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mathematics
may 2018
28

Mathematics Questions and Answers May 28, 2018

Expert-verified solutions to help you succeed

Evaluate the integral. 0 6 s i n 3 6 x d x

Where does the line x = 2 5 t , y = 1 - 4 t intersect a . the x - axis b . the y - axis c . the curve y = 5 1 x 2 ?

Find the solution t o the initial value problem d d t y ( t ) - 9 t y ( t ) = 0 , y ( 0 ) = 6

Given that Alisa invests $ 2 2 0 0 into a savings account that has an annual interest rate of 3 . 7 5 % compounded continuously. What model represents the amount of money in the account after 8 years? = 2 2 0 0 ( 0 . 0 3 7 5 2 3 ) = 2 2 0 0 ( 0 . 0 3 7 5 8 ) = 2 2 0 0 ( 1 + 0 . 0 3 7 5 ) 8

lim h 0 ( h - 3 ) 2 - 9 h =

Evaluate the indefinite integral given below for x 8 3 . 2 x 9 x 2 - 6 4 2 d x Provide your answer below:

Attempt 2 : One or more answers is incorrect. You will be told if you get them all right. Vectors: Find the vector from the point A = ( - 2 , 3 , 5 ) to the point B = ( 3 , - 5 , - 5 ) . vec ( A B ) = l Equations of lines: Consider the vector equation of the line through the two points listed above. For each equation listed below, answer T if the

1 7 of 2 0 Evaluate the following integral. 0 8 s i n 4 x d x Use a power - reducing formula to write the integrand using lower powers. 0 8 s i n 4 x d x = 0 d x Evaluate the integral. 0 8 s i n 4 x d x = ( Type an exact answer, using as needed. )

Solve: 1 5 / ( 2 + 6 ) 3 / ( 2 ) = 2 / ( + 3 )

C for the arbitrary constant. Absorb into C a s much a s possible. x 7 * 5 x 8 d x =

Evaluate the limit , if it exists. ( If an answer does not exist, enter DNE. ) lim x 7 3 x 2 + 2 0 x 7 x 2 4 9

Evaluate the integral. 5 dt / 4 5 t 2

Use the point on the line and the slope of the line to find an additional point that the line passes through. ( There is more than one correct answer. ) Point: ( 4 , 4 ) Slope: m = 0

Find the slope given the points ( 6 , 4 ) and ( 6 , 5 ) . Enter DNE if the slope between the points is undefined.

9 . ) Find the first and second derivatives of the following functions: ( a ) D ( x ) = R T ( B x 3 x 2 C x ) ; R , T , B , C are constants ( b ) P ( x ) = R T ( 1 x + B x 3 + C x 5 ) ; R , T , B , C are constants. ( c ) F ( x ) = A + B x + C x 2 + D x 3 + E x 2 ; A , B , C , D , and E are constants. 1 0 ) What are the symbolic integrals of the

Calculate 0 ( c o s ( 3 ( t - 2 ) ) ( t 2 + 4 t + 4 ) ) ( 1 - t ) d t .

( 1 point ) Evaluate the definite integral 0 7 2 2 2 4 9 - x 2 2 d x

Aug 2 7 lim x 2 x 2 - 4 x - 2 Hide 1 Rep

The function f is differentiable. Given: h ( x ) = 3 [ f ( x ) ] 4 + 4 f ( 3 x ) find h ' ( x ) .

solve 1 ( x 2 - 1 ) d x

Question 4 Find t c o s ( t ) d t . t 2 2 s i n ( t ) C t c o s ( t ) - s i n ( t ) C t s i n ( t ) - c o s ( t ) C t c o s ( t ) s i n ( t ) C t s i n ( t ) c o s ( t ) C

1 7 - 2 0 Show that the equation represents a sphere, and find its center and radius. 3 x 2 + 3 y 2 + 3 z 2 = 1 0 + y + 1 2 z

Evaluate integral using integration b y parts. e - 6 s i n 1 8 d e - 6 s i n 1 8 d =

Use the properties of limits to help decide whether the limit exists. I lim x 8 x 6 x - 9 Select the correct choice below and, if necessary, fill in the answer A . lim x 8 x 6 x - 9 = 4 3 ( Simplify your answer. Type an integer or a fraction. ) B . The limit does not exist and is neither nor - .

n 2 . 3 Hommwork Past 1 4 3 Painse 0 of 1 Let y woreent the OT The liver equation that best modih the CPA a ( Serpeth roor ancert the nteges or decreasts tor any nambes in the equilion fillond to the reared handrath as medid )

If y = ( x 6 5 ) s i n ( 3 x ) , find d y d x .

find the exac value of sec ( sin ^ - 1 ( x / 5 ) )

Let R be the reglos bounded by y = x 2 and the lines y = 0 and x = 3 . ( a ) Use the disk / walber method to find the volume of the solid of revolution obtained by revolving R aboet the x axis. Express your asswer na a multiple of .

Help Determine which differential equation corresponds to each phase line. You should be able to state briefly how you know your choices are correct. d y d t = y 3 - 4 y d y d t = y ( y - 2 ) d y d t = 3 y - y 2 A B C D 4 . d y d t = y ( 2 - y ) 2 d y d t = 4 y - y 3 d y d t = y 2 - 3 y d y d t = 2 y - y 2 d y d t = y 2 | y - 2 |

Evaluate the integral. ( R e m e m b e r the constant o f integration. ) x 3 8 1 + x 2 2 d x Evaluate the integral. ( R e m e m b e r the constant o f integration. ) x 2 - 3 6 2 x 4 d x Evaluate the integral. 3 0 a d x ( a 2 + x 2 ) 3 2 , a > 0

Write the equation of the line described. through ( 3 , 1 ) and perpendicular to 5 x - 6 y = 4 ( explain the same )

For which value ( s ) of x is g ( x ) > 0 ? Write your answer using interval notation

Evaluate 0 4 * 1 - c o s x 2 2 d x .

Let lim x 2 f ( x ) = 6 4 . Use the limit rules to find the following limit . lim x 2 f ( x ) 2 lim x 2 f ( x ) 2 =

What can you say about the relation between the tangent to the circle and its radius? Justify your answer.

In the plane, the equation x = 2 defines a q , in space, x = 2 defines a q ,

Find the given limit . lim x - 2 ( - x 2 + 3 x - 9 ) lim x - 2 ( - x 2 + 3 x - 9 ) = , ( S i m p l i f y your answer. )

Find the distance from ( 1 , - 9 , 7 ) t o each o f the following. ( a ) the x y - plane ( b ) the y z - plane ( c ) the x z - plane ( d ) the x - axis ( e ) the y - axis ( f ) the z - axis

a . Choose the natural numbers from the given set. Select all that apply. A . 6 . b a r ( 6 ) B . C . - 6 5 8 D . 7 2 E . 6 F . - 1 2 q , H . - 3 7

2 Find the given limit . lim x 9 + x 2 - 8 1 2 Select the correct choice below and, if necessary, fill in the answer box to complete A . lim x 9 + x 2 - 8 1 2 = B . The limit does not exist and is not or - . an example Get more help

For vectors vec ( B ) = - vec ( i ) - vec ( 4 j ) and vec ( A ) = - vec ( 3 ) i - vec ( 2 j ) calculate ( a ) vec ( A ) + vec ( B ) and its magnitude and direction angle. vec ( A ) + vec ( B ) = - vec ( 4 i ) - vec ( 6 j ) ; Magnitude 7 . 2 1 and direction 2 3 6 degree vec ( A ) + vec ( B ) = - vec ( 4 i ) - vec ( j ) ; Magnitude 7 . 2 1 and

1 . 4 6 x 1 0 ^ 1 3 meters to tetrameter

Solve Differential Equation x d y d x - y = x , y ( 1 ) = 5

Determine the following indefinite integral. 2 x 8 d x 2 x 8 d x =

Oil is leaking from an oil tanker at the rate of 2 , 5 0 0 gallons per day. At this rate the radius of the circular slick of oil is increasing at a rate of 4 miles per day. a . Create a function, call it r ( t ) , that models the radius of the circular slick of oil at a time, t , days after the beginning of the leak. That is , find an expression

Evaluate the integral x 5 ( x 6 - 2 ) 2 3 d x , b y making the appropriate substitution: u = x 5 ( x 6 - 2 ) 2 3 d x =

Find the the general antiderivative F ( x ) f ( x ) = 4 x 5 c o s ( x 6 ) antiderivative F ( x ) =

SCalcET 9 DT . A . 0 0 6 b . Rationalize the numerator and simplify. 4 9 + h 7 h

Evaluate the indefinite integral given below for x 8 7 . 1 0 x 4 9 x 2 - 6 4 2 d x Provide your answer below:

Use the properters of lonits to help docibe whetver the linal exns. Fthe lind exash, find its walle. lim x - 1 x 2 - 1 x 1 Smplity the rabonal expression x 2 - 1 x 1 =

1 1 5 1 pts 2 2 0 0 Resources Solution Al Tutor Question 1 4 of 2 2 The population of Integraton ( in millions ) at time t ( in years ) is P ( t ) = 3 . 5 e 0 . 0 5 t , where t = 0 is the year 2 0 0 0 . What is the population at time t = 0 ? ( Use decimal notation. Round your answer to one decimal place, if necessary. ) P ( 0 ) When will the

openstax Calculus volume 2 book, section 2 . 1 question 2 1

Let y = f ( x ) = 4 x 2 - 6 . A . Find the value o f y when x i s zero. B . Find f ( 1 ) .

Question 2 Which of the following is equal to x 2 c o s ( 2 x 3 ) d x = 1 6 s i n ( 2 x 3 ) C s i n ( 1 2 x 4 ) C s i n ( 2 x 3 ) x 1 3 x 3 s i n ( 2 x 3 ) C 1 2 s i n ( 2 x 3 ) C

Find a + b , 9 a + 3 b , | a | , and | a - b | . ( S i m p l i f y your vectors completely. ) a = 7 i - 6 j + 3 k , b = 3 i - 9 k a + b = 9 a + 3 b = | a | = | a - b | =

x = - ( 8 ) - ( 8 ) 2 - 4 ( 1 ) ( - 1 2 ) 2 2 ( 1 )

The function f ( x ) = 2 x + 4 ^ x is 1 - 1 . Find f ^ - 1 ( 6 )

Give a geometric description of the set of points in space whose coordinates satisfy the given pairs of inequalities. a . zzless than or equals xxsquared 2 , yyless than or equals 0 b . xxless than or equals yysquared 2 , negative 3 less than or equals z less than or equals 0 3 z 0 Question content area bottom Part 1 a . Choose the correct

For what non - zero value of s , if any, is y = x 2 a solution to the differential equation y y ' ' - 1 2 ( y ) 2 on the interval ( 0 , ) ? Enter the woed none if there is no such value. s =

if c = 2 4 , what values of a and b complete Ax + by = 2 4

Evaluate the integral by interpreting it in terms of areas. - 5 7 ( 2 x - 1 ) d x

Find parametric equations of the line passing through the points ( 4 , 5 , 4 ) and ( 2 , 9 , 2 ) . Use t as a parametric variable.

Use integration by parts to evaluate the indefinite integral. ( If necessary, use C to represent a constant. ) $$ \ int x ^ 3 ln ( 4 x ) dx = $$

Find the derivative of the given function. y = c o s ( e - 2 0 2 )

For the straight line defleed by the points ( 4 , 5 5 ) and ( 6 , 8 9 , determine the slope ( A ) and y ratercept ( B ) . Do not roond the anawers. saci ) b

A plane has equation z = 5 x + 3 y + 4 . ( a ) By how much does z increase if x is increased by one? ( Give an exact answer. ) ( b ) By how much does z increase if y is increased by one? ( Give an exact answer. ) ( c ) By how much does z increase if x is increased by 5 and y is increased by 2 ? ( Give an exact answer. )

Find the vertex of the parabola y = - x 2 4 x 3 . ( 2 , 7 ) ( 4 , 3 ) ( - 2 , - 9 ) ( 2 , 1 5 )

code class = "asciimath" > Paul runs a small farm. After the last harvest, he weighed the amount of squash he collected. He had 4 2 . 2 total pounds of green and yellow squash. If yellow squash made up ( 1 ) / ( 5 ) of the harvest by weight, how many pounds of green squash did he have?

V ( t ) = 2 - 2 e - 2 t ( t s i n a l ) for t > 0 for t 0 , i ( t ) = 0 ! inV ( t ) = 0 for t > 0 , i ' ( t ) = e - 2 t

Why does u ^ 1 6 turn into u ^ 1 5 ?

Assume that f i s a one - t o - one function. ( a ) I f f ( 6 ) = 1 6 , find f - 1 ( 1 6 ) . ( b ) I f f - 1 ( 3 ) = 5 , find f ( 5 ) .

Perform the indicated operation. - 5 i ( 8 2 i )

com / Student / PlayerTest . aspx?testId = 2 7 4 9 1 6 4 5 2 all 2 0 2 5 ) If 7 - 5 x 2 g ( x ) 7 c o s x for all x , find lim x 0 g ( x ) .

Question 7 , 9 . 1 . 4 3 Points: 0 of 5 Given that lim x 3 f ( x ) = - 7 and lim x 3 g ( x ) = 4 , find the following limit . lim x 3 6 - f ( x ) x g ( x ) lim x 3 6 - f ( x ) x g ( x ) = ( Simplify your answer. )

write a model for the decay of a particular radioactive isotope

find the l i m i t . x - 9 x 5 - x x 4 + 7

Compute the slope of the line that passes through: ( 4 , - 3 ) and ( 2 , 9 ) .

differentiate the folowing function. y = 2 l n ( x 2 ) + 7 l n ( 3 )

se the properties of logarithms to write the expression as a sum, difference, or product of simpler logarithms. For example, log 2 ( 3 x ) = 1 2 log 2 3 + log 2 x . ln 3 7 2 3 In 3 7 2 3 = ( Use integers or fractions for any numbers in the equation. )

1 1 : 0 4 PM Wed Aug 2 7 Done myopenma Homework 3 . 1 Part 2 - Limits from DS and Algebra Score: 1 0 . 4 / 1 9 Answered: 5 / 7 Question 3 Score on last try: 1 of 3 pts . See Details for more. All submitted parts correct. Jump to last submitted part. Get a similar question You can retry this question below Evaluate the limit: lim h 0 ( 5 h ) 2 - 2

Find an equation, or a set of equations, to describe the set of points that are equidistant from the points P ( 5 , 0 , 0 ) and Q ( 3 , 0 , 0 ) . ( Enter your answers as a comma - separated list of equations. )

Find the Laplace transforms o f the following 1 . t + t 2 + t 3 2 . e - t c o s 2 t t 7 2 e 5 t 4 . s i n 3 2 t 5 . s i n t c o s t t 2 c o s a t

Exercise 3 . ( 1 . 3 , 1 . 4 ) Let i n b e the effective interest rate between time t = n - 1 and t = n . I f A ( 3 ) = 1 0 0 and i n = . 0 2 n , find A ( m ) for m 0 .

Given: f ( x ) = x - 4 x 9 , Find the domain of f ( x ) . Write your answer in interval notation. If necessary, you can we tro - ? copies of the lower case letter " o " ( oo ) for the symbol and an uppercase letter U for the symbol U . Domain = q ,

Consider the integral value G . G = 2 1 0 4 4 t 2 4 ( t 1 ) dt Find the numerical value of the integral. The numerical value of the integral is .

A geologist measures the height of a mountain. The height is 4 . 9 7 2 7 km . What is the height in meters? Write your answer as a decimal.

Define the points P ( - 9 , 1 ) and Q ( - 1 , 7 ) . Carry out the following calculation. Express vec ( P Q ) i n the form a i + b j . vec ( P Q ) = , | i + ( , ) j ( S i m p l i f y your answers. )

Let R be the triangular region bounded by the lines y = 5 5 1 , y = 2 6 - 2 x and y = 2 . ( c ) Use the washer method to set up an integral ( or a sum of integrals ) that comprites the wolume of the solid chalsed loy revolving R shout the x axis. Do not evaluate the integral ( s ) . ( b ) Use the washer method to set up an integral ( or a sum of

code class = "asciimath" > ( 0 , 5 ) Sobre o baricentro, julgue as afirmativas a seguir: 1 - - O baricentro sempre um ponto interno do triangulo. | | - > O baricantro o ponto de encontro das mediatrizes. iit - > O baricentro equidistante dos v rtices do tri ngulo . Marque a afternativa correta. A , , B ( 5 , 6 ) e C ( 0 , 1 ) . Durante os testes,
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