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  5. january 2018
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Mathematics Questions and Answers January 5, 2018

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Q 3 : Use the Laplace transform method to solve the following ordinary differential equiation for t 0 9 d 2 y d t 2 + 1 2 d y d t - 5 y = 1 When the initial conditions are given as When t = 0 , y = 0 , y ' = 0 .
Q 3 : Use the Laplace transform method to solve

Evaluate the definite integral. 1 7 cos ( t / 2 ) dt 0

You are told that x = - 9 and x = 1 3 are solutions to a particular quadratic and the x ^ ( 2 ) term's coefficient is 1 . Find the quadratic.

The graphs of the revenue, R ( x ) , and cost function, C ( x ) , for the production and sale of x units are shown below. The cost function is the straight line, and the revenue function is the curve, 2 9 a . Use the graph to estimate the production level x that maximizes profit. You may assume the x value for the maximum profit is a multiple of 5
The graphs of the revenue, R ( x ) , and cost

Assignment 5 : Problem 1 0 ( 1 point ) The system of first order differential equations y 1 ' = - 6 y 1 + 1 0 y 2 + 1 y 2 ' = 1 0 y 1 - 6 y 2 + 1 where y 1 ( 0 ) = 0 , y 2 ( 0 ) = 0 has solution y 1 ( t ) = y 2 ( t ) =
Assignment 5 : Problem 1 0 ( 1 point ) The system

( 1 point ) The revenue from selling q items is R ( q ) = 7 0 0 q - q 2 , and the total cost is C ( q ) = 5 0 + 9 q . Write a function that gives the total profit earned, and find the quantity which maximizes the profit. ( Throughout this problem, use q as the variable for the number of items instead of x as the variable for the number of items. )
( 1 point ) The revenue from selling q items is R

Rewrite the expression ( - 2 1 6 ) ^ ( ( 1 ) / ( 3 ) ) using radicals; then simplify if possible.

After a large earthquake the number of aftershocks changes with time in accordance with Omori's law. What is the rate of change in the number of earthquakes? falls by half every month doubles every six months grows logarithmically decreases with a rate that depends on mainshock magnitude decreases as an inverse of time after the mainshock

A culture of bacteria in a particular dish has an initial population of 4 0 0 4 0 0 cells grows at a rate of Upper N prime left parenthesis t right parenthesis equals 5 0 e Superscript 0 . 3 5 8 3 5 tN ( t ) = 5 0 e 0 . 3 5 8 3 5 t cells / day . a . Find the population N ( t ) at any time tgreater than or equals 0 . b . What is the population

In the following problem, begin by drawing a diagram that shows the relations among the variables. If w equals 3 x squared plus y squared plus z squaredw = 3 x 2 + y 2 + z 2 and z equals x squared plus y squaredz = x 2 + y 2 , find a . left parenthesis StartFraction partial derivative w Over partial derivative y EndFraction right parenthesis

find the fourh degree polynomial f ( x ) that has - 3 i and 2 i as zeros n where f ( - 2 ) = - 2 0 8

Find the indefinite integral of the following function and check the result by differentiation. s 4 ( 8 + s 5 ) 2 d s a . ( 8 + s 5 ) 3 2 4 0 + C b . 2 ( 8 + 5 5 ) 2 3 4 5 + C c . ( 8 + s 5 ) 3 2 4 5 + C d . 2 ( 8 + s 5 ) 3 2 1 5 + C e . none of the above
Find the indefinite integral of the following

Problem 4 : A box with a square base and top and rectangular sides is being constructed out of cardboard. Suppose that - to build the base and top of the box, it costs \ ( \ $ 1 \ ) per square inch, and - to build the other sides of the box, it costs \ ( \ $ 0 . 5 0 \ ) per square inch. If you are spending \ ( \ $ 5 4 \ ) , find the side lengths \
Problem 4 : A box with a square base and top and

Suppose h is a function such that h ( 2 ) = 3 , h ( 2 ) = 6 , h ( 2 ) = 5 , h ( 5 ) = 7 , h ( 5 ) = 1 2 , and h ( 5 ) = 2 2 , and h is continuous everywhere. Evaluate 5 2 h ( u ) du .

Find dy / dx given e ^ ( xy ) + y ^ 3 = 9

( 1 0 pts . ) Find the area of the parallelogram with vertices P ( 1 , 0 , 1 ) , Q ( 0 , 1 , 2 ) , R ( 1 , 2 , 3 ) .
( 1 0 pts . ) Find the area of the parallelogram

Consider the function f ( x ) = 9 / x ^ 3 9 / x ^ 7 . Let F ( x ) be the antiderivative of f ( x ) with F ( 1 ) = 0 . Then F ( x ) =

n f n ( x ) = n x 1 + n x , xin [ 0 , 1 ] , . ( a ) { f n } f finR [ 0 , 1 ] . ( b ) { f n } f . ( c ) lim n 0 1 f n ( x ) d x = 0 1 [ lim n f n ( x ) ] d x .
n f n ( x ) = n x 1 + n x , xin [ 0 , 1 ] , . ( a

A cubical metal block is heated such that its edge x increases by 3 mm and its volume V is doubled. Write polynomial equation for x and find the value for x .

In a town whose population is 3 5 0 0 , a disease creates an epidemic. The number N of people infected t days after the disease has begun is given by the function N ( t ) = 3 5 0 0 / 1 + 1 5 . 9 e ^ 0 . 5 t Find the number infected after 5 days.

Evaluate the following limit using L'Hospital's rule.limx ( 9 x ) ^ 8 / x

( 5 ) Let vec ( F ) ( x , y , z ) = z 2 x vec ( ) + z 2 y vec ( ) + 2 z l n x y v e c ( k ) . Evaluate C vec ( F ) * d v e c ( s ) where C is the path of straight line segments from P = ( 1 , 2 , 1 ) to Q = ( 4 , 1 , 7 ) to R = ( 5 , 1 1 , 7 ) , and then back to P .
( 5 ) Let vec ( F ) ( x , y , z ) = z 2 x vec ( )

Find C x 2 z d s , where C is the line segment from ( 0 , - 6 , 4 ) to ( 1 , - 4 , 2 )
Find C x 2 z d s , where C is the line segment

Use the definition to find the Taylor series ( centered at c ) for the function then find the radius of convergence. f ( x ) = e 6 x , c = 0 Your paperwork is what will be scored for this problem. This may cause your score to drastically increase or drastically decrease upon grading. On your paperwork, be sure to correctly follow the procedure for
Use the definition to find the Taylor series (

Consider the following initial value problem: y ' ' + 6 y ' + 8 y = ( t - 5 ) + u 1 0 ( t ) ; , y ( 0 ) = 0 , y ' ( 0 ) = 1 4 a ) Find the solution y ( t ) . y ( t ) = u c ( t ) + 1 where c = and d =
Consider the following initial value problem: y '

Evaluate the line integral, where C is the given curve. \ int _ C xsin ( y ) ds , C is the line segment from ( 0 , 1 ) to ( 3 , 5 )
Evaluate the line integral, where C is the given

Find the circumference of the circle given by x = 2 c o s t and y = 2 s i n t for 0 t 2 .
Find the circumference of the circle given by x =

Use Mathematica. Find the equation of the tangent line for the following function. Then plot the original equation and the tangent line on the same graph. x = l n ( s e c t + t a n t ) - s i n t , y = c o s t , t = 6
Use Mathematica. Find the equation of the tangent

Use integration by parts to find an antiderivative for $x e ^ { x } $ . Before starting ask yourself: " Do either of these functions get nicer when integrated? Do either get nicer when differentiated? Which function do I want to differentiate and which do I want to integrate?" Do the same for $x \ ln x$ .

A population of butterflies decreases exponentially at a rate of 1 8 . 3 % per year. What is the equivalent monthly rate to the nearest hundredth of a percent?

A baseball team plays in a stadium that holds 6 0 0 0 0 spectators. With the ticket price at $ 8 the average attendance has been 2 4 0 0 0 . When the price dropped to $ 7 , the average attendance rose to 3 0 0 0 0 . Assume that attendance is linearly related to ticket price. What ticket price would maximize revenue?

[ - / 1 Points ] A particle starts at the origin, moves along the x - axis to ( 2 , 0 ) , then along the quarter - circle x 2 + y 2 = 4 , x 0 , y 0 to the point ( 0 , 2 ) , and then down the y - axis back to the origin. Use Green's theorem to find the work done on this particle by the following force field. F ( x , y ) = ( : s i n ( x ) , s i n (
[ - / 1 Points ] A particle starts at the origin,

The future value at 3 . 7 5 % interest, compounded continuously for 3 years, of the continuous income stream with rate of flow f ( t ) = 1 , 5 0 0 e - 0 . 0 2 t , is $ 4 , 6 2 5 . Compute the interest earned. The interest earned is $ ( Round to the nearest dollar as needed. )
The future value at 3 . 7 5 % interest,

Evaluate the integral. 3 4 4 + u 2 u 3 d u
Evaluate the integral. 3 4 4 + u 2 u 3 d u

Problem 1 [ 4 marks ] Use the Squeeze Theorem to prove that lim x 0 ( x 2 ) 1 0 + 6 c o s ( 1 x ) 2 = 0
Problem 1 [ 4 marks ] Use the Squeeze Theorem to

Evaluate the integral. - 2 0 ( 1 3 t 5 + 1 8 t 4 - t ) d t
Evaluate the integral. - 2 0 ( 1 3 t 5 + 1 8 t 4

0 2 f ( x ) d x , f ( x ) = { x 2 , 0 x 1 1 x , 1 x 2 .
0 2 f ( x ) d x , f ( x ) = { x 2 , 0 x < 1 1 x ,

A projectile is fired with an initial speed of 2 2 0 m s and angle of elevation 6 0 . ( Use g = 9 . 8 m s 2 . Round your answers to the nearest whole number. ) ( a ) Find the range ( in m ) of the projectile. m ( b ) Find the maximum height ( in m ) reached. m ( c ) Find the speed ( in m s ) at impact. m s
A projectile is fired with an initial speed of 2

Evaluate the expression for the given value of the variables. 3 x + 2 y - 5 0 , for x = 5 y and y = 5

Find the integrating factor of the following differential equation & hence solve the eq lation for hence solve the equation for the inital value given. A d x d t + 2 t x = ( 2 t - 1 ) e - t x ( 0 ) = 1 b . The following differential equation shows a non - linear Bernoulli differential equation with inital conditions with inital conditions 6 d x d
Find the integrating factor of the following

Evaluate the definite integral. 6 intergl 4 ( x 2 + 2 x 7 ) dx

Find the points of intersection of the following pair of curves. y = x 2 - 2 x + 2 , y = - x 2 - 1 0 x - 4 The points of intersection are ( Type an ordered pair. Use a comma to separate answers as need
Find the points of intersection of the following

Determine the vertical asymptote ( s ) of the function. If none exists, state that fact. f ( x ) = 3 x - 5 x - 6

The volume in cubic feet of a workshop's storage chest can be expressed as the product of its three dimensions: V ( x ) = x ^ ( 3 ) + 2 x ^ ( 2 ) - 1 3 x + 1 0 . The depth is x + 5 . a . Find linear expressions with integer coefficients for the other dimensions.

Evaluate the integral by making a change of coordinates. I = 0 2 0 4 - x 2 2 x 2 + y 2 2 8 - x 2 - y 2 2 y ( x 2 + y 2 + z 2 ) d z d y d x I = Tries 3 / 3 0 Previous Tries
Evaluate the integral by making a change of

Use implicit differentiation to find an equation of the line tangent to the curve x 2 + y 2 = 1 0 at the point ( 3 , 1 ) . y = 3 x + 8 y = 3 x 8 y = 3 x + 9 y = 3 x 1 0

Consider the function f ( x ) = e 1 / x 2 if x = 0 0 if x = 0 ( a ) ( 3 points ) Show that f ( 0 ) = 0 .

The pollution level near a dump site has been modeled by the equation , P ( t ) = 0 . 0 5 + 0 . 1 2 e ^ 0 . 3 8 t where is the volume of pollutants ( in cubic meters ) and is the time ( in years ) . a ) What is the rate change in the pollution level with respect to time?

3 a . The 6 th term of an AP is 3 5 and the 1 3 th term is 7 7 . Find the 2 0 th term

[ - / 2 . 5 Points ] SCALC 9 M 7 . Evaluate the integral. ( Remember to use absolute values where app 5 ( x - 1 ) ( x 2 + 4 ) d x
[ - / 2 . 5 Points ] SCALC 9 M 7 . Evaluate the

Evaluate the definite integral. 0 2 sin ( 2 t ) dt

You arrive at the gate that holds the spaceship. Your computer translates the password requirement as follows: Find the indefinite integral on the domain of positive real numbers for the following function: f ( x ) = 1 5 x + 6 5 x To appropriately translate the password, you will need to enter an exact answer. Your computer reminds you to include

integral of ln ( 2 x )

The growth of the rabbit population on a certain island is proportional to the size of the population. Two measurements, 1 5 years apart show the population has multiplied by a factor of 4 . If the population is currently at 1 0 , 0 0 0 rabbits ( at t = 0 ) , when will the population be at 1 0 0 , 0 0 0 ? Round your answer to the nearest year.

Find the integral. 1 - x 2 x 2 d x + C
Find the integral. 1 - x 2 x 2 d x + C

A company's production is estimated to be P ( L , K ) = 3 L 0 . 6 K 0 . 4 . Find P ( 2 4 0 , 3 0 0 ) . ( Round your answer to one decimal place. ) P ( 2 4 0 , 3 0 0 ) =

integral of cot ( 7 x ) dx

A can in the shape of a right circular cylinder is required to have a volume of 5 0 0 cubic centimeters. The top and bottom are made of material that costs 1 0 ! i n per square centimeter, while the sides are made of material that costs 6 per square centimeter. ( a ) Express the total cost C of the material as a function of the radius r of the
A can in the shape of a right circular cylinder

Points: 0 of 1 Save list A box is to be made where the material for the sides and the lid cost $ 0 . 2 0 per square foot and the cost for the bottom is $ 0 . 5 0 per square foot. Find the dimensions of a box with volume 2 0 cubic feet that has minimum cost. 1 L W H = ftx f t ft ( Round to four decimal places as needed. )
Points: 0 of 1 Save list A box is to be made

whats the produces of light dependent and light indpendent in biology

ewrite without parentheses. - 6 w ^ ( 6 ) ( - 9 w ^ ( 3 ) - 7 w ^ ( 2 ) + 6 w ) implify your answer as much as possible.

Lines L 1 , L 2 , and L 3 are defined by:
Lines L 1 , L 2 , and L 3 are defined by:

Find the indefinite integral. ( Rem d x x ( l n ( x 2 ) ) 8
Find the indefinite integral. ( Rem d x x ( l n (

Water flows from the bottom of a storage tank at a rate of \ ( r ( t ) \ ) gallons per minute. Over a 3 0 - minute period, the rate \ ( r ( t ) \ ) is decreasing. The table below gives the rate at 5 - minute intervals. Since the rate \ ( r ( t ) \ ) is decreasing, the left endpoint approximations will give the upper estimate ( i . e . overestimate
Water flows from the bottom of a storage tank at

Determine limx 3 f ( x ) given the definition of f ( x ) below. ( If the limit does not exist, enter . ) f ( x ) = x 2 x + 3 x 2 + x + 2 3 xifx 1 if 1 3 Provide your answer below:

Derive the equations of principal stresses, their direction and the maximum shear stress: + example

1 9 4 4 Evaluate the integral. 2 3 . y 9 1 sx dx

An object is projected upward from ground level with an initial velocity of 4 2 0 feet per second. In this exercise, the goal is to analyze the motion of the object during its upward flight. ( a ) If air resistance is neglected, find the velocity of the object as a function of time. Use a graphing utility to graph this function. v ( t ) = ( b )
An object is projected upward from ground level

( 2 pts ) Consider the sequence: { 1 , - 2 3 , 4 5 , - 8 7 , dots } . Write an explicit formula for the n t h term of the sequence. If you want the sequence to start with any index other than n = 1 , then you must state the starting index.
( 2 pts ) Consider the sequence: { 1 , - 2 3 , 4

Draw a graph of ( generalized ) derivative d f t d t below the graph of the discontinuous function shown in Figure: Show both derivative graphs and all work
Draw a graph of ( generalized ) derivative d f t

The price p ( in dollars ) and the demand x for a particular clock radio are related by the equation x = 3 0 0 0 - 1 0 p . ( A ) Express the price p in terms of the demand x , and find the domain of this function. ( B ) Find the revenue R ( x ) from the sale of x clock radios. What is the domain of R ? ( C ) Find the marginal revenue at a
The price p ( in dollars ) and the demand x for a

de fulier
de fulier

Find y and y for y = 5 xln ( x ) . y = y =

( b ) 0 2 ( 1 - | c o s x | ) d x
( b ) 0 2 ( 1 - | c o s x | ) d x

Find I x ' I y ' I 0 ' b a r ( x ) , and ? b a r ( ? b a r ( y ) ) for the lamina bounded by the graphs of the equations. y = x 2 , y = 0 , x = 6 , = k x y I x = I y = I 0 = ? b a r ( x ) = ? b a r ( ? b a r ( y ) ) =
Find I x ' I y ' I 0 ' b a r ( x ) , and ? b a r

Evaluate the definite integral. Integral from 1 to 5 StartFraction 1 2 left parenthesis ln x right parenthesis cubed Over x EndFraction dx 1 5 1 2 ( lnx ) 3 x dx Question content area bottom Part 1 Integral from 1 to 5 StartFraction 1 2 left parenthesis ln x right parenthesis cubed Over x EndFraction dx 1 5 1 2 ( lnx ) 3 x dxequals = enter your

Find the derivative of y = ( Lnx ) ^ 4

( 3 pts ) Use the Alternating Series Test to determine if the series below converges or diverges. n = 1 ( - 1 ) n * n - 1 5 n
( 3 pts ) Use the Alternating Series Test to

limx 2 + x + 1 x - 2 = , limx 2 - x + 1 x - 2 = -

Find the indefinite integral. ( Use C for the constant of integration. ) Original IntegralRewriteIntegrateSimplify 1 ( 3 x ) 2 dx 1 9 x 2 dx ( Use negative exponents. ) x 1 1 9 x + C

Integrate 0 ( x 2 + 5 ) 2

integrate ( x ^ ( 1 / 2 ) + 1 ) ( t + 1 ) dt

Evaluate the definite integral. 1 0 1 4 x 2 / square root ( 4 x 6 ) dx

\ ( \ int _ { 0 } ^ { \ infty } \ frac { \ sin z } { z } ~dz \ )

A 0 d / ( a + Cos ) ^ 2 = a / ( a ^ 2 - 1 ) ^ 3 / 2 for a > 1 .

Consider the following linear programming problem: Minimize : C = 0 . 3 0 x + 0 . 4 0 y Subject t o : , 2 1 0 x + 1 5 0 y 2 1 1 5 2 4 0 x + 3 8 0 y 3 4 6 0 x , y 0 When graphed and shaded, the following corner points are discovered: ( 0 , 1 4 . 1 ) ( 6 . 5 , 5 ) ( 1 7 3 1 2 , 0 ) What is the solution to the problem? C is minimized at 3 . 9 5 when
Consider the following linear programming

find all roots: x ^ 6 + 2 x ^ 4 - x ^ 2 - 2 = 0

Evaluate the integral. 5 tan 3 ( 6 x ) dx

consider the second order cauchy euler differential equation t ^ 2 y ' ' + 6 ty ' - 8 4 y

Calculate 0 4 x 3 2 - x 2 x 2 + y 2 dydx in polar coordinates. Show the region of integration.

Find the length of the curve. r ( t ) = 8 i + 2 t 2 j + 5 t 3 k , 0 t 1
Find the length of the curve. r ( t ) = 8 i + 2 t

( 1 point ) You are given the four points in the plane A = ( 4 , - 3 ) , B = ( 6 , 2 ) , C = ( 1 1 , - 1 ) , and D = ( 1 3 , 4 ) . The graph of the function f ( x ) consists of the three line segments A B , B C and C D . Find the integral 4 1 3 f ( x ) d x by interpreting the integral in terms of sums and / or differences of areas of elementary
( 1 point ) You are given the four points in the

Two linearly independent solutions of the differential equation y ' ' - 5 y ' + 6 y = 0 are Select the correct answer. y 1 = e - 2 x , y 2 = e - 3 x y 1 = e - 6 x , y 2 = e - x y 1 = e - 6 x , y 2 = e x y 1 = e 6 x , y 2 = e - x y 1 = e 2 x , y 2 = e 3 x
Two linearly independent solutions of the

Let A be the wedge in the first octant that is cut from the cylindrical solid y 2 + z 2 2 5 by the planes y = x and x = 0 . Evaluate the integral z d V over the wedge A .
Let A be the wedge in the first octant that is

Compute - 1 1 ( 1 + 2 x + x 2 ) d x using the definition. Use the right - endpoint approximation in your computation.

Evaluate the following integral using Simpsons one third rule with h = 0 . 2 , taking your answer to 4 d . p I = 0 1 . 2 1 ( 1 + x 2 ) d x Evaluate the following integral using Trapezoidal rule with h = 1 . 0 , taking your answer 4 d . p , I = - 3 3 x 4 d x
Evaluate the following integral using Simpsons

Find the antiderivative for the given function. sech ^ 2 ( 9 x + 6 )

Evaluate the triple integral B f ( x , y , z ) d V over the solid B . f ( x , y , z ) = 1 - x 2 + y 2 + z 2 2 , B = { ( x , y , z ) | x 2 + y 2 + z 2 9 , y 0 , z 0 }
Evaluate the triple integral B f ( x , y , z ) d

Evaluate the integral 0 1 ( x 2 + 1 ) ( 3 x 2 + 1 ) dx

Perform the integration. Indefinite integral tan ^ 2 ( x ) / csc ^ 1 2 sec ^ 3 ( x ) . use a c to represent a constant

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