Find the area between f(x) = 3x and f(x) = x2 on the interval (0,3]

Answers

Answer 1

Answer:

[tex]A=4.5[/tex]

Step-by-step explanation:

The area between two curves over the interval [tex][a,b][/tex] is [tex]A=\int\limits^b_a {f(x)-g(x)} \, dx[/tex] where [tex]f(x)[/tex] is the upper function and [tex]g(x)[/tex] is the lower function.

Therefore:

[tex]A=\int\limits^3_0 {3x-x^2} \, dx[/tex]

[tex]A=\frac{3}{2}x^2-\frac{x^3}{3}\Big|_0^3[/tex]

[tex]A=[\frac{3}{2}(3)^2-\frac{(3)^3}{3}]-[\frac{3}{2}(0)^2-\frac{(0)^3}{3}][/tex]

[tex]A=\frac{3}{2}(9)-\frac{27}{3}[/tex]

[tex]A=\frac{27}{2}-\frac{27}{3}[/tex]

[tex]A=\frac{9}{2}[/tex]

[tex]A=4.5[/tex]

So, the area between [tex]f(x)=3x[/tex] and [tex]g(x)=x^2[/tex] on the interval [tex](0,3][/tex] is [tex]4.5[/tex] square units.

Find The Area Between F(x) = 3x And F(x) = X2 On The Interval (0,3]

Related Questions

explain or show that the point (5,-4) is a solution to this system of equations

Answers

Answer:

You could substitute the point (5,-4) into each equation

Step-by-step explanation:

x=5    y=-4

3x-2y=23

3(5)-2(-4)=23

15+8=23

23=23

2x+y=6

2(5)+(-4)=6

10-4=6

6=6

The points go into each equation which proves that the point (5,-4) is the solution.

(i don't know if I did this right, I apologize if I didn't

estimate quotients using compatible numbers lesson 4.5 answer key

Answers

4 its the correct answer do it

Step-by-step explanation:

its correct

SOMEONE HELP ME WITH THIS ASAP FOR BRAINLIEST THANK YOU!

Answers

Answer:1. (1,2)    2.(-1,0)

Step-by-step explanation:

1.  5x-4(-3x+5)=3  x=1             2. 3(2y-1)-2y=-3    y=0                                                  

y=-3x1+5    y=2 Plug them in                       X=2x0-1            x=-1       plug them in                

Evaluate the following expression 6⋅2+6^4 khan academy

Answers

Answer:

6.2+6^4

6.2+1.296

7.496

Suppose x=7 is a solution to the equation 4x-2(x+a)=8 how can you find the value of a that make the equation true

Answers

Answer:

a = 3

Step-by-step explanation:

Since x = 7 is a solution, substitute x = 7 into the equation and solve for a

4(7) - 2(7 + a) = 8 , that is

28 - 2(7 + a) = 8 ( subtract 28 from both sides )

- 2(7 + a) = - 20 ( divide both sides by - 2 )

7 + a = 10 ( subtract 7 from both sides )

a = 3

Can someone please help me!!?

Answers

Answer:

Step-by-step explanation:

Domain is all the x's on the graph. The graph does go from -3 to 4 (not including the -3 but including the 4). Pay attention to the use of () as well as [] on the answers. Those answers are not weird coordinates, they are intervals where the first number is the starting place and the second number is the end. Also on the graph one end point is an open circle which means it's not included on the graph and the other endpoint is a darkened circle which means it is included. The range is all the y's. It does go from -3 to 3. Increasing means the graph is going up from left to right and decreasing means the graph is going down left to right. The graph is positive when it is above the x-axis and negative when its below the x-axis. It seems like ALL of the statements about the graph are true.

I'll mark you brainlest if you answer this correctly please help

Answers

Answer:

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

Solve: 2sec(x) 5 = 9 Which equation is equivalent to the given equation?.

Answers

Answer

9=5 equivalent

Step-by-step explanation:

Answer:

A. cos(x) = 1/2

Step-by-step explanation:

2sec(x) = 9-5 = 4

sec(x) = 4/2 = 2

1/cos(x) = 2

cos(x) = 1/2

Simplify.
(2⁴)³

its telling me to write at least 20 characters so uhm-- ignore the rest of this weeeeeeeeeeeeeeeeee

Answers

Answer:

4096

Step-by-step explanation:

Answer:  2^12

Explanation:

The rule we use is (a^b)^c = a^(b*c). It says to multiply the exponents when we raise one exponential expression to another exponent. The base stays the same.

So, (2^4)^3 = 2^(4*3) = 2^12

You could take the slightly longer path to say the following

(2^4)^3 = (2^4)*(2^4)*(2^4) = 2^(4+4+4) = 2^12

help wanted will mark brainiest

Answers

Answer:

For question a the answer is option  b at 50$

For question b the answer is 50 miles and option a is less

Step-by-step explanation:

What is the slope of the line

Answers

The answer is 4/6 .

a farm is sold for $457000, which gives a profit of 19%. Find the profit
The answer sheet says it is $73,000

Answers

Answer: its 73,000

Step-by-step explanation: the answer sheet has the answers...

i have a very hard question,

what is 1+2

please help asap

Answers

Answer:

The answer is 3.

Step-by-step explanation:

3y=6
Find the slope of the line described by each equation

Answers

Not sure of this answer
But I think the slope is 0
Please correct me if I’m wrong.

Help I’ll give brainliest

Answers

Answer:

Is it 95 If it is give me brainliess

Step-by-step explanation:

The answer is 95 I want it

Braden bought a piece of commercial real estate for $101,234. The value of the real estate appreciated at a constant rate per year. The table shows the value of the real estate after the first and second years: Year 1 2 Value (in dollars) $104,271. 02 $107,399. 15 Which function best represents the value of the real estate after t years? f(t) = 101,234(1. 03)t f(t) = 101,234(0. 03)t f(t) = 104,271. 02(1. 03)t f(t) = 104,271. 02(0. 03)t.

Answers

The function that best represents the value of the real estate after t years is: [tex]f(t) = 101234(1.03)^t[/tex]

The table is represented as:

Years  - Values

1          -  $104,271. 02

2         -  $107,399. 15

Appreciation and depreciation are often represented using exponential function as follows:

[tex]f(x) = ab^x[/tex]

At year 1, we have:

[tex]104271. 02 = ab^1[/tex]

[tex]104271. 02 = ab[/tex]

At year 2, we have:

[tex]107399. 15 = ab^2[/tex]

Divide both equations

[tex]\frac{107399.15}{104271.02} = \frac{ab^2}{ab}[/tex]

[tex]1.03 = b[/tex]

Rewrite as:

[tex]b = 1.03[/tex]

He bought the real estate for $101,234.

So, we have:

[tex]a = 101234\\[/tex]

Substitute values for (a) and (b) in [tex]f(x) = ab^x[/tex]

[tex]f(x) = 101234(1.03)^x[/tex]

Replace x with t

[tex]f(t) = 101234(1.03)^t[/tex]

Hence. the function that best represents the value of the real estate after t years is: [tex]f(t) = 101234(1.03)^t[/tex]

Read more about exponential functions at:

https://brainly.com/question/12940982

8:07, 8:58, ?, 10:43, 11:37

9:51
9:50
9:53
9:49

Answers

Answer:

9:50

Step-by-step explanation:

because, 8:07 ->8:58 +51

...+52

...+53

A pattern can either follow an arithmetic sequence, a geometric sequence or a user defined sequence.

The term that completes the sequence is (d) 9:49

The sequence is given as:

8:07, 8:58, ?, 10:43, 11:37

The above sequence follows an arithmetic sequence, and the common difference (d) is calculated using:

d = 8:58 - 8:07

This gives

d = 51 seconds

The missing term (which is the third term) is then calculated using:

T3 = 8:58 + 51 seconds

This gives

T3 = 9:49

Hence, the term that completes the sequence is (d) 9:49

Read more about arithmetic sequence at:

https://brainly.com/question/6561461

What is 7/6 as a decimal

I need it I the next 5 mins please!

I’ll give brainliest

Answers

Hey there!

7/6

= 7 ÷ 6

= 1.166667

Therefore, your answer is: 1.166667 which is approximately 1.67 or 1.7

Good luck on your assignment and enjoy your day!

~Amphitrite1040:)

Could someone answers these! I Really NEED HELP

Answers

Answer:

(3x + 5) (x - 3)

Step-by-step explanation:

This is the quadratic expression

2 people start from the same spot one walking east the other walking west, the person walking east walks slowly at 4mph and the other person walks fast at 6mph writr and solve a system of equations that can be used to determine how ong until 2 people are 2 1/2 miles apart from ach otherr

Answers

Answer:

3\5

Step-by-step explanation:

A baseball team won about 62% of 162 games in a season.
About how many games did they win?

Answers

Answer:

the one about 100 games

Step-by-step explanation:

62 percent *162 =

(62:100)*162 =

(62*162):100 =

10044:100 = 100.44

this rounds to 100

Answer:

About 100 games

Step-by-step explanation:

162 * 0.62 = 100.4

100.4 rounded is 100

x^2-x+2=0
Please use the quadratic formula

Answers

Answer:

[tex]\boxed{\sf x=\cfrac{1\pm \sqrt{-7} }{2}}[/tex]

Step-by-step explanation:

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

Use quadratic formula:

[tex]\boxed{\sf \frac{-b\pm \sqrt{b^2-4ac}}{2a}}[/tex]

[tex]\sf a=1, b=-1, c=2[/tex]

___________________________

[tex]\sf x_1,_2=\cfrac{-\left(-1\right)\pm \sqrt{\left(-1\right)^2-4\times \:1\times \:2}}{2\times \:1}[/tex]

[tex]\sf \sqrt{\left(-1\right)^2-4\times \:1\times \:2}[/tex][tex]\sf =\sqrt{-7}[/tex]

_________________

[tex]\sf x_1,_2\cfrac{-\left(-1\right)\pm \sqrt{-7}}{2\times \:1}[/tex]

[tex]\sf -(-1)=1[/tex][tex]2\times 1=2[/tex]

[tex]\sf x_1,_2=\cfrac{1\pm \sqrt{-7} }{2}[/tex]

_______________________________________

Learn more: brainly.com/question/22286698

The average laundry worker folds five
towels in a minute, but Miss Parker
folds eight! At the end of an hour,
how many more towels has she
folded than the average worker?

Answers

Answer:

Miss Parker folded 180 more towels than the average laundry worker

Step-by-step explanation:

5 multiplied by 60 gives you the average laundry worker- 5x60=300 towels per hour. Miss Parker can fold 8 per minute so you do 8 multiplied by 60 which would give you her average- 8x60=480. To find how many more towels she has folded than the average luandry worker you subtract miss Parker’s total from the average laundry person’s total giving you- 480-300=180

a)
3
NIX 01/x
b
b)
=
= 8.5

Answers

Answer:

a = 8.5  

Step-by-step explanation:

Eight times a certain number plus ten is equal to twelve times the same number minus seven

Answers

The answer is: 8x+10=12x-7
So the number you are looking for is: -12x+8x=-7-10
-4x=-17
4x=17
The answer is 17/4 or 4.25

Help me please ;-;

For the function y = 4x – 2, what is the value of the function when x is equal to -3?

A. -10
B. 14
C. -14
D. 10

Answers

Answer:

-14

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

y=4x - 2                                  x= -3

y=4(-3) - 2

y= -12 - 2

y= -14

pls help on my maths

Answers

Answer:[tex]r = 2.82[/tex]Step-by-step explanation:

Given:

[tex]A = 25[/tex]

Let's simplify.

=> [tex]25 = \frac{22}{7} r^{2}[/tex]=> [tex]\frac{25}{\frac{22}{7} } = \frac{\frac{22}{7}r^{2} }{\frac{22}{7\\} }[/tex]=> [tex]\frac{7(25)}{22} = r^{2}[/tex]=> [tex]\sqrt{\frac{25(7)}{22}}= \sqrt{r^{2}}[/tex]=> [tex]\sqrt{\frac{25(7)}{22}}= r[/tex]=> [tex]r = 2.82[/tex] (Estimated)

Therefore, r ≈ 2.82.

Hoped this helped.

Answer:

r= 5/√  π

or

r=2.820948 or simplified =2.82

Step-by-step explanation: it could be either one of these

please help me it's important

Answers

Answer:

circumference=2×3.142×radius

radius=16.8÷2=8.4

so,

circumference=52.7856cm

Can someone please answer this no bots answer this please… I’ll give you brainliest

Answers

Answer:

Part one:

Y=13.5x+1

Part two:

Y=12x+40

Part three:

After 15 seconds Sam: 203.5ft Alice:220ft

Alice won

Step-by-step explanation:

What is the equation of the line that passes through the point (-6, -6) and has a
slope of -1/3?

Answers

Answer:

Step-by-step explanation:

Let's find an equation by starting with the slope intercept form:

y = mx + b

where m is the slope and b the y-intercept (the value of y when x=0).

We are given the slope, so:

y = -(1/3)x + b

Now we need to find a value for b that will force the line to go through point (-6,-6).  We can determine by putting the point (-6,-6) into the equation and solving for b:

y = -(1/3)x + b

-6 = -(1/3)(-6) + b   [Enter the point (-6,-6]

-6 = 2 + b

b = - 8

The equation becomes y = -(1/3)x - 8.

See the attachment.

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