Expert Answers to Algebra 2 Problems

${\log }_{6}x(x+5)=2$

Scientists are working with a sample of cobalt-56 in their laboratory. They begin with a sample that has 60 mg of cobalt-56, and they measure that after 31 days, the mass of cobalt-56 sample is 45.43 mg. Recall that the differential equation which models exponential decay is ${\displaystyle \frac{dm}{dt}=-km}$ and the solution of that differential equation if ${\displaystyle m\left(t\right)=m_0{e}^{-kt}}$, where ${\displaystyle m_0}$ is the initial mass and k is the relative decay rate.
a) Use the information provided to compute the relative decay rate k. Show your calculation (do not just cit a formula).
b) Use the information provided to determine the half-life of cobalt-56. Give your answer in days and round to the second decimal place. Show your calculation (do not just cite a formula).
c) To the nearest day, how many days will it take for the initial sample of 60mg of cobalt-56 to decay to just 10mg of cobalt-56?
d) What will be the rate at which the mass is decaying when the sample has 50mg of cobalt-56? Make sure to indicate the appropriate units and round your answer to three decimal places.

To simplify:
The given expression ${\displaystyle \sqrt{3}\left\{\frac{54x^2{y}^4}{2x^{5}y}\right\}}$

For each sequence, decide whether it could be arithmetic,
$a)\hspace{0.17em}\hspace{0.17em}25,\hspace{0.17em}\hspace{0.17em}5,\hspace{0.17em}\hspace{0.17em}1,\hspace{0.17em}\hspace{0.17em}...$
$b)\hspace{0.17em}\hspace{0.17em}25,\hspace{0.17em}\hspace{0.17em}19,\hspace{0.17em}\hspace{0.17em}13,\hspace{0.17em}\hspace{0.17em}...$
$c)\hspace{0.17em}\hspace{0.17em}4,\hspace{0.17em}\hspace{0.17em}9,\hspace{0.17em}\hspace{0.17em}16,\hspace{0.17em}\hspace{0.17em}...$
$d)\hspace{0.17em}\hspace{0.17em}50,\hspace{0.17em}\hspace{0.17em}60,\hspace{0.17em}\hspace{0.17em}70,\hspace{0.17em}\hspace{0.17em}...$
$e)\hspace{0.17em}\hspace{0.17em}\frac{1}{2},\hspace{0.17em}\hspace{0.17em}3,\hspace{0.17em}\hspace{0.17em}18,\hspace{0.17em}\hspace{0.17em}...$

${\displaystyle \ln (n^2+12)=\ln (-9n-2)}$

Decide whether ${\displaystyle z\left(\sqrt{-5}\right)}$ unique factorization domain or not (ring theory)

Write the system of equations in the image in matrix form
${\displaystyle x_1^{\prime }\left(t\right)=3x_1\left(t\right)-2x_2\left(t\right)+e^t{x}_3\left(t\right)}$
${\displaystyle x_2^{\prime }\left(t\right)=\sin \left(t\right)x_1\left(t\right)+\cos \left(t\right)x_3\left(t\right)}$
${\displaystyle x_3^{\prime }\left(t\right)=t^2{x}_1\left(t\right)+t{x}^2\left(t\right)+x_3\left(t\right)}$

How do you factor ${\displaystyle \left(64a^3{x}^3\right)-125}$ ?

Tell whether the function represents exponential growth or exponential decay. Then graph the function.
${\displaystyle y=3e^{2x}}$

Discuss the data modeling concepts in DynamoDB.

The explanation of how to multiply polynomialswhen neither is monomial with an examplw:
${\displaystyle (2x^2+4y^3)(3x^3+4y^2)}$

Describe what is meant by the augmented matrix of a system of linear equations.

The missing terms for the given polynomal p, q, r, and s such that
$q\ne 0,r\ne 0ands\ne 0,\frac{p}{q}-:\frac{r}{s}=\frac{ps}{qr}$

a) Find parametric equations for the line. (Use the parameter t.)
The line of intersection of the planes
x + y + z = 2 and x + z = 0
(x(t), y(t), z(t)) =
b) Find the symmetric equations.

Which of the following statements is/are correct about logistic regression? (There may be more than one correct answer) Logistic regression can be used for modeling the continuous response variable with dichotomous explanatory variable. Logistic regression can be used for modeling the dichotomous response variable with dichotomous explanatory variable Logistic regression can be used for modeling the continuous response variable with dichotomous or other type of categorical explanatory variables. Logistic regression can be used for modeling the dichotomous response variable with dichotomous and not for continuous explanatory variables. Logistic regression can be used for modeling the dichotomous response variable with categorical explanatory variables and/or continuous explanatory variables.

${\displaystyle 6^x+2=4^x}$

We need find:
The real zeros of polynomial function form an arithmetic sequence
$f(x)=x^4-4x^3-4x^2+16x.$

Need to calculate:The factorization of $3p^3-2p^2-9p+6$.

Determine whether the sequence is arithmetic. If so, identify the common difference 1, 2, 4, 8, 16, …