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alexandr402 [8]
3 years ago
6

Determine the volume of the solid that lies between planes perpendicular to the x-axis at x=0 and x=4. The cross sections perpen

dicular to the x-axis on the interval 0≤x≤4 are squares whose diagonals run from the curve y=x√ to the curve y=−x√.
Mathematics
1 answer:
OverLord2011 [107]3 years ago
3 0

Answer:

Volume = 16 unit^3

Step-by-step explanation:

Given:

- Solid lies between planes x = 0 and x = 4.

- The diagonals rum from curves y = sqrt(x)  to  y = -sqrt(x)

Find:

Determine the Volume bounded.

Solution:

- First we will find the projected area of the solid on the x = 0 plane.

                              A(x) = 0.5*(diagonal)^2

- Since the diagonal run from y = sqrt(x) to y = -sqrt(x). We have,

                              A(x) = 0.5*(sqrt(x) + sqrt(x) )^2

                              A(x) = 0.5*(4x) = 2x

- Using the Area we will integrate int the direction of x from 0 to 4 too get the volume of the solid:

                              V = integral(A(x)).dx

                              V = integral(2*x).dx

                               V = x^2

- Evaluate limits 0 < x < 4:

                               V= 16 - 0 = 16 unit^3

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barxatty [35]

Answer:

  -29/20

Step-by-step explanation:

The cosecant function is the inverse of the sine function. Both sine and cosecant are odd functions, meaning csc(-x) = -csc(x) = -1/sin(x).

  csc(-θ) = -1/sin(θ) = -1/(20/29) = -29/20

6 0
3 years ago
A movie complex is showing the same movie and three theaters in theater and a 60 of the 80 seats are taken and theater B 42 seat
Anna [14]

Answer:

Theatre C.

Step-by-step explanation:

Theatre A:

60 of the 80 seats are taken.

% seats taken = seats taken/total seats * 100

= 60/80 * 100

= 75%

Theatre B:

Total seats = number of seats taken + number of empty seats

= 42 + 18

= 60

% seats taken = seats taken/total seats * 100

= 42/60 * 100

= 70%

Theatre C:

Total seats = number of seats taken + number of empty seats

90 = X + 18

X = 72

% seats taken = seats taken/total seats * 100

= 72/90 * 100

= 80%

Theatre C with 80% of seats taken.

4 0
3 years ago
Read 2 more answers
A hummingbird can fly between 0.34 and 0.81 miles per minute. Create an inequality to
Sergeu [11.5K]

Answer: .34 ≤ x ≤ .81

Step-by-step explanation:

An inequality is writted like __ ≤ x ≤ ___

Since the humming bird can fly between .34 and .81 we use the the less than or equal to sign because it can fly max .81 mpm or less than that. with a minimum speed of .34 mpm.

3 0
3 years ago
One canned juice drink is 25% orange juice another is 10% orangw juice. How many liters of each should be mixed together in orde
Vsevolod [243]

Answer:

There should be 10 l of 25% orange juice and 5 l of 10% orange juice.

Step-by-step explanation:

Let the amount of the 25% orange juice be "x", while the amount of the 10% one be "y". The sum of these must be equal to 15 l, therefore:

x + y = 15

The sum of the concentration of juice on each can must be equal to the final product, therefore:

25\%*x + 10\%*y = 15*20\%\\0.25*x + 0.1*y = 3

We can now solve the system of equations as shown below:

\left \{ ({{x + y=15})*(-0.1) \atop {0.25*x + 0.1*y=3}} \right. \\\left \{ {{-0.1*x - 0.1*y=-1.5} \atop {0.25*x + 0.1*y=3}} \right. \\-0.1*x + 0.25*x = 3 - 1.5\\0.15*x = 1.5\\x = \frac{1.5}{0.15} = 10\\y = 15 - x = 15 - 10 = 5

There should be 10 l of 25% orange juice and 5 l of 10% orange juice.

4 0
3 years ago
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ludmilkaskok [199]

Answer:

3

Step-by-step explanation:

5 times 3 is 15

15 plus 4 equals 19

Hope this helps :)

4 0
2 years ago
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