Expert Answers to Algebra 2 Problems

Find the extreme values of f subject to both constraints. ${\displaystyle f(x,y,z)=x^2+y^2+z^2;x-y=1,y^2-z^2=1}$

Describe in words the region of ${\displaystyle R^3}$ represented by the equations or inequalities. x=5

Show that the series is convergent. How many terms of the series do we need to add in order to find the sum to the indicated accuracy? summation n=1 to infinity ${\displaystyle {(-1)}^n+\frac{1}{n^6}}$ (|error|<0.00005)

Solve the equation. (Find all solutions of the equation in the interval (0, ${\displaystyle 2\pi }$).
${\displaystyle \cos \left(2x\right)-\cos \left(x\right)=0}$

The given equation involves a power of the variable. Find all real solutions of the equation.
${\displaystyle 8x^2-64=0}$

The given equation involves a power of the variable. Find all real solutions of the equation.
${\displaystyle 3x^2=48}$

The process by which we determine limits of rational functions applies equally well to ratios containing noninteger or negative powers of x: Divide numerator and denominator by the highest power of x in the denominator and proceed from there. Find the limits.
${\displaystyle \underset{x\to -\mathrm{\infty }}{lim}\sqrt{\frac{x^2-5x}{x^3+x-2}}}$

Data points (x, y) are given. Is a linear, power, or exponential function appropriate for modeling these data?
x 2 4 6 8 10 12 y 0.08 0.12 0.18 0.26 0.35 0.53

Weather forecasting and severe weather warning systems rely on data collection, data analysis, and computer modeling. They also rely on fast communication systems. Explain why communication is an important part of forecasting and warning systems.

Is a linear, power, or exponential function appropriate for modeling these data?
x136101416 y7.224.612.380.990.410.26

Convert the function
${\displaystyle f\left(x\right)=x^2-4x+5}$
into vertex form.

The interval notation of the given inequality
GIven: ${\displaystyle \frac{2x-5}{2}<\frac{5x+1}{5}}$

a) Find the mass density of a proton, modeling it as a solid sphere of radius ${\displaystyle 1.00\times 10-15m.}$
b) What If ? Consider a classical model of an electron as a uniform solid sphere with the same density as the proton. Find its radius.
c) Imagine that this electron possesses spin angular momentum ${\displaystyle lw=\frac{h}{2}}$ because of classical rotation about the z axis. Determine the speed of a point on the equator of the electron.
d) State how this speed compares with the speed of light.

The value of m and b for the linear function ${\displaystyle f\left(x\right)=-8x}$

Whether the given data is linear or exponential and find the corresponding model.
Given: The table
$\begin{array}{|cccccc|}\hline x& 0& 1& 2& 3& 4\\ y& 2& 0.8& -0.4& -1.6& -2.8\\ \hline\end{array}$

The inverse, domain and range of inverse and verify that they are inverses of each other.
Given: The function ${\displaystyle f\left(x\right)=2x^3}$

The normal body temperature of a camel is ${\displaystyle {37}^{\circ }C}$. This temperature varies by up ${\displaystyle 3^{\circ }}$ throughout the day. Write and solve an absolute value inequality that represents the range of normal body temperatures (in degrees Celsius) of a camel throughout the day.
Given information:
Normal temperature of camel ${\displaystyle ={37}^{\circ }C}$
This temperature can vary by up to ${\displaystyle 3^{\circ }C}$

A stained glass artist has a fixed cost of $150. It costs the artist $15 to procedure each piece, but each piece sells for $35. The equation ${\displaystyle C=150+15n}$ represents the total cost, C, for producing n pieces. The total revenue for n pieces is determined by the equation ${\displaystyle R=35n}$. What constaint is necessary to include when modeling this situation?
- n must be greater than or equal to 0, since the number of items created cannot be negative.
- R must be greater than or equal to 35, since the number of items will always be positive.
- R-C must be less than or equal to 0, since the artist wants to make money.
- C must be 150, since there is a fixed cost to produce each piece.

Your uncle purchases a new car for $22,499. The value of the car decreases by 11% each year.
Write the exponential equation that models the car's value after t years.

Show that f is inverse of g and vice-versa, if
$f(x)=x-6$ and $g(x)=x+6$