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Lyrx
2 months 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:
babunello [11.8K]2 months ago
3 0

Answer:

Volume = 16 unit^3

Step-by-step explanation:

Given:

- The solid is situated between x = 0 and x = 4.

- Diagonal lines stretch from y = sqrt(x) to y = -sqrt(x)

Find:

Calculate the volume enclosed.

Solution:

- We will begin by finding the area projection of the solid on the plane at x = 0.

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

- The diagonal ranges from y = sqrt(x) to y = -sqrt(x), thus

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

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

- By utilizing the area function, we will integrate across x from 0 to 4 to determine the solid's volume:

V = integral(A(x)).dx

V = integral(2*x).dx

V = x^2

- Evaluating from 0 to 4:

V= 16 - 0 = 16 unit^3

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Answer:

a.  P(x = 3) = 0.061313

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Step-by-step explanation:

Based on the provided details:

A Poisson process is utilized to model the occurrence of this event:

Minor radio blackouts occur, on average, two times annually.

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time t = 1/2 (i.e., six months)

Let x represent the likelihood of 3 incidents during the remaining months of the year.

Then:

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P(x = 3) = 0.061313

b).

The expected number of radio blackouts over two years is calculated as follows:

We start with:

t = 2 years

E(x) = λ × t

E(x) = 2 × 2

E(x) = 4

Thus, the predicted number of radio blackouts = 4

c).

The time we must wait until the probability of witnessing the next radio blackout reaches at least 0.5 is as follows:

In this case, time (t) =???

Thus:

P(x =1) = 0.5

P(x = 1) = \dfrac{e^{-\lambda t} \times (\lambda t)^x}{x!} = 0.5

\dfrac{e^{-\lambda t} \times (\lambda t)^x}{x!} = 0.5

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d)

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x =4, t = 2

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P(x = 4) = \dfrac{e^{-4 } \times (4)^4}{4!}

P(x = 4) = 0.19537

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An element with mass 970 grams decays by 27.7% per minute. How much of the element is remaining after 13 minutes, to the nearest
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Each minute, you need to multiply the mass by 27.7% or 0.277

after 1 minute, it's one multiplication
after 2 minutes, it’s two multiplications
3, three times
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thus what is 970g * 0.277^13 =?

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2 months ago
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Answer:

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Explicación paso a paso:

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\angle R> (\angle s +\angle T)

Ahora, según la condición, un ángulo es mayor que la suma de los otros dos ángulos.

En un triángulo, la suma de los tres ángulos es 180°

Por lo tanto, si un ángulo mide  90°, la suma de los otros dos debe ser igual a 90°

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De lo anterior, se concluye que

Para, \angle R> (\angle s +\angle T)

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