Expert Answers to Algebra 2 Problems

Modeling: Draw models to represents ${\displaystyle \frac{3}{4}}$ and ${\displaystyle 2\frac{3}{5}.}$

Assume that an object moves on a trajectory according to the equations ${\displaystyle x\left(t\right)=t+\cos t,y\left(t\right)=t-\sin t}$. Find the magnitude of the acceleration vector.

Use a calculator with a $y^x$ key or a key to solve: India is currently one of the world’s fastest-growing countries. By 2040, the population of India will be larger than the population of China, by 2050, nearly one-third of the world’s population will live in these two countries alone. The exponential function $f(x)=574(1.026{)}^x$ models the population of India, f(x), in millions, x years after 1974.
a. Substitute 0 for x and, without using a calculator, find India’s population in 1974.
b. Substitute 27 for x and use your calculator to find India’s population, to the nearest million, in the year 2001 as modeled by this function.
c. Find India’s population, to the nearest million, in the year 2028 as predicted by this function.

Use exponential regression to find a function that models the data. $\begin{array}{|cccccc|}\hline x& 1& 2& 3& 4& 5\\ f(x)& 14& 7.1& 3.4& 1.8& 0.8\\ \hline\end{array}$

Find and solve the exact value of each of the following under the given conditions $\tan \alpha =-\frac{7}{24},\alpha$ lies in quadrant 2,
$\cos \beta =\frac{3}{4},\beta$ lies in quadrant 1
a. $\sin (\alpha +\beta )$
b. $\cos (\alpha +\beta )$
c. $\tan (\alpha +\beta )$

Create equations to represent a relationship between quantities.
Define appropriate quantities for $\cdots$ descriptive modeling.
Two trains leave a station heading in opposite directions. The first train travels at two-thirds the rate of the second train. If the trains are 360 miles apart after three hours, then at what rate (in mph) was each train traveling?

The exponential models describe the population of the indicated country, A, in millions, t years after 2010. Which countries have a decreasing population? By what percentage is the population of these countries decreasing each year?
Country B ${\displaystyle A=1193.1e^{0.006t}}$
Country C ${\displaystyle A=36.5e^{0.017t}}$
Country D ${\displaystyle A=121.7e^{-0.005t}}$
Country E ${\displaystyle A=145.3e^{-0.004t}}$

Determine whether each function is an example of exponential growth or decay. Then find the y-intercept. $y=100(0.25{)}^x$

${\displaystyle \log 8(28k-20)+15=18}$

${\displaystyle (3{\sqrt{-\left\{\frac{1}{8}\right\}}}^3+3\left(\frac{3}{4}\right)}$

Answer true or false to each of the following statements and explain your answers. The term “linear” in “multiple linear regression” refers to using only first-degree terms in the predictor variables.

Perform the indicated divisions of polynomials by monomials.
$\frac{-35x^5-42x^3}{-7x^2}$

If x is a real number, for what values of x is the equation $(3x-6)(x-2{)}^{-1}=3$ true.
F. all values of x G. some values of x H. no values of x l. impossible to determine

graph the following. be sure to include the ordered pairs, including any existing x-intercepts (logarithms) and y-intercept (exponentials) along with asymptotes.
$f(x)=2^{(}x-3)-3$

Use the properties of logarithms to rewrite each expression as the logarithm of a single expression. Be sure to use positive exponents and avoid radicals.
a. $2\ln 4x^3+3\ln y-\frac{1}{3}\ln z^6$
b. $\ln (x^2-16)-\ln (x+4)$

Enzo's profit over the last few months has been failing. In December, he made $900. In January, his profit was $500, and in March, he lost $300. is the sequence that represents his profit arithmetic? if it is, what is the recursive formula for the sequence?

Suppose that $\{a1,a2,a3,\cdots \}$ is an arithmetic sequence with common difference d. Explain why $\{a1,a3,a5,\cdots \}$ is also an arithmetic sequence.

Consider the following sequence.
$s_n=2n-1$
(a) Find the first three terms of the sequence whose nth term is given.
$s_1=$
$s_2=$
$s_3=$
(b) Classify the sequence as arithmetic, geometric, both, or neither. arithmetic, geometric bothneither
If arithmetic, give d, if geometric, give r, if both, give d followed by r. (If both, enter your answers as a comma-separated list. If neither, enter NONE.)

Complete Factorization Factor the polynomial completely, and find all its zeros.State the multiplicity of each zero.
$P(x)=x^4+2x^2+1$

Write an equation to solve each problem. Two brothers are saving money to buy tickets to a concert. Their combined savings is $\mathrm{\$}55$. One brother ha s $\mathrm{\$}15$ more than the other. How much has each saved?