, but sulphur which is in the same group 16 as oxygen, reacts with fluorine to form #SF_2#, #SF_4# and #SF_6#. Explain?

With the assumption that the ammonium ion is formed from the reaction between ammonia and hydrogen io ,describe the formation of bond between these two species and state the type of bond formed?

Determine the geometries using vsepr theory .State the approximate bond angle(s) in each molecule and determine whether each molecule is polar or non polar a)BCl3 b)PCl5 c)NCl3 d)SO3 e)XeF4 f)HBF2?

Find f"(x) given that 3x²+y²=2 using implicit differentiation?

Differentiate with respect to y : (2xcos3y)^4sec(ln(1xy))+√(1+(√y))?

If 4(xy^3)xy=16 ,evaluate dy/dx at the point (2,3)?

(A) Sin(y/x) +ye^(2x) = xy (B) √y  4ln x = cos (x+y) (C) e^(2y) + tan(1/x) =(x²/y) (D) ln y+2x =(3y)^3 (E)xy²sin(x+2y)=2x . Find the dy/dx (implicit differentiation)?

O2NN2O is homolysis or heterolysis? What is the product?

Express as a natural log,then differentiate with respect to x,Find dy/dx (a)y=(2x3)^5/(x²+1)^6√(x^32x). (B)y=log4 2x (c) y=x^(2x)?

What is the second derivative for #y(x)=5e^(pi x)+cos (y(x))# ?

A portable conveyor user by roofers is 11.0m long. The angle between the conveyor and the ground can be adjusted from 30° to 70°. What is the range of heights that the conveyor can reach?

How to determine the type of hybridization, can you guys explain how?

Given tan x tan y = p and cos(x+y)=q .Show that sin x sin y =(pq)/(1q) and cos(xy)= (q(1+p))/(1p) ?

If x a third quadrant angle and y an acute angle such that cos x=(3/5) and sec y= (3/2) ,find the exact value of sin(xy) , exact value of tan(xy) and quadrant containing (xy)?

Find the exact value of sin(pi/12) , cos (11pi/12) , and tan (7pi/12)?

Find the exact value of sin(pi/12) , cos (11pi/12) , and tan (7pi/12)?

Find the exact value of sin(pi/12) , cos (11pi/12) , and tan (7pi/12)?

How to draw overlapping of pure or hybridized orbitals for Br2 and NO+? Explain the need for the orbital of an atom to hybridized based on the Lewis structures

Find dy/ddx for xy²  sin(x+2y)= 2x?

A curve has parametric equations x=2tln2t and y=t²ln t² where t>0. Find the value of t at the point on the curve where dy/dx =2 . Hence ,find the coordinates of that point?

A curve has parametric equations x= zcos z , y=sin z , for pi<z<pi. Find the coordinates of the point at which the gradient of this curve is zero?

Find d²y/dx² in terms of t if x= (1t²)/(1+t²) and y=t/(1+t²)?

A conical water tank with its vertex at bottom has radius 20m and depth 20m.Water is being pumped into the tank at rate 40m^3/min.how fast is the level of the water rising when water is 8m deep? ( v=(pi x r² x h)/3 )

A point moves along the graph y= x^(5/2) so that its x coordinate increases at the constant rate of 2units/second. Find the rate at which its y coordinate is increasing as it passes the point (4 ,32)?

A snowball, in the shape of a sphere, is melting so that the radius is decreasing at a uniform rate of 1cm/s. How fast is the volume decreasing when the radius equals 6cm?

Give the different combinations of RX and R'X that can be used to synthesize 3methylpentane. Write the IUPAC name for rach of the RX and R'X?

Write a stepwise mechanism that shows how a small amount of CH3CH3 could form during the bromination of CH4?

What alkane of molecular C8H18 gives a single product of monohalogenation when heated with Cl2? Write the IUPAC name for the product of monohalogenation?

Draw and name all structural isomers formed by monochlorination of each alkane cyclopentane , CH3CH2CH2CH2CH3 , and (CH3)3CH?

Explain.(i)Pentane is distilled off first when a liquid mixture containing pentane,heptane and nonane is heated.(ii)Hexane floats on water. (iii) cyclopentane may be easily separated from an aqueous salt solution?

Arrange the alkanes in each set in order of increasing boiling point.explain.(i) 2methylheptane,octane, and 2,2,4trimethylpentane.(ii)butane,octane and hexane?

Draw 2ethyl5secbutylheptane and what is the correct iupac name?

Write equations to show how 2,3dimethylbutane may be prepared from each of the following compounds. (i)an alkene (ii)A grignard reagent (iii)a haloalkane (iv)a sodium alkanoate?

Write the reaction equations of (i)2bromo2methylpropane + magnesium in dry ether; (ii)product of (i) + water?

2bromo3methylbutane , 2chlorobutane , 1chloro2,2dimethylpropane. Name the haloalkanes which can be prepared in high yield by monohalogenation of an alkane?

Write the equation for the preparation of a Grignard reagent using 2bromo3methylbutane and name the alkane produced after its hydrolysis?

Of 2bromo3methylbutane , 2chlorobutane , 2chloro2methylpropane, which haloalkanes will give 3,4dimethylhexane when treated with sodium metal (Wurtz reaction)? Write the reaction equation?

A stone is dropped from rest into a well. The sound of the splash is heard exactly 2.00s later. Find the depth of the well if the air temperature is 10.0°c ?

For maximum safety, the distance between the base of a ladder and a building should be 25% of the length of the ladder. Find the safest angle between the ladder and the ground?

Given that 7tan a + 2 cos a= 5sec a,derive a quadratic equation for sin a. Hence, find all values of a in the interval [0,pi] which satisfy the given equation?

Find all exact angles x in the interval [0,360°] that satisfy the following equations without the use of calculator a)sin x +cos 2x=0 b)cos 2x= sin52 ?

The warning tag on a lawn mower states that it produces noise at level of 91.0dB. What is this in Wm^2?

Calculate the level in decibels for a sound having an intensity of 5.00x10^4Wm^2?

Show that sin 3x = 3 sin x  4sin^3 x ?

Prove that tan x = (sin 2x)/(1+cos 2x) . Hence find the value of tan 15° and tan 67.5° , giving your answer in term of surds in simplest form?

Verify the following identities (a) tan 3x =[ tan x(3tan²x]/(13tan²x)?

Find all exact angles,x in the interval[pi, pi] that satisfy (a)2cos x=√3 (b)√3 sin x = cos x (c) 4sin²x = √(12) sin x (d) sec² x=2 ?

Draw and name all structural isomers formed by monochlorination of (CH3)3CH?

Determine the points on the curve 5x² + 6xy +5y² =8 where the tangent is parallel to the line xy= 1?

A curve has parametric equations x= 2tln 2t and y= t²  ln t² where t>0 . Find the value of t at the point on the curve where dy/dx=2 . Hence find the coordinates of that point?

Write the following products as a sum or difference (a)sin 2xcos3x (b) cos 5x cos 3x (c)sin4xsin2x (d)cos3xsin6x ?

Write the following sums or differences as a product (a)sin 2x + sin 3x (b)cos 5x cos 3x (c)sin 4x sin 2x (d)cos 3x + cos 6x?

Verify the following identities: (a) #2sin^2(2x) + cos4x=1# (b) #tanx+co x =2sec2x# (c) #tan3x =[tanx(3tan^2x)]/ (13tan^2x)#?

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