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Mathematics Questions and Answers May 14, 2018

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\ int _ ( ( \ pi ) / ( 8 ) ) ^ ( ( \ pi ) / ( 6 ) ) cot ^ ( 3 ) ( 2 x ) csc ^ ( 2 ) ( 2 x ) dx

4 / x = 9 / 5 - 7 x - 4 / 5 x

y = in ( x + 4 ) find the inverse

How long will it take for the concentration of A to decrease from 0 . 9 1 0 M to 0 . 5 5 5 for the reaction A Products? ( k = 0 . 1 5 3 M / s )

Use the given conditions to write an equation for the line in slope - intercept form. Slope = 4 , passing through ( 7 , 7 )

find the derivative of the function y = ( 5 + 2 e ^ ( 7 x ) ) ^ 1 / 2

The length of a rectangle is 3 yd more than twice the width x . The area is 3 2 4 yd ^ ( 2 ) . ( a ) Write an equation in terms of x that represents the given relationship.

Find dydx , where y is defined as a function of x implicitly by the equation below.x 2 x 2 = 2 y 2 2 yDo not include " dydx = " in your answer. Provide your answer below:

Pls Solve this problem and each part of it
Pls Solve this problem and each part of it

The function f is defined by f ( x ) = 2 x ^ 2 + 5 . Find f ( 5 x ) .

Multiply and simplify complet ( ( 2 x ^ ( 5 ) ) / ( 5 y ^ ( 4 ) ) ) ^ ( 5 ) * ( ( 5 ^ ( 4 ) y ^ ( 1 0 ) ) / ( 2 ^ ( 2 ) x ^ ( - 4 ) ) ) Enter your answers for the

h ( x ) = 2 x c s c ( x ) s e c ( x ) Which sequence of rules can be used in order to differentiate h in its current form? Choose 1 answer: Chain rule, then product rule Chain rule, then chain rule again Product rule, then chain rule Product rule, then product rule again
h ( x ) = 2 x c s c ( x ) s e c ( x ) Which

1 0 ( 3 8 ) The expression 1 2 + x + 4 represents the permeter of a trangle. simplify the expression.

4 . Piecewise linear system. As discussed in class, many systems are piecewise linear, meaning that they are linear only within certain range of operation. Consider the following differential equation: 2 2 + 1 7 + 5 0 = ( )

Algebra 1 Name q , Factor out GCF Day 2 Factor the common factor out of each expression. - 4 x - 4

Determine whether the integral is divergent or convergent. If it is convergent, evaluate it . If not, state your answer as "DNE". - 1 5 / ( 2 x - 3 ) ^ 2 dx

code class = "asciimath" > Use the product rule to simplify. ( - 7 x ^ ( 5 ) ) ( 7 x ^ ( 6 ) ) ( - 7 x ^ ( 5 ) ) ( 7 x ^ ( 6 ) ) = 3 . 9 ( Simplify the coefficient. Type using an exponent. )

evalute the integral using the formula 0 to b x ^ 3 dx = b ^ 4 / 4 0 to 2 ( 4 x ^ 3 - 9 x + 2 ) dx =

find lim x - - > negative infinity ( 3 t ^ 2 + t ) / ( t ^ 3 - 4 t + 1 )

Evaluate the limit , or type "DNE" if the limit Does Not Exist: lim ( x , y ) ( 5 , 5 ) x 2 - x y x 2 - y 2 =
Evaluate the limit , or type "DNE" if the limit

Identify the restricted values. ( z + 1 6 ) / ( z ^ ( 2 ) + 4 z - 1 2 ) If there is more than one restricted val

Given f ' ' ( x ) = 9 x + 5 and f ' ( - 1 ) = - 6 and f ( - 1 ) = 1 . Find f ' ( x ) = and find f ( 2 ) =
Given f ' ' ( x ) = 9 x + 5 and f ' ( - 1 ) = - 6

c ) By adding the first n terms in this sequence we get the series: 2 1 + ( 1 / 2 ) ( 1 / 4 ) + + 2 ^ ( 1 ) ( 1 ) What is the explicit formula for the sum of the series

integral xf ( x ) dx

Find the unit vector in the direction of v . v = - 6 . 5 i + 2 . 5 j u =
Find the unit vector in the direction of v . v =

y = 2 x 3 , y = 1 8 x 2 , 0 x 6 Sketch the region and find the area under the curves
y = 2 x 3 , y = 1 8 x 2 , 0 x 6 Sketch the region

Note: It is known that i = 1 n i = n ( n + 1 ) 2 . Let n 0 , 1 f ( x ) = x R n = i = 1 n i n = n ( n + 1 ) 2 n R n = i = 1 n i n * 1 n = n ( n + 1 ) 2 n 2 R n = i = 1 n i - 1 n * 1 n = ( n - 1 ) n 2 n 2
Note: It is known that i = 1 n i = n ( n + 1 ) 2

Write sum n = 4 to 7 ( 3 n - 2 ) in expanded form and also find its value

Evaluate f ( x - 2 ) when f ( x ) = 3 x 2 - x + 1 ( Be sure to simplify your answer )
Evaluate f ( x - 2 ) when f ( x ) = 3 x 2 - x + 1

[ - / 0 . 6 2 Points ] TAMUBUSCALC 1 1 . 1 . 0 1 2 . 0 6 Submissions Used Approximate the given limit numerically and verify your answer graphically. Round your answer to four decimal places if necessary. lim x 1 x 9 - 1 x 1 0 - 1
[ - / 0 . 6 2 Points ] TAMUBUSCALC 1 1 . 1 . 0 1

Figure 1 shows a variable length board whose width measures 1 cm . If you want said table moves and can traverse the path shown in figure 2 . Calculate the maximum value of the length x . You have to use derivatives and trigonometry.
Figure 1 shows a variable length board whose

find all points of discontinuity
find all points of discontinuity

( 4 points ) There is a line through the origin that divides the region bounded by the parabola y = 8 x - 7 x 2 and the x - axis into two regions with equal area. What is the slope of that line? Hint: Draw a picture, write the area between the parabola and the line in terms of the slope of the line, and solve for the slope.
( 4 points ) There is a line through the origin

Please help me solve 2 6 , 2 8 , 2 9 , 3 2 and 3 4 by sketching graphs. I will rate well
Please help me solve 2 6 , 2 8 , 2 9 , 3 2 and 3

Find an antiderivative for the following s e c 2 ( x ) t a n ( x ) d x l n ( s e c 2 ( x ) ) + C c s c ( x ) s e c ( x ) + C l n | t a n ( x ) | + C c s c ( x ) s e c ( x )
Find an antiderivative for the following s e c 2

Fina the postion and vellocity of an object moving along a st a ( T ) = 8 e - t , v ( 0 ) = - 8 , and s ( 0 ) = 1 0 v ( t ) = s ( t ) =
Fina the postion and vellocity of an object

Formula 1 point Find the general solution to the given differential equation: y ' ' + ( 2 7 ) y ' + ( 7 2 ) y = 0 with y ( 0 ) = 1 0 0 , and y ' ( 0 ) = 1 - 1 0 0 7 . For t 0 = 0 . 7 , find y ( t 0 ) . Include at least 3 decimal places in each step in your calculation. Use = 3 . 1 4 1 5 9 and e = 2 . 7 1 8 2 8 .
Formula 1 point Find the general solution to the

Instantaneous rate of change for function f ( x ) = x ^ 2 - x at x = 3

Given that f ( x ) = g ( x ) 2 + 1 , and g ( x ) is a linear function of form y = m x + b , the domain of f ( x ) is set of all x such that [ Select ] nge of f ( x ) is x is greater than or equal to zero g ( x ) is greater than or equal to zero x is greater than 1 g ( x ) is greater than zero
Given that f ( x ) = g ( x ) 2 + 1 , and g ( x )

integral e ^ x ^ 2 dx

find the region 2 x + y ^ 2 = 8 , x = y

Evaluate the integral. / 2 9 cos 2 ( ) d 0

rocket travels during the first four seconds. \ ( X \ ) units Then estimate using right endpoints. \ ( [ \ ) \ ( x \ ) units
rocket travels during the first four seconds. \ (

Integral of dt / ( e ^ t - e ^ - t ) ^ 2

En los siguientes ejercicios halle la masa y las coordenadas solicitadas del centro de masa del s lido de densidad dada acotado por las gr ficas de las ecuaciones. Determine ? b a r ( y ) para la regi n Q : 3 x 3 y 5 z = 1 5 , x = 0 , y = 0 , z = 0 , y densidad ( x , y , z ) = k y Determine ? b a r ( z ) , para la regi n Q : z = 4 - x , z = 0 , y
En los siguientes ejercicios halle la masa y las

Solve for j . - 3 = | j | - 6 Write your answers as integers or as proper or improper fractions in simplest form.

Let g ( x ) = { - 6 x 2 x i f x 5 a i f x = 5 3 x 7 i f x > 5 . a . Determine the value of a for which g is continuous from the left at 5 . b . Determine the value of a for which g is continuous from the right at 5 . c . Is there a value of a for which g is continuous at 5 ? a . The value of a for which g is continuous from the left at 5 is (
Let g ( x ) = { - 6 x 2 x i f x < 5 a i f x = 5 3

Suppose a 5 0 L tank initially contains 1 0 L of fresh water. At t = 0 , a brine solution containing 1 kg / L of salt is poured in at a rate 4 L / min , while the mixture leaves at 2 L . / min . At what time will the tank overflow?

what is derivative of f ( x ) = x 3 - 2 x 2 + 1 5 x + 7

Example 3 ( in space ) : Evaluate where C is the curve = 2 cos , = 2 sin , = , 0 2

Company X has been contracted to build five ships for a local freight company. It took 5 0 0 days to build the first ship. Estimate the total amount of time required to build the remaining four ships. Assume an 8 5 % learning curve.

A graphing calculator is recommended. If a ball is thrown into the air with an initial velocity of 5 2 ft / s , its height in feet after t seconds is given by y = 5 2 t 1 6 t 2 . ( a ) Find the average velocity of the ball ( in ft / s ) for the time interval beginning at t = 2 and lasting for each of the following. ( i ) 0 . 5 seconds ft / s ( ii

Solve fort using natural logarithms. 2 1 = 1 5 0 . 5 t Round your answer to three decimal places.

Find the inverse of the following function. f ( x ) = 5 x 2 + 6 x 0

Find the sum or difference of the polynomials. answer in descending order. 9 w ^ ( 2 ) - ( 4 ) / ( 7 ) ( 1 4 w ^ ( 2 ) - 2 8 w - 7 ) + 3 w

given the functionf ( x ) = 0 . 0 0 6 2 3 8 x ^ ( 2 ) - 2 . 0 8 5 4 7 2 x + 1 4 . 3 2 8 9 6 5 , state the coefficient of the linear ( x ) term rounded to two three decimal places

The y - value is fourfour lessless than four timesfour times the x - value.

If a number decreases from 2 , 5 0 0 to 7 5 0 , what is the rate of decrease?

Question content area top Part 1 Find a function Bold r left parenthesis t right parenthesisr ( t ) that describes the line passing through Upper P left parenthesis 4 comma 2 comma 5 right parenthesisP ( 4 , 2 , 5 ) and Upper Q left parenthesis 8 comma 3 comma 4 right parenthesisQ ( 8 , 3 , 4 ) .

a population of rabbits is growing. in 2 0 1 2 , there were 1 0 , 0 0 0 , 0 0 0 rabbits, and the population was increasing at a rate of 1 0 % per decade. what is the predicted rabbit population in 2 0 2 7 ? round to the nearest rabbit.

determine if y ( t ) = 5 t + t ^ 3 is a solution of the differential equation ty ' - y = t ^ 3 find y ' ( t )

A submarine's descent can be represented as y = - 2 4 0 x , where y is the elevation and x is the time in hours. How long will it take this submarine to make the descent?

valuate the following integral. 1 0 1 3 6 x 2 + 1 7 6 4 dx

Find the equation at the tangent line x = - 6 for f ( x ) = x 3 2 Write the equation in the format y = mx + b

MODELING REAL LIFE The volume ( in cubic feet ) of a rectangular birdcage can be modeled by V = 3 x ^ ( 3 ) - 1 1 x ^ ( 2 ) + 8 x , where x is the length ( in feet ) . Determine the values of x for which the model makes sense

Question Write the equation in standard form for a circle with center ( - 2 , 3 ) and tangent to the x - axis.

mass hanging from a spring is set in motion and its ensuing velocity is given by v ( t ) = 3 sin / 2 t for t 0 . Assume that the positive direction is upward and s ( 0 ) = 3 . ( a ) Determine the position function for t 0 .

Use the Read - Draw - Write process to solve each problem. A container has ( 9 ) / ( 1 0 ) liters of vinegar. ( 2 ) / ( 3 ) of the vinegar spills. How many liters of vinegar spill?

The volume V of a cone is given by V = 1 3 r 2 h , where h denotes the height of the cone and the radius of the circular base is r . The surface area A of a cone is given by A = B + C , where B = r 2 is the area of the circular base and C = r r 2 + h 2 2 is the area of the curved part of the surface. For a fixed value of the volume V , use a

Solve the given differential equation. All solutions should be found. d y d x = x 6 - 6 y x NOTE: Use c for the constant of integration. y =
Solve the given differential equation. All

Locate the relative extremum and point of inflection. Use a graphing utility to confirm your results. ( If an answer does not exist, enter y = 5 x 2 l n ( x 2 ) relative extremum , ( x , y ) = point of inflection , . ( x , y ) = Need Help?
Locate the relative extremum and point of

The total number of people, P , who have been infected with a contagious virus t weeks after the epidemic began is given by the following formula. P = 8 3 1 6 1 + 2 0 ( 0 . 5 ) t Complete parts a through d below. a . How many people originally had the virus? Originally people were infected.
The total number of people, P , who have been

Eliminate from the following system of equations: x = s i n y = t a n
Eliminate from the following system of equations:

3 . 1 0 Which solutions of the following equations will exhibit convergent behavior? Which are oscillatory? Assume zero initial conditions for y and its derivatives. ( a ) d 3 x d t 3 2 d 2 x d t 2 2 d x d t x = 3 ( b ) d 2 x d t 2 - x = 2 e t ( c ) d 3 x d t 3 x = s i n t ( d ) d 2 x d t 2 d x d t = 4 Note: All of the above differential equations
3 . 1 0 Which solutions of the following

3 4 7 . Determine the intersection points of elliptic cone x ^ 2 - y ^ 2 - z ^ 2

( 1 0 points ) Suppose the supply function for a certain item is given by S ( x ) = x 2 + 1 0 x , and the demand function is given by D ( x ) = 9 0 0 - 2 0 x - x 2 , determine the following: a ) Find the equilibrium point. 1 a ) b ) Find the consumer surplus at the equilibrium point. 1 b ) c ) Find the producer surplus at the equilibrium point. 1
( 1 0 points ) Suppose the supply function for a

Find the standard equation of the sphere that has the point ( - 4 , 6 1 , - 5 ) and ( - 2 , 6 , 0 ) as endpoints of a diameter. Center of the Sphere is If necessary, write your answer as a decimal. ) Radius of the Sphere is Equatian of the Sphere is
Find the standard equation of the sphere that has

Using the information on the slope of the lines tangent to the curve at points B and D , plot the slope of the total revenue curve on the graph below. ( As it turns out, it's a straight line, so the two points you plot will determine a line. ) Slope of TR I need help with the graph.
Using the information on the slope of the lines

Current Attempt in Progress A product costs $ 1 2 0 today. How much will the product cost in t days if the price is reduced by ( a ) $ 3 a day $ ( b ) 4 % a day $
Current Attempt in Progress A product costs $ 1 2

Half - life. Radium ( 2 2 4 / 8 8 ) Ra has a half - life of about 3 . 6 days. Given 1 gram, determine how much will still be present after 1 day to at least three decimal places?

Use properties of integrals and formulas to calculate the integral. ( Give your answer as a whole or exact number. ) 0 to 6 ( 1 0 t - 6 ) dt =

a 5 Ecologists predict the population of white - tailed deer in the state of Kentucky t years after 2 0 0 4 will be P ( t ) = 1 , 0 7 2 , 7 6 4 e 0 . 2 3 1 1 t 0 . 1 9 1 9 6 + e 0 . 2 3 1 1 t According to the ecologists' model, what is the long term population of white - tailed deer?
a 5 Ecologists predict the population of white -

Find the direction cosines and direction angles of the vector. ( Give the direction angles correct to the nearest tenth of a degree. ) 6 i - j - 3 k c o s ( ) = c o s ( ) = c o s ( ) = = = =
Find the direction cosines and direction angles

If m f ( x ) M for a x b , where m is the absolute minimum and M is the absolute maximum of f on the interval [ a , b ] , then \ int _ 0 ^ 4 ( 2 xe ^ { - x } dx )

Let y = tan ( 4 x + 5 ) . Find the differential dy when x = 2 and dx = 0 . 2 Find the differential dy when x = 2 and dx = 0 . 4

How many real solutions does the equation have? q ^ ( 2 ) = - 8 6

Use multiplying by 1 to find an expression equivalent to StartFraction 1 1 Over 1 8 EndFraction 1 1 1 8 with a denominator of 1 6 2 y 1 6 2 1 6 2 yy .

An equation of a line l and the coordinates of a point P are given. y = 2 x 3 ; ( 4 , 3 ) ( a ) Find an equation for the line that is parallel to l and passes through P .

Evaluate limx 5 ( 1 x + 5 + 1 1 ( x + 5 ) ( x 6 ) ) .

Attempt 1 : 1 0 attempts remainifig. Suppose w = x y y z , where x = e 2 t , y = 2 s i n ( t ) , and z = 2 c o s ( 3 t ) . Use the chain rule to find d w d t as a function of x , y , z , and t . Do not rewrite x , y , and z in terms of t , and do not rewrite e 2 t as x . d w d t = Note: Your answer should be an expression in x , y , z , and t ; e
Attempt 1 : 1 0 attempts remainifig. Suppose w =

Find the limit . limx 0 1 + x - 1 x Question 7 options: A ) 6 B ) 1 / 4 C ) 0 D ) - 2 E ) Does not exist. F ) 1 / 2

5 - f ( x ) = s i n x c o s x is given, find f ' ( 0 ) ( Hint: s i n 2 ( x ) + c o s 2 ( x ) = 1 ) 6 - Find the limit lim x 6 x 2 + 5 x - 1 2 x 2 + 5 7 - f ( x ) = 1 2 x 3 + 2 x 2 + 1 x 2 - 5 x + 4 is given, Find f ' ( x ) 8 - Find the limit of lim x 1 x - 1 x + 3 2 - 2 9 - If f ( x ) = ( x 2 + 3 x - 9 ) 1 5 , find f ' ( 2 ) 1 0 - If x 2 + 5 x - 1
5 - f ( x ) = s i n x c o s x is given, find f '

Suppose the position of a particle in motion at time t is given by the vector parametric equation vec ( r ) ( t ) = ( : 2 ( t - 2 ) 2 , 7 , 2 t 3 - 6 t 2 : ) . ( a ) Find the velocity of the particle at time t . vec ( v ) ( t ) = ( b ) Find the speed of the particle at time t . Speed = ( c ) Find the time ( s ) when the particle is stationary. If
Suppose the position of a particle in motion at

In a big city, 1 5 speed enforcement officers each write an average of $ 2 7 0 0 in ticket finest. Every day one extra officer is added to the patrol, and the average amount in finest written drops by $ 1 2 0 per officer. How fast is the total number of finest written changing on the second day ( Round to the nearest whole number . )

INTEGRAL of 1 / ( sqrt ( - x + 1 2 x - 3 2 )

h ( x ) = \ sqrt { 1 - x ^ 2 } sin ^ - 1 ( x ) h ' ( x ) =

Find dy / dx by implicit differentiation. x ^ 4 y ^ 8 y = x

Use Simpson's Rule with n = 4 and the given data to estimate 7 1 1 f ( x ) d x Enter an exact value or round your final answer to three decimal places. \ table [ [ x , 7 , 7 . 5 , 8 , 8 . 5 , 9 , 9 . 5 , 1 0 , 1 0 . 5 , 1 1 ] , [ f ( x ) , 1 . 7 , 1 . 4 , 1 . 8 , 4 . 5 , 3 . 9 , 3 . 6 , 3 . 8 , 7 . 7 , 4 ] ] 7 1 1 f ( x ) d x ~~ By: Dr . Roberto
Use Simpson's Rule with n = 4 and the given data

Solve lnx + ln ( x + 3 ) = 4 . Round your answer to the nearest hundredth. Check for extraneous solutions.

Evaluate the integral using integration by parts. 1 e 5 x 3 l n ( x ) d x 1 e 5 x 3 l n ( x ) d x = ( Type an exact answer. )
Evaluate the integral using integration by parts.

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