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3 years ago

3p(2p^2–2) Please do. QUICKLY! y e s

Mathematics

2 answers:

andrew11 [14]3 years ago

7 0

Expand by multiply outside term with each of the inside terms to get
6p^3-6p

katrin2010 [14]3 years ago

6 0

Answer:

$- 6p + 6 {p}^{3}$

Step-by-step explanation:

According to the Product-to-Power Exponential Rule, whenever you multiply terms with exponents and coefficients, you add the exponents:

3p[2p² - 2]

6p³ - 6p

The above answer is written in reverse, but it is the exact same result.

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3 years ago

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3 years ago

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3 years ago

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Find the length of the arc and express your answer as a fraction times pie

Elina [12.6K]

Solution:

Given a circle of center, A with radius, r (AB) = 6 units

Where, the area, A, of the shaded sector, ABC, is 9π

To find the length of the arc, firstly we will find the measure of the angle subtended by the sector.

To find the area, A, of a sector, the formula is

$\begin{gathered} A=\frac{\theta}{360\degree}\times\pi r^2 \\ Where\text{ r}=AB=6\text{ units} \\ A=9\pi\text{ square units} \end{gathered}$

Substitute the values of the variables into the formula above to find the angle, θ, subtended by the sector.

$\begin{gathered} 9\pi=\frac{\theta}{360\degree}\times\pi\times6^2 \\ Crossmultiply \\ 9\pi\times360=36\pi\times\theta \\ 3240\pi=36\pi\theta \\ Divide\text{ both sides by 36}\pi \\ \frac{3240\pi}{36\pi}=\frac{36\pi\theta}{36\pi} \\ 90\degree=\theta \\ \theta=90\degree \end{gathered}$

To find the length of the arc, s, the formula is

$\begin{gathered} s=\frac{\theta}{360\degree}\times2\pi r \\ Where \\ \theta=90\degree \\ r=6\text{ units} \end{gathered}$

Substitute the variables into the formula to find the length of an arc, s above

$\begin{gathered} s=\frac{\theta}{360}\times2\pi r \\ s=\frac{90\degree}{360\degree}\times2\times\pi\times6 \\ s=\frac{12\pi}{4}=3\pi\text{ units} \\ s=3\pi\text{ units} \end{gathered}$

Hence, the length of the arc, s, is 3π units.

4 0

1 year ago

Write an exponential function to model the situation. A population of 470 animals decreases at an annual rate of 12%.

Tamiku [17]

$\bf \qquad \textit{Amount for Exponential Decay}
\\\\
A=P(1 - r)^t\qquad 
\begin{cases}
A=\textit{accumulated amount}\\
P=\textit{initial amount}\to &470\\
r=rate\to 12\%\to \frac{12}{100}\to &0.12\\
t=\textit{elapsed time}\\
\end{cases}
\\\\\\
A=470(1-0.12)^t\implies A=470(0.88)^t$

5 0

3 years ago