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3 years ago

What value of a is a solution to this equation? 1=3+a 4

Mathematics

1 answer:

Romashka-Z-Leto [24]3 years ago

6 0

Answer:

1=a4+3

Step 1: Subtract a^4+3 from both sides.

1−(a4+3)=a4+3−(a4+3)

−a4−2=0

Step 2: Add 2 to both sides.

−a4−2+2=0+2

−a4=2

Step 3: Divide both sides by -1.

−a4

−1

a4=−2

Step 4: Take root.

a=±(−2)(

)

Answer:

No real solutions.

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GaryK [48]

Answer:

Step-by-step explanation:

Count the number of places it takes to get one place past 3

There are 5 zeros in the given question. That gets you to just before the 3.

Add one more to get past the 3. That makes 5 zeros + 1 more place = 6

Since you are moving right, the 6 is minus. Your answer is 3 * 10^-6

7 0

3 years ago

Use Simpson's Rule with n = 10 to estimate the arc length of the curve. Compare your answer with the value of the integral produ

SOVA2 [1]

$y=\ln(6+x^3)\implies y'=\dfrac{3x^2}{6+x^3}$

The arc length of the curve is

$\displaystyle\int_0^5\sqrt{1+\frac{9x^4}{(6+x^3)^2}}\,\mathrm dx$

which has a value of about 5.99086.

Let $f(x)=\sqrt{1+\frac{9x^4}{(6+x^3)^2}}$ . Split up the interval of integration into 10 subintervals,

[0, 1/2], [1/2, 1], [1, 3/2], ..., [9/2, 5]

The left and right endpoints are given respectively by the sequences,

$\ell_i=\dfrac{i-1}2$

$r_i=\dfrac i2$

with $1\le i\le10$ .

These subintervals have midpoints given by

$m_i=\dfrac{\ell_i+r_i}2=\dfrac{2i-1}4$

Over each subinterval, we approximate $f(x)$ with the quadratic polynomial

$p_i(x)=f(\ell_i)\dfrac{(x-m_i)(x-r_i)}{(\ell_i-m_i)(\ell_i-r_i)}+f(m_i)\dfrac{(x-\ell_i)(x-r_i)}{(m_i-\ell_i)(m_i-r_i)}+f(r_i)\dfrac{(x-\ell_i)(x-m_i)}{(r_i-\ell_i)(r_i-m_i)}$

so that the integral we want to find can be estimated as

$\displaystyle\sum_{i=1}^{10}\int_{\ell_i}^{r_i}p_i(x)\,\mathrm dx$

It turns out that

$\displaystyle\int_{\ell_i}^{r_i}p_i(x)\,\mathrm dx=\frac{f(\ell_i)+4f(m_i)+f(r_i)}6$

so that the arc length is approximately

$\displaystyle\sum_{i=1}^{10}\frac{f(\ell_i)+4f(m_i)+f(r_i)}6\approx5.99086$

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3 years ago

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Dennis_Churaev [7]

Answer:

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Step-by-step explanation:

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3 years ago

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zubka84 [21]

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Grace [21]

Answer:

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Step-by-step explanation:

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