SUBJECT: inverse Trigonometric Ratios please help me asap

Mathematics

1 answer:

san4es73 [151]3 years ago

4 0

Answer:

sert

Step-by-step explanation:

Which two of the following sentences from the article include central ideas of the article?

In 43 B.C., Octavian, Antony and Marcus Aemilus Lepidus established the Second Triumvirate.

Cleopatra’s seized treasure allowed him to pay his soldiers, making them more loyal.

During his 40-year rule, Augustus nearly doubled the size of the empire.

The family tree became more tricky after Augustus had his stepson Tiberius briefly marry his daughter, and then adopted Tiberius outright as son in A.D. 4 and named him next in line to rule.Which two of the following sentences from the article include central ideas of the article?

In 43 B.C., Octavian, Antony and Marcus Aemilus Lepidus established the Second Triumvirate.

Cleopatra’s seized treasure allowed him to pay his soldiers, making them more loyal.

During his 40-year rule, Augustus nearly doubled the size of the empire.

The family tree became more tricky after Augustus had his stepson Tiberius briefly marry his daughter, and then adopted Tiberius outright as son in A.D. 4 and named him next in line to rule.

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Find r(t) if r'(t) = 5t4i + 6t5j + t k and r(1) = i + j.

Vladimir [108]

$\mathbf r(t)=\displaystyle\int(5t^4\,\mathbf i+6t^5\,\mathbf j+t\,\mathbf k)\,\mathrm dt$
$\mathbf r(t)=(t^5+C_1)\,\mathbf i+(t^6+C_2)\,\mathbf j+\left(\dfrac12t^2+C_3\right)\,\mathbf k$

Given $\mathbf r(1)=\mathbf i+\mathbf j$ , we have

$\begin{cases}1^5+C_1=1\\\\1^6+C_2=1\\\\\dfrac121^2+C_3=0\end{cases}\implies C_1=0,C_2=0,C_3=-\dfrac12$

so that the particular solution is

$\mathbf r(t)=t^5\,\mathbf i+t^6\,\mathbf j+\dfrac12(t^2-1)\,\mathbf k$