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AURORKA [14]
3 years ago
11

(5) Rewrite the integral Z 1 0 Z x 0 Z √ 1−x2 0 z dz dy dx in the order dy dx dz, and evaluate it. Hint: You will need a reasona

bly good idea of what the solid over which the integration is being done looks like to have any hope of getting correct limits for the iterated integral in the new order of integration.
Mathematics
1 answer:
Natalija [7]3 years ago
5 0

Looks like the integral is supposed to read

\displaystyle\int_0^1\int_0^x\int_0^{\sqrt{1-x^2}}z\,\mathrm dz\,\mathrm dy\,\mathrm dx

The same integral in the required order is

\displaystyle\int_0^1\int_0^{\sqrt{1-z^2}}\int_0^xz\,\mathrm dy\,\mathrm dx\,\mathrm dz

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Solve the following equation:<br> 9n² - n - 2/3 = 0
KIM [24]

Answer:

see explanation

Step-by-step explanation:

Given

9n² - n - \frac{2}{3} = 0 ← multiply through by 3 to clear the fraction

27n² - 3n - 2 = 0 ← factoring

Consider the factors of the product of the n² term and the constant term which sum to give the coefficient of the n- term

product = 27 × - 2 = - 54 and sum = - 3

The factors are - 9 and + 6

Use these factors to split the n- term

27n² - 9n + 6n - 2 = 0 ( factor the first/second and third/fourth terms )

9n(3n - 1) + 2(3n - 1) = 0 ← factor out (3n - 1) from each term

(3n - 1)(9n + 2) = 0

Equate each factor to zero and solve for n

3n - 1 = 0 ⇒ 3n = 1 ⇒ n = \frac{1}{3}

9n + 2 = 0 ⇒ 9n = - 2 ⇒ n = - \frac{2}{9}

3 0
3 years ago
What are the steps to linear equations
timofeeve [1]

Answer:

Here is how you do it step by step.

Step-by-step explanation:

Step 1: Simplify each side, if needed.

Step 2: Use Add./Sub. Properties to move the variable term to one side and all other terms to the other side.

Step 3: Use Mult./Divide

Step 4: Check your answer.

I find this is the quickest and easiest way to approach linear equations.

Example 6: Solve for the variable.

<u>Hope this helps!</u>

4 0
3 years ago
Which equation is equivalent to
rosijanka [135]

Answer:

3 and 2 r equivalent i belive

5 0
3 years ago
News cameras take an overhead picture of a part of a crowd at an outdoor event. Journalists then count the number of people in t
aliina [53]

Answer:

cluster system

Step-by-step explanation: For edgunity

4 0
3 years ago
Read 2 more answers
Simplify: x0 y-3 / x2 y-1
svetlana [45]

\frac{x {}^{0}y {}^{ - 3}  }{x {}^{2}y {}^{ - 1}  }  \\  =  \frac{1y {}^{ - 3} }{ {x}^{2}y {}^{ - 1}  }  \\  =  \frac{1 \times 1}{ {x}^{2} y {}^{2} }  \\    \\  =  \frac{1}{ {x}^{2}y {}^{2}  }

Step by Step Explanation:

  • Evaluate the power: Any non-zero expression raised to the power of 0 equals 1
  • Simplify: Simplify the expression
  • Calculate the product: Any expression multiplied by 1 remains the same.

<h2>☆彡Hanna</h2>

#CarryOnLearning

8 0
3 years ago
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