use limits to find the area of the region bounded by the graph f(x)=4-2x^3 , the x-axis , and the vertical lines x=0 and x=1

A) 7
B) infinity
C) 7/2
D) 7/4

Answers

Answer 1

Answer:

[tex]\frac{7}{2}[/tex] square units.

Step-by-step explanation:

We have to use limits to find the area of the region bounded by the graph [tex]f(x) = 4 - 2x^{3}[/tex] , the x-axis, and the vertical lines x=0 and x=1.

So, the area will be

A = [tex]\int\limits^1_0 {(4 - 2x^{3})} \, dx[/tex]

= [tex][4x - \frac{x^{4}}{2} ]^{1} _{0}[/tex]

= [tex]4 - \frac{1}{2}[/tex]

= [tex]\frac{7}{2}[/tex] square units. (Answer)


Related Questions

CAN SOMEONE HELP ME WITH THE QUESTION IN THE IMAGE. I WILL MARK THE PERSON WHO GETS IT RIGHT AS BRAINLIEST

Answers

Answer:

[tex]x = 8[/tex] units

Step-by-step explanation:

The diagonals of a parallelogram bisect each other.

From the diagram, the half of the diagonal measure 5x units and 6x-8 units.

This halves must be equal in length.

[tex]6x - 8 = 5x [/tex]

Group similar terms to get:

[tex]6x - 5x = 8[/tex]

Simplify to get:

[tex]x = 8[/tex]

Cleo bought 10 feet of ribbon for costumes. He used 2 feet of ribbon last week. He cut of the remaining ribbon into one- sixth foot pieces. How many pieces of ribbon does Cleo have?

Answers

Answer:

48 pieces

Step-by-step explanation:

Given:

Cleo bought 10 feet of ribbon.

He used 2 feet of ribbon last week.

He cut of the remaining ribbon into one- sixth foot pieces.

Question asked:

How many pieces of ribbon does Cleo have ?

Solution:

Total length of ribbon = 10 feet

He has used  length of ribbon = 2 feet

Remaining length of ribbon = 10 - 2 = 8 feet

He cut remaining ribbon into = [tex]\frac{1}{6}foot[/tex]

Number of pieces of ribbon = [tex]8\div\frac{1}{6}[/tex]

                                              = [tex]8\times6 = 48 pieces[/tex]

Therefore, Cleo have 48 pieces of ribbon.

2apples and I add 1 more how many apples are there?

Answers

Answer:

3

Step-by-step explanation:

2+1=3

Answer:

3 apples

Step-by-step explanation:

2 apples + 1 apple = 3 apples

An Impressionist painting increases in value
at an average rate of 9% a year. If the origi-
nal cost of the painting to the Museum of
Art was $1500, what was the value of the
painting (to the nearest dollar) at the end of
a 20-year holding period?

Answers

Answer:

A = $8406.6

Step-by-step explanation:

Given:

Average rate [tex]r=9\%[/tex]

Initial cost of painting [tex]a = \$1500[/tex]

Time [tex]t = 20\ years[/tex]

We need to find the final amount of painting at the end of a 20-year.

Solution:

Using Exponential Growth rate formula as:

[tex]A = a(1+r)^t[/tex]  ----------(1)

Where:

A = Final amount

a = Initial amount.

r = Rate as a decimal.

t = Time.

Now, we substitute all given values in equation 1.

[tex]A = 1500(1+0.09)^{20}[/tex]

[tex]A = 1500(1.09)^{20}[/tex]

Substitute [tex]1.09^{20} = 5.60[/tex] in above equation.

[tex]A = 1500\times 5.60[/tex]

A = $8406.62

Therefore, value of the  painting at the end of  a 20-year A = $8406.6

If E be an event, then P(E) + P(not E) = _____________.

Answers

Answer:

1

Step-by-step explanation:

If P(E) = p

Then P(not E) = 1-p

Answer:

A

Step-by-step explanation:

what is an equation of a line that passes through the point (3,-1) and has a slope of 2

Answers

Answer:

y=2x-7

Step-by-step explanation:

y-y1=m(x-x1)

y-(-1)=2(x-3)

y+1=2x-6

y=2x-6-1

y=2x-7

how many triangles can be drawn with side lengths of 3 inches, 5 inches, and 6 inches???

Answers

Answer:

4 congruent triangles

Step-by-step explanation:

since there is no one of the sum of two sides is less then the third side, so it's possible to form a triangle

Use straightedge and compass, it can draw 4 triangles at a common base

The number of triangles that can be drawn with side lengths of 3 inches, 5 inches, and 6 inches is 1 triangle due to the triangle inequality theorem.

To determine the number of triangles, we can use the triangle inequality theorem. For a triangle to exist, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. In this case, 3 + 5 is less than 6, so only 1 triangle can be formed.

is The fraction 3/7 is smaller than 5/7 . True False

Answers

Answer:

Yes

When comparing fractions such as 3/7 and 5/7, you could also convert the fractions

The statement is false. 5/7 is closer to a whole than 3/7 is. Think about it in terms of pizza.

How do I solve these using the elimination method:
x+y+z=20
13x+0y+6z=132
150x+90y+139z=2601

Answers

Answer:

(x=6,y=5,z=9)

Step-by-step explanation:

The given system is

x+y+z=20 ------>(1)

13x+0y+6z=132 ------->(2)

150x+90y+139z=2601------>(3)

Make y the subject in the first equation to get: [tex]y=20-x-z-------(4)[/tex]

Put equation (4) in equation (3) to get:

150x+90(20-x-z)+139z=2601

150x+180-90x-90z+139z=2601

60x+49z=801---->(5)

We solve equation (2) and (5) simultaneously

13x+6z=132 ------->(2)

60x+49z=801---->(5)

Make x the subject in equation (2) to get:

[tex]x=\frac{132-6z}{13}[/tex]

Put it in (5)

[tex]60(\frac{132-6z}{13})z+49z=2601[/tex]

[tex]\frac{277z+7920}{13}=801[/tex]

[tex]277z+7920=10413[/tex]

[tex]277z=2493[/tex]

[tex]z=9[/tex]

[tex]x=\frac{132-6*9}{13}=6[/tex]

From 6+y+9=20

y=20-15=5

What is the answer to r/10+4=5

Answers

Answer:

r=10

Step-by-step explanation:

Take 4 away from 5 to isolate your variable. Now you have r/10= 1. figure out the unknown value by placing ten on top which is the same as 1.

Here you gooooooooooo.

Given that ​f(x)
equals
= 3x+2
and ​g(x)=x^2−2x−6
find ​(g◦​f)(6).

Answers

​(g◦​f)(6) means we have to find g(f(6)).

So f(6)=3(6)+2=20

And g(20)=20^2-(20)(2)-6=400-40-6=360-6=354

So ​(g◦​f)(6) is 354

Hope this helped!

What is the best estimate of 11 1/5÷2 3/4

Answers

Answer:4

Step-by-step explanation:

If the store bought a leash for $6.20, how much will the retail price be for that leash?​

Answers

Answer:

2.50 punds

Step-by-step explanation:

plus with the money

What is 10/24 as a improper fraction

Answers

Answer:

10/24 cannot be written as an improper fraction.

Step-by-step explanation:

a faction is only an improper fraction when the numerator is a larger number than the denominator. Therefore, this fraction, 10/24, can only be simplified or transformed into a decimal.

Simplified: 5/12

Decimal: 0.416 or 0.42

I hope this was helpful!

What two fractions equal 1 1/5

Answers

I also need help with this one also

Answer:

4/5 + 2/5

Step-by-step explanation:

They would equal 6/5 which is equivalent to 1 1/5


Which expressions have a value of 16/81? Check all that apply.

Answers

Which expression have a value of 16/81? check all that apply. (2/3)^4, (16/3)^4, (4/81)^2, and (4/9)^2

Answer:

First and last option is correct.

[tex](\frac{2}{3})^{4}=\frac{16}{81}[/tex]

[tex](\frac{4}{9})^{2}=\frac{16}{81}[/tex]

Step-by-step explanation:

Given:

There are four options.

(2/3)^4, (16/3)^4, (4/81)^2, and (4/9)^2

We need to check all given options for value of 16/81.

Solution:

Using rule.

[tex](\frac{a}{b})^{n}=\frac{a^{n}}{b^{n}}[/tex]

Solve for option [tex](\frac{2}{3})^4[/tex].

[tex](\frac{2}{3})^{4}=\frac{2^4}{3^4}=\frac{2\times 2\times 2\times 2}{3\times 3\times 3\times 3}=\frac{16}{81}[/tex]

Solve for option [tex](\frac{16}{3})^4[/tex].

[tex](\frac{16}{3})^{4}=\frac{16^4}{3^4}=\frac{16\times 16\times 16\times 16}{3\times 3\times 3\times 3}=\frac{65536}{81}[/tex]

Solve for option [tex](\frac{4}{81})^2[/tex].

[tex](\frac{4}{81})^{2}=\frac{4^2}{81^2}=\frac{4\times 4}{81\times 81}=\frac{16}{6561}[/tex]

Solve for option [tex](\frac{4}{9})^2[/tex].

[tex](\frac{4}{9})^{2}=\frac{4^2}{9^2}=\frac{4\times 4}{9\times 9}=\frac{16}{81}[/tex]

Therefore, expression [tex](\frac{2}{3})^4[/tex] and [tex](\frac{4}{9})^2[/tex] have a value of  [tex]\frac{16}{81}[/tex].

Answer: Which expressions have a value of StartFraction 16 Over 81 EndFraction? Check all that apply.

Best Option A, D

(A)  <=====  correct answer

(D)  <=====  correct answer

Step-by-step explanation:

graph the equation
y = - 4

Answers

Answer:

Hi! Use a calculator thats math... way!

Step-by-step explanation: The negative 4 on the graph would just have a direct slope going through the negative side of the graph!

1/3 divided by 5/6a what is the answer please I don’t get it;(

Answers

Answer:to divide you have to have the same number for the bottom number so you will divide 2\6 by 5\6a and you will probably get a answer with a graphing calculator i hope this helps

Step-by-step explanation:

What is y=x-4 and y=4x-10

Answers

Answer:

I got an answer of X = 2

Step-by-step explanation:

I used subtituion and got 2

Answer:

Step-by-step explanation:

I've already answered this question.

Jin bought a book that costs 5.60 if the tax rate is 7% how much tax did he pay

Answers

Answer:

$5.99

Step-by-step explanation:

5.6*1.07

1.07 is the tax plus the original price

is 5.992

which rounds up to $5.99

What is the solution to the equation 5 (x minus 6) = 2 (x + 3)?

Answers

Answer:

1. Distribute

5x-30=2x+6

2. Combine like terms

5x=2x+36

3. Simplify to get x by itself(36 divide 3)

3x=36

x=12

Step-by-step explanation:

The value of the given equation  5 (x minus 6) = 2 (x + 3) will be x = 19.5.

What is the equation?

There are many different ways to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of 2 mathematical expressions.

In another word, the equation must be constrained with some constraints.

As per the given,

5 (x minus 6) = 2 (x + 3)

5(x - 6) = 3(x + 3)

5x - 30 = 3x + 9

5x - 3x = 9 + 30

2x = 39

x = 19.5

Hence "The value of the given equation  5 (x minus 6) = 2 (x + 3) will be x = 19.5".

For more about the equation,

brainly.com/question/10413253

#SPJ6

What postulate or theorem proves the two triangles are similar?

Answers

Answer:

sss therom

Step-by-step explanation:

they are congruent on all sides

What is the measure of angle x?

Enter your answer in the box.

Answers

Answer:

Step-by-step explanation:

Just like regular numbers, angles can be added to obtain a sum, perhaps for the purpose of determining the measure of an unknown angle. Sometimes we can determine a missing angle because we know that the sum must be a certain value. Remember -- the sum of the degree measures of angles in any triangle equals 180 degrees. Below is a picture of triangle ABC, where angle A = 60 degrees, angle B = 50 degrees and angle C = 70 degrees.

The angles of this triangle are 50, 60, and 70 degrees.

If we add all three angles in any triangle we get 180 degrees. So, the measure of angle A + angle B + angle C = 180 degrees. This is true for any triangle in the world of geometry. We can use this idea to find the measure of angle(s) where the degree measure is missing or not given.

Answer:

48 degrees

Step-by-step explanation:

The sum of 42 and x should get 90 degrees, so if you subtract 42 from 90 you get 48.

Hope this helped :)

Scientists determined that Antarctica’s average winter temperature was −34.44°C. The difference between this temperature and Antarctica’s highest recorded temperature was 49.44 degrees. What was Antarctica’s highest recorded temperature? A 83.88°C B 15°C C −83.88°C D −15°C

Answers

Answer:

The answer is C. -83.88

What is the value of Negative 3 StartAbsoluteValue 15 minus 2 EndAbsoluteValue + 2 s cubed when s = negative 3?
-108
0
108
216

Answers

Answer:

The right answer is - 93 and none of the alternatives given is correct.

Step-by-step explanation:

Let's find the value of:

- 3 |15 –2 | + 2s³ , when s = -3

Replacing s, we have:

- 3 |15 –2 | + 2 * -3³

- 3 | 13 | + 2 * - 27

- 39 - 54 = -93

The right answer is - 93 and none of the alternatives given is correct.

Answer:

A; -108

Step-by-step explanation:

Siven that f(x)=x2 - 7 and g(x)= 4 - x, find (f - g)(1), if it exists.

Answers

Answer:

- 9

Step-by-step explanation:

Note that (f - g)(x) = f(x) - g(x)

f(x) - g(x)

= x² - 7 - (4 - x)

= x² - 7 - 4 + x

= x² + x - 11

Thus

(f - g)(1) ← substitute x = 1 into (f - g)(x)

= 1² + 1 - 11

= 1 + 1 - 11

= - 9

Mia deposits $300 into an account that pays simple interest at a rate of 5% per year, how much interest would she be payed in the first 2 years?

Answers

Answer: $30

Step-by-step explanation:

I=PRT

I= (300)(0.05)(2)

I= 15(2)

I= 30

Can someone explain this to me? ​

Answers

Answer:

y=42 degrees.

Step-by-step explanation:

The sum of angles in a triangle = 180 degrees.

One angle in that small triangle is y, one is 48, and one is unknown.

The sum of angles on one line is 180 degrees.

One of the angles on the line that unknown angle lies on is 90 degrees, so the unknown angle is 90 degrees, too.

90 + 48 = 138

180 - 138 = 42.

Which of the following is a solution to the inequality below?
5 > v

Answers

Answer:

v = 4

Step-by-step explanation:

4 is less than 5. 7,8 and 10 are all greater than 5.

Javier used the expression below to represent his score in a game of mini-golf.

3x + x + 5 – 2x

If he simplifies the expression, which statements are true about the parts of the simplified expression? Select three options.

The constant is 2.
The coefficient is 2.
The constant is 5.
The coefficient is 5.
There are two terms.

Answers

Answer:

The three true options are B, C and E.

Step-by-step explanation:

Let's simplify the expression that represent the score of Javier in a game of mini-golf:

3x + x + 5 – 2x

2x + 5

Which statements are true about the parts of the simplified expression? Select three options.

A. The constant is 2.

It's false. The constant is 5.

B. The coefficient is 2.

It's true. The coefficient of x is 2.

C. The constant is 5.

It's true.

D. The coefficient is 5.

It's false. 5 is the constant and the coefficient of x is 2.

E. There are two terms.

It's true. The two terms are 2x and 5.

The three true options are B, C and E.

tHE ANSWER IS 3 ANSWERS. bce

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