$a_{n} \: = \: 2(a_{n - 1})^{2} \\ a_{1} = 4 \: (given) \\ a_{2} = \: 2(a_{2 - 1})^{2} \\ = 2(a_{ 1})^{2} \\ = 2 \times {4}^{2} \\ = 32 \\ \\ a_{3} = \: 2(a_{3 - 1})^{2} \\ = 2(a_{ 2})^{2} \\ = 2 \times {32}^{2} \\ = 2 \times 1024 \\ = 2048$

so first 3 terms are

4, 32, 2048

8 0

3 years ago

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If x = –3 is the only x-intercept of the graph of a quadratic equation, which statement best describes the discriminant of the e

noname [10]

The Answer Is Letter "C" Or Discriminate 0

6 0

3 years ago

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Trisha packs x boxes with 12 bottles in each box. The total number of bottles she packs is 216. Which equation and solution repr

LiRa [457]

Answer:

Number of boxes Trisha pack = 18 boxes

Step-by-step explanation:

Given:

Number of boxes Trisha pack = X

Number of bottles in each box = 12

Total number of bottle = 216

Find:

Number of boxes Trisha pack

Computation:

Total number of bottle = Number of boxes Trisha pack x Number of bottles in each box

216 = X × 12

X = 216 / 12

X = 18

Number of boxes Trisha pack = 18 boxes

4 0

3 years ago

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Evaluate the indefinite integral. <br> integar x4/1 + x^10 dx

ivann1987 [24]

Answer:

$\int\ {\frac{x^4}{1 + x^{10}}} \, dx = \frac{1}{5}( \arctan(x^5)) + c$

Step-by-step explanation:

Given

$\int\ {\frac{x^4}{1 + x^{10}}} \, dx$

Required

Integrate

We have:

$\int\ {\frac{x^4}{1 + x^{10}}} \, dx$

Let

$u = x^5$

Differentiate

$\frac{du}{dx} = 5x^4$

Make dx the subject

$dx = \frac{du}{5x^4}$

So, we have:

$\int\ {\frac{x^4}{1 + x^{10}}} \, dx$

$\int\ {\frac{x^4}{1 + x^{10}}} \, \frac{du}{5x^4}$

$\frac{1}{5} \int\ {\frac{1}{1 + x^{10}}} \, du$

Express x^(10) as x^(5*2)

$\frac{1}{5} \int\ {\frac{1}{1 + x^{5*2}}} \, du$

Rewrite as:

$\frac{1}{5} \int\ {\frac{1}{1 + x^{5)^2}}} \, du$

Recall that: $u = x^5$

$\frac{1}{5} \int\ {\frac{1}{1 + u^2}}} \, du$

Integrate

$\frac{1}{5} * \arctan(u) + c$

Substitute: $u = x^5$

$\frac{1}{5} * \arctan(x^5) + c$

Hence:

$\int\ {\frac{x^4}{1 + x^{10}}} \, dx = \frac{1}{5}( \arctan(x^5)) + c$

7 0

3 years ago