Use the definition of the integral (the long way) to evaluate the integral

Use The Definition Of The Integral (the Long Way) To Evaluate The Integral

Answers

Answer 1

The answer is 10.67. It can be calculated by integrating and then applying the limits.

What is the integration of [tex]x^n[/tex]?

The integration of power of a variable is given by the following formula:

[tex]\int x^ndx=\frac{x^{n+1}}{n+1}[/tex]

If limits are there then limits can be applied after integration.

Consider the given function.

[tex]\int^3_1(x^2-4x+9)dx[/tex]

Now, apply integration on each term as follows:

[tex]\int^3_1x^2dx-4\int^3_1xdx+9\int^3_1dx[/tex]

Now, use the following formula to integrate:

[tex]\int x^ndx=\frac{x^{n+1}}{n+1}[/tex]

Now, the integration will look like as follows:

[tex][x^3/3]^3_1-4[x^2/2]^3_1+9[x/1]^3_1[/tex]

Now, apply limits to find the answer as follows:

[tex][3^3/3-1^3/3]-4[3^2/2-1^2/2]+9[3-1]\\[/tex]

[tex][9-\frac{1}{3}]-4[9/2-1/2]+18\\10.67[/tex]

Hence, the answer is 10.67. It can be calculated by integrating and then applying the limits.

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Related Questions

Write an equation of the line that passes through the pair of points. (5/12, −1), (−3/4, 1/6)

Answers

Answer:

[tex]y=-x-\frac{7}{12}[/tex]

Hope this helps!

Simplify quantity x squared plus 5 x plus 4 end quantity over quantity x plus 4 (5 points) x − 1 x + 1 x2 + 1 x2 − 1

Answers

Answer:

Step-by-step explanation:

there is no  oblique asymptote

en una expresion algebraica la reduccion de terminos semejantes se da entre los terminos de igual

Answers

Answer:990

990

990

990

990

990

Step-by-step explanation:

Answer:

Variable y exponente.

Step-by-step explanation:

En una expresión algebraica la reducción de términos semejantes se da entre los términos de igual variable o incógnita y exponente.

Por ejemplo:

3x² + 5x²

se pueden reducir pues tienen la misma variable x y el mismo exponente 2, su resultado se genera solo sumando, restando, los coeficientes, en este caso 3 y 5

3x² + 5x² = 8x²

En el caso:

3y² + 5x²

No se puede reducir pues la variable o incógnita no son iguales:

x≠y

En el caso:

3x² + 5x³

No se pueden reducir pues su exponente no es igual.

Im stuck on this ones i dont know how to get the answers

Answers

The measurements of [x] and [y] are 37 and 61 respectively.

What is Parallelogram? What is triangle?

In Euclidean geometry, a parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure. A triangle is a polygon with three edges and three vertices. The sum of all the angles of a triangle is 180 degrees. Mathematically -

∠x + ∠y + ∠z = 180°

There are different types of triangles such as -

equilateral triangle , scalene triangle , isosceles triangle etc.

Given are two triangles as shown in the figure.

Triangles ΔMPN and ΔSTU are congruent. We can write -

2x - y = 13

2x - 50 = 24

Now -

2x - 50 = 24

2x = 74

x = 37

then -

2 x 37 - y = 13

74 - 13 = y

y = 61

Therefore, the measurements of [x] and [y] are 37 and 61 respectively.

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How do I write a two-column proof for this problem?


Given: Isosceles △ABC with legs AB and AC, BD ⊥DC and CE⊥BE

Prove: BD ≅ CE

Answers

BD ≅ CE is proved and is shown below.

What is Parallelogram? What is triangle?

In Euclidean geometry, a parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure. A triangle is a polygon with three edges and three vertices. The sum of all the angles of a triangle is 180 degrees. Mathematically -

∠x + ∠y + ∠z = 180°

There are different types of triangles such as -

equilateral triangle , scalene triangle , isosceles triangle etc.

Given are two triangles as shown in the figure.

Triangles ΔMPN and ΔSTU are congruent. We can write -

2x - y = 13

2x - 50 = 24

Now -

2x - 50 = 24

2x = 74

x = 3The measurements of [x] and [y] are 37 and 61 respectively.

What is Parallelogram? What is triangle?

In Euclidean geometry, a parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure. A triangle is a polygon with three edges and three vertices. The sum of all the angles of a triangle is 180 degrees. Mathematically -

∠x + ∠y + ∠z = 180°

There are different types of triangles such as -

equilateral triangle , scalene triangle , isosceles triangle etc.

Given is isosceles △ABC with legs AB and AC, BD ⊥DC and CE ⊥ BE.

In △BDC and △CEB, we can write -

∠D = ∠E = 90°

BC = BC {Common}

∠B = ∠C  {Angles opposite to equal sides are equal}

By SAS criteria △BDC △CEB.

So, we can write -

BD ≅ CE

Therefore, BD ≅ CE is proved and is shown above.

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You are planning a picnic for Memorial Day. You need to buy enough hot dogs and hamburgers so that each of your 10 guests can have two servings. You determined that hot dogs cost $0.40 each and hamburgers cost $0.80 each. You have $12 to spend on the hamburgers and hot dogs. How many hot dogs and how many hamburgers should you buy?

Answers

Answer:

hamburgers cost $0.80 each

Step-by-step explanation:

in the figure pictured below DF=3 BF =14 GF =8 find the lengths of:

A. cf
B. ef
C. ag

Answers

The lengths of CF, EF and A.F are 6 units, 28 units and 16 units, respectively

How to determine the lengths of these sides?

From the question, the given parameters to solve the question are represented as

DF = 3

BF = 14

GF = 8

The point F in the triangle is the centroid of the triangle

This means that the point F divides the lines that passes through it in the ratio 1 : 2 or 2 : 1 (as the case may be)

The claim above also  means that

CF = 2 * DF

EF = 2 * BF

A.F = 2 * GF

Substitute the known values in the above equation, so, we have the following representation

CF = 2 * 3 = 6

EF = 2 * 14 = 28

A.F = 2 * 8 = 16

Hence, the lengths are 6 units, 28 units and 16 units

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(9√-81)(-10√64) is the answer -6480i? im confused

Answers

Imaginary Numbers

[tex]i=\sqrt{-1}[/tex]

Solving the Question

[tex](9\sqrt{-81})(-10\sqrt{64})[/tex]

⇒ Take out i from the first square root:

[tex]= (9i\sqrt{81})(-10\sqrt{64})[/tex]

⇒ Evaluate the square roots:

[tex]= (9i\times9)(-10\sqrt{64})\\= (9i\times9)(-10\times 8)[/tex]

⇒ Multiply:

[tex]= (81i)(-10\times 8)\\= (81i)(-80)\\= -6480i[/tex]

Answer

-6480i

100 POINTS AND BRAINLIEST

For what values of c does the quadratic equation -x^2+4x+c=0


1. Have no real roots?

2. Have two roots with the same sign?

3. Have one negative root and one root equal to 0?

4. Have two roots with opposite sides?

Answers

Answer:its c

Step-by-step explanation:

Answer:

1.  c < -4

2.  -4 < c < 0

3.  c = 0

4.  c > 0

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{6.8 cm}\underline{Discriminant}\\\\$b^2-4ac$ \quad when $ax^2+bx+c=0$\\\\when $b^2-4ac > 0 \implies$ two real roots.\\when $b^2-4ac=0 \implies$ one real root.\\when $b^2-4ac < 0 \implies$ no real roots.\\\end{minipage}}[/tex]

Given quadratic equation:

[tex]-x^2+4x+c=0[/tex]

Question 1

If the quadratic equation has no real roots, then the discriminant is less than zero:

[tex]\implies b^2-4ac < 0[/tex]

[tex]\implies (4)^2-4(-1)(c) < 0[/tex]

[tex]\implies 16+4c < 0[/tex]

[tex]\implies 4c < -16[/tex]

[tex]\implies c < -4[/tex]

Question 2

If the quadratic equation has two real roots, then the discriminant is greater than zero:

[tex]\implies b^2-4ac > 0[/tex]

[tex]\implies (4)^2-4(-1)(c) > 0[/tex]

[tex]\implies 16+4c > 0[/tex]

[tex]\implies 4c > -16[/tex]

[tex]\implies c > -4[/tex]

Using Descartes' Rule of Signs, if c > 0 there would be one sign change and so a maximum of one positive root.  If c < 0 there would be 2 sign changes and therefore a maximum of 2 negative roots.

Therefore, for the two roots to have the same sign, -4 < c < 0.

Question 3

If c = 0 then:

[tex]\implies -x^2+4x=0[/tex]

[tex]\implies -x(x+4)=0[/tex]

[tex]\implies x(x+4)=0[/tex]

Therefore, the roots would be 0 and -4 so there would be one negative root and one root equal to zero.

Question 4

Using Descartes' Rule of Signs, if c > 0 there would be one sign change and so a maximum of one positive root.

Therefore, for the equation to have two roots with opposite signs, c > 0.

Need help asap! thanks

Answers

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

The value of the given expression is  1479.40

What is an expression?

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Sum of [tex]2(\frac{4}{3})^n[/tex] from n = 0 to n = 6.

This can be written as,

= [tex]2(4/3)^0 + 2(4/3)^1 + 2(4/3)^2 + 2(4/3)^3 + 2(4/3)^4 + 2(4/3)^5 + 2(4/3)^6[/tex]

= 2 x 1 + 8/3 + 2 x 16/9 + 2 x 64/27 + 2 x 256/81 + 2 x 1024/243 +

2 x 4096/729  

= 2 + 2.67 + 3.56 + 4.74 + 6.32 + 8.43 + 1458

= 1479.40

Thus,

The value of the given expression is  1479.40

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Reagan is running toward school twice as fast as her brother. If her brother is running at 2meterspersecond, how much time will it take Reagan to run 28meters?
Write your answer as a whole number.

Answers

The time taken by the Reagan to cover the distance of 28 meters will be 7 seconds.

What is speed?

Speed is defined as the ratio of the time distance travelled by the body to the time taken by the body to cover the distance. Speed is the ratio of the distance travelled by time. The unit of speed in miles per hour.

Given that Reagan is running toward school twice as fast as her brother. If her brother is running at 2 meters per second.

The time taken to cover the distance of 28 meters will be calculated as,

R = 2B

Brother's speed = 2 m / s

Reagan's speed = 2 x 2 = 4 m/s

The time will be,

T = Distance / Speed

T = 28 / 4

T = 7 seconds

Therefore, the time taken by Reagan to cover the distance of 28 meters will be 7 seconds.

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NEED HELP ASAP!!!

I am 20 years older than twice my daughter's age. How old is my daughter? ( 1. 17 years ago, I was half the age I am now. How old am I? - Part of 2.)

Answers

The daughter's age is 7 years old.

What is the equation?

An equation is a mathematical statement that shows that two mathematical expressions are equal.

Given that, a parent is 20 years older than twice his daughter's age, and he was half of his present age 17 years back.

Let the age of the parent be x,

He/she was half of the age 17 years back, then,

x/2 = x-17

x = 34

Therefore, parent's present age is 34 years.

He is  20 years older than twice his daughter's age,

Let his daughter's age be y,

2y+20 = 34

2y = 14

y = 7

Hence, his daughter's age is 7 years old.

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I need help on my homework ASAP!! PLEASE HURRY I HAVE 20 MINUTES

Answers

Answer: 10) 18x+21     11) 20 + 30a     12)  8x + 10y

Step-by-step explanation:

Distributive property means to multiply each number within the parenthesis by the number outside of the parenthesis.

10) 3(6x + 7)

     3*6x + 3*7

     18x + 21.

With that, you should be able to see how the other questions were answered.

A movie theater sells popcorn in a reusable bucket for $3.50. They offer refills for $2.50 each.
Write an equation in slope-intercept form to model the cost in dollars, y, for x refills.

Answers

The linear function that models the problem of movie theater sells popcorn is

y = 2.50x + 3.50

How to model the required equation

A linear function consists of functions where the variables has exponents of 1.

The graph of linear functions is a straight line graph and the relationship is expressed in the form.

y = mx + c

definition of variable to suit the problem

y = output variable

m = slope

x = input variable

c = y intercept

The equation as described in the problem is represented using linear function as as follows

c = cost of the bucket = $3.50

m = cost of refills = $2.50

y = 2.50x + 3.50

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Find the x-intercept of the line 14x–11y= – 1.

Answers

Answer:

x- intercept = - [tex]\frac{1}{14}[/tex]

Step-by-step explanation:

to find the x- intercept, that is where the line crosses the x- axis, let y = 0 in the equation and solve for x

14x - 11(0) = - 1

14x = - 1 ( divide both sides by 14 )

x = - [tex]\frac{1}{14}[/tex] is the x- intercept

4. Solve the quadratic equation 4x² + 7 = 25.

Answers

4x²+7= 254x²+7-25=04x²-18=0

use the formula 「x= [-b±✓(b²-4ac)]/2a」

a= 4, b= 0, c= -18

x= [-0±✓(0²-4(4)(-18))]/2(4)x= 2.1213... , x= -2.1213...
Hope this helps you

Your friend bought a new pair of shoes. He said the regular price was $75 but he got a 40% discount from the sales clerk. What is the sale price of the shoes

Answers

Answer:

40% off of 75 is 45$

Step-by-step explanation:

Divide the number by 100 (move the decimal place two places to the left).Multiply this new number by the percentage you want to take off.Subtract the number from step 2 from the original number. This is your percent off number.

Explain how to find the distance between 1 and -3 on a number line.

Answers

Answer:

count backwards

Step-by-step explanation:

1, 0, -1, -2, -3

Answer:two ways

Step-by-step explanation: you can either count the spaces or you could just add until you get one of the answers -3 +4 =1 1- 4=-3

Solve the radical equation. Please explain each step in detail.

Answers

Answer:

[tex]x=\frac{1}{2}[/tex]

Step-by-step explanation:

Even roots can NEVER have a negative result, therefore the value of x can ONLY be positive values.

how much would it cost to replace all the windows on all the building in the united states?

Answers

The cost to replace all the windows on all the building in the United States is $7,200,000.

What is the expression to find the total cost?

Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both.

Given that the cost to replace a window is $3 per window. IT should be noted that when there are 2,400,000 windows, the cost to replace all the windows on all the building in the United States will be:

= Cost of replacement × Total window

= $3 × 2,400,000

= $7,200,000

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The cost to replace a window is $3 per window. If there are 2,400,000 windows, how much would it cost to replace all the windows on all the building in the United States?

. Lin's family has completed 60% of a trip. They have traveled 30 miles
How many miles is the trip?
A 50 miles
B. 48 miles
C. 30 miles
D. 18 miles

Answers

Answer: A 50 miles

Step-by-step explanation:

Its A becuase 60%=0.6 and 0.6 times 50 is 30 which means 60 percent of 50 is 30.

The answer is 50. 30 is 60% of 50

Kinda urgent
Will mark brainliest
:)

Answers

The function rule for the transformation of the graph f(x) = 2x

reflection over the x - axis (x, y) → (x, -y)

f(x) = -2x

vertical compression of a factor of 1/4

g(x) = -x/2

How to find the required transformation

Considering the given function  f(x) = 2x that requires reflection and vertical compression

The transformation rule for reflection over the x - axis

(x, y) → (x, -y)

comparing to the equation y = f(x) = 2x

-y = -2x

hence f(x) = -2x

vertical compression involves multiplying by 1/4

= 1/4 * f(x)

= 1/4 - 2x

= -x/2

Hence g(x) = -x/2

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Please help this is URGENT

Answers

TQ/VQ=TV/VR is true for the given triangle. Option B is correct

What is Triangle?

A triangle is a three-sided polygon that consists of three edges and three vertices.

Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion .

Two pairs of corresponding angles are equal

Three pairs of corresponding sides are proportional

Two pairs of corresponding sides are proportional and the corresponding angles between them are equal.

From these we can say that the sides TV is proportional to Rs and TQ is proportional to VQ

Hence, TQ/VQ=TV/VR is true for the given triangle. Option B is correct

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NEED AN ANSWER PLEASE HELP!!

Answers

Answer:

5.12

Step-by-step explanation:

If u times 1.6 and 3.2 you get 5.12 also i got it correct on my test

Write the expression as a single logarithm.
7log6z - 1/2log6x +3log6y

Answers

The value of the logarithm in one logarithm will be [tex]log_{6} z^7x^\frac{1}{2} y^3[/tex].

What is a logarithm?

The exponent indicates the power to which a base number is raised to produce a given number called a logarithm.

In another word, a logarithm is a different way to denote any number.

As per the given logarithm,

7[tex]log_{6} z[/tex] + (1/2)[tex]log_{6} x[/tex] + 3[tex]log_{6}y[/tex]

Since,[tex]alog_{b}c = log_{b}c^\frac{1}{a}[/tex]

Thus,

7[tex]log_{6} z[/tex] + (1/2)[tex]log_{6} x[/tex] + 3[tex]log_{6}y[/tex] =d [tex]log_{6}z^7 +log_{6}x^\frac{1}{2}+log_{6}y^3[/tex]dddd

Since,[tex]log_{a}b+log_{a}c=log_{a}bc[/tex]

Therefore,

[tex]log_{6}z^7 +log_{6}x^\frac{1}{2}+log_{6}y^3[/tex]= [tex]log_{6} z^7x^\frac{1}{2} y^3[/tex].

Hence "The value of the given logarithm in one logarithm will be [tex]log_{6} z^7x^\frac{1}{2} y^3[/tex]".

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Multiply. 2u*3u^2 please help me

Answers

Answer: 6u^3

Step-by-step explanation:

You have to add the exponents when you multiply them.

But before that, you can multiply the coefficients of 2 and 3 so you get 6.

Now you have u and u^2 left.

u = u^1

u^2 = u^2

1+2 =3

Andrew decided so joys a tenner clench. Below is a chart that displays how many games of lenis he has played and the meatal cost of playing those panes. In this scenario, C ( y ) represents the total cost for playing games.

Answers

The linear function that represents the situation is of:

C(y) = 13y + 145.

The intercept is of:

C(0) = 145, meaning that the flat fee to pay the game is of $145.

What is the linear function?

The slope-intercept representation of a linear function is given by the rule presented as follows:

y = mx + b

The coefficients of the function and their meaning are listed as follows:

m is the slope of the function, representing the rate of change of the function.b is the y-intercept of the function, representing the initial value of the function.

Two points of the function, from the table, are given as follows:

(8, 249) and (13,314).

The slope is given by the change in y of the two points divided by the change in x, hence:

m = (314 - 249)/(13 - 8) = 13.

Hence:

C(y) = 13y + b

When y = 8, C(y) = 249, hence the intercept b of the function is obtained as follows:

249 = 13(8) + b

b = 249 - 13 x 8

b = 145.

Meaning that the flat fee to pay the game is of $145.

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30 POINTS!!!!!! HELP ASAP! At cruising speed a car burns fuel at a rate of 2.5 kilograms per hour the mass of the car including the fuel when it reaches cruising speed is 1,550 kg and the mass of the car when the fuel tank is empty is 1,520 kg. the domain of the function f(t) is best described as

Answers

The domain of the function f(t) is best described as 608 ≤ t ≤ 620

How to determine the domain of the function?

From the question, we have the following parameters that can be used in our computation:

Rate = 2.5 kilograms per hour

Mass of the car (including the fuel) = 1550 kg

Mass of the car (not including the fuel) = 1520 kg

Calculate the times using the rate and the masses above

So, we have the following representations

Time 1 = 1550/2.5

Time 1 = 620

Time 2 = 1520/2.5

Time 2 = 608

Express as an interval

608 ≤ t ≤ 620

Hence, the domain is 608 ≤ t ≤ 620

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help meeeeeeeeeeeeeeee pleaseeeeeeehelp meeeeeeeeeeeeeeee pleaseeeeeeehelp meeeeeeeeeeeeeeee pleaseeeeeeehelp meeeeeeeeeeeeeeee pleaseeeeeeehelp meeeeeeeeeeeeeeee pleaseeeeeeehelp meeeeeeeeeeeeeeee pleaseeeeeee

Answers

Answer:

500 rounded to the nearest tenth equal 500

Write an expression to represent: 4 less than the quotient of x and 5.

Answers

x/5 - 4 represents 4 less than the quotient of x and 5.

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Solve for bbb.-11b+7 = 4011b+7=40minus, 11, b, plus, 7, equals, 40b =b=b, equals MAKING AN ARGUMENT Your friend claims that given f(0) and any other value of a linear function f, you can write anequation in slope-intercept form that represents the function. Your cousin disagrees, claiming that the two points could lie on avertical line. Who is correct? Explain.O Your friend. You can write an equation in slope-intercept form even if the two points are on a vertical line.O Your cousin. You may need more than two points to write an equation in slope-intercept form.O Your friend. If f is a function, then the line is not vertical.O Your cousin. If the line is vertical, it will not have a slope. which type of conflict relates to how the work gets done? group of answer choices task process communication relationship job Suppose you go to work for a company that pays one penny on the first day, 2 cents on the second day, 4 cents on the third day and so on.Hint: use an= a1 (r)^n-1 and Sn= a1 (1-r^n) / 1 - rA. If the daily wage keeps doubling, what would your income be on day 31? Give your answer in dollars NOT pennies.Income on day 31 = $ __________B. If the daily wage keeps doubling, what will your total income be for working 31 days? Give your answer in dollars NOT pennies.Total Income for working 31 days = $ _________ Is playing board games are a waste of time?(its just for a debate) help A ball is thrown from a height of 3 meters with an initial downward velocity of 5 m/s The ball's height h (in meters) after t seconds is given by the following. how long after the ball is thrown does it hit the ground after allison had been a manager for a few years, she realized that her employees liked to feel as though their ideas were valued. after she made a decision, she would hold a meeting in which she would let her staff make decisions about some of the details of implementation. which perspective on motivation is closest to allisons thinking at this point in her career? a cylindrical specimen of cold-worked copper has a ductility (%el) of 25%. if its cold-worked radius is 10 mm (0.40 in.), what was its radius before deformation? What parts of the brain ultimately plan and coordinate complex motor activities?. what amount of cash would result at the end of one year, if $21,000 is invested today and the rate of return is 10%? (pv of $1 and pva of $1) which nursing interventions would best address mr. davis's safety issues if his ciwa-ar score were to rise to 8 or above? (select all that apply.) dr. knight, who teaches psychology at a local community college, has been asked by the institution to provide expertise in an area that she lacks proper training. what should dr. knight do in this situation? An ice hockey player begins at one goal and skates forward at constant speed to the other goal, 54 meters away, in a time of 9seconds. He then instantly reverses direction and and skates 27 m backwards, in an additional 6 seconds.Considering "forwards" to be the positive direction, what is the player's total displacement and average velocity over the whole 15seconds? a client is diagnosed with rheumatoid arthritis. when teaching the client and family about rheumatoid arthritis, the nurse should provide which information? after the 2004 election, president geroge w. bush announced that would be the center piece of his domesic policy you have 2,000 feet of fencing to enclose a rectangular pasture. one side of the pasture is up against a river. what is the maximum area you could enclose? one great value of the pentavalent vaccine is that it: a. reduces the number of contacts needed to fully immunize a child b. is noninvasive c. costs less than the older generation of vaccines d. none of these are correct 1. Solve for the missing angle measures.1)a = 75dbC2)abd = 104 One day in February, the temperature at 9 A.M. is -6.8F. At 3 P.M. on the same day, The temperature is 1.72F. a) Find the change in temperature. b) Find the average hourly rate of change in temperature a 40-year-old client tells the nurse that a parent died of gastric cancer and that the client wants to do everything one can do to avoid the disease. which recommendation should the nurse provide?