1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Travka [436]
3 years ago
6

Find the volume of the solid generated by revolving the region bounded by the x-axis, the curve y = 3x^4 , and the lines x = 1 a

nd x = -1 about the x-axis.
Mathematics
1 answer:
Marysya12 [62]3 years ago
8 0

Answer:

Let's define A as the area given by the integral:

\int\limits^1_{-1} {3x^4} \, dx

Which is the area between the curve y = 3*x^4 and the x-axis between x = -1 and x = 1

To find the volume of a revolution around the x-axis, we need to multiply the area by 2*pi (a complete revolution)

where pi = 3.14

First, let's solve the integral:

\int\limits^1_{-1} {3x^4} \, dx = \frac{3}{5}(1^5 - (-1)^5) = \frac{3*2}{5} = \frac{6}{5}

Then the volume of the solid is just:

V = (6/5)*2*3.14 = 7.536

You might be interested in
Find the average rate of change of f(x) = x^2–5x+1 from x = 2 to x= 5.
Agata [3.3K]

Answer:

12

Step-by-step explanation:

it should be the answer if not messge me so we can work it out

3 0
3 years ago
Giving 100 points.
Nitella [24]

Answer:

1.   <u>Cost per customer</u>:  10 + x

     <u>Average number of customers</u>:  16 - 2x

\textsf{2.} \quad  -2x^2-4x+160\geq 130

3.    $10, $11, $12 and $13

Step-by-step explanation:

<u>Given information</u>:

  • $10 = cost of buffet per customer
  • 16 customers choose the buffet per hour
  • Every $1 increase in the cost of the buffet = loss of 2 customers per hour
  • $130 = minimum revenue needed per hour

Let x = the number of $1 increases in the cost of the buffet

<u>Part 1</u>

<u></u>

<u>Cost per customer</u>:  10 + x

<u>Average number of customers</u>:  16 - 2x

<u>Part 2</u>

The cost per customer multiplied by the number of customers needs to be <u>at least</u> $130.  Therefore, we can use the expressions found in part 1 to write the <u>inequality</u>:

(10 + x)(16 - 2x)\geq  130

\implies 160-20x+16x-2x^2\geq 130

\implies -2x^2-4x+160\geq 130

<u>Part 3</u>

To determine the possible buffet prices that Noah could charge and still maintain the restaurant owner's revenue requirements, solve the inequality:

\implies -2x^2-4x+160\geq 130

\implies -2x^2-4x+30\geq 0

\implies -2(x^2+2x-15)\geq 0

\implies x^2+2x-15\leq  0

\implies (x-3)(x+5)\leq  0

Find the roots by equating to zero:

\implies (x-3)(x+5)=0

x-3=0 \implies x=3

x+5=0 \implies x=-5

Therefore, the roots are x = 3 and x = -5.

<u>Test the roots</u> by choosing a value between the roots and substituting it into the original inequality:

\textsf{At }x=2: \quad -2(2)^2-4(2)+160=144

As 144 ≥ 130, the <u>solution</u> to the inequality is <u>between the roots</u>:  

-5 ≤ x ≤ 3

To find the range of possible buffet prices Noah could charge and still maintain a minimum revenue of $130, substitute x = 0 and x = 3 into the expression for "cost per customer.  

[Please note that we cannot use the negative values of the possible values of x since the question only tells us information about the change in average customers per hour considering an <em>increase </em>in cost.  It does not confirm that if the cost is reduced (less than $10) the number of customers <em>increases </em>per hour.]

<u>Cost per customer</u>:  

x =0 \implies 10 + 0=\$10

x=3 \implies 10+3=\$13

Therefore, the possible buffet prices Noah could charge are:

$10, $11, $12 and $13.

8 0
2 years ago
What is the greatest common factor of 27,45,63 and then 24 40 64
Aleks [24]

Answer:

27

Step-by-step explanation:

5 0
3 years ago
Find the distance between (5, 9) &amp; (-7, -7). Round to the nearest tenth.
prisoha [69]
See picture hope it helps

8 0
3 years ago
Read 2 more answers
I need the answer in 1 minute
Varvara68 [4.7K]

Answer:

4 Units.

Step-by-step explanation:

7 0
3 years ago
Read 2 more answers
Other questions:
  • Can someone edit the the middle of my poem by adding literary devices like personification, alliteration, simile's, etc.
    14·1 answer
  • How to solve 10 (g+5)=2(g+9)
    7·1 answer
  • What is the dimension of a rectangle if the perimeter is 198
    5·1 answer
  • Solve the equation- 5y -9 = -(y - 1)
    7·2 answers
  • What is the value of x? Enter your answer as a decimal
    12·1 answer
  • Can you conclude that the figures are congruent? Justify your answers.
    8·1 answer
  • How to make 1/3 and 1/1/2 into a 1
    13·1 answer
  • 5 to 7 and please solve with equations thx
    8·2 answers
  • Can someone help me with this
    14·1 answer
  • Using the table, if there are 5 flowers, how many petals are there?
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!