 Recent questions in Matrices
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### If the roots of $$ax^{2}+bx+c=0$$ are $$\frac{3}{2},\frac{4}{3}$$ then $$(a+b+c)^{2} =$$

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ANSWERED ### For each topic, decide how a scatterplot of the data would likely look. Explain your reasoning. Speed of a runner and amount of time to complete a race

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ANSWERED ### Investigate the change in the graph of a sinusoidal function of the form and $$= \sin x$$ or and$$= \cos x$$ when multiplied by a polynomial function. Describe the behavior of the graph of and$$=x^2 \sin x$$ in relation to the graphs of and$$=x^2\ and\ =−x2a$$.

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ANSWERED ### For the following exercises, enter the data from each table into a graphing calculator and graph the resulting scatter plots. Determine whether the data from the table could represent a function that is linear, exponential, or logarithmic. $$\begin{array}{|c|c|c|c|c|c|c|c|c|} \hline x & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 \\ \hline f(x) & 2.4 & 2.88 & 3.456 & 4.147 & 4.977 & 5.972 & 7.166 & 8.6 & 10.32 & 12.383 \\ \hline \end{array}$$

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ANSWERED ### Use the definition of continuity and the properties of limits to show that the function is continuous on the given interval. $$\displaystyle{g{{\left({x}\right)}}}={2}\sqrt{{{3}}}-{x},{\left(-\infty,{3}\right]}$$

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ANSWERED ### Marilda has a block of modeling clay that is 8 inches by 5 inches by 3 inches. She is experimenting with different shapes that can be made from the clay. Give your answers to the nearest tenth. What is the volume of the clay?

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ANSWERED ### Substitution and elimination, and matrix methods such as the Gauss-Jordan method and Cramer's rule. Use each method at least once when solving the systems below. include solutions with nonreal complex number components. For systems with infinitely many solutions, write the solution set using an arbitrary variable. $$2x+3y+4z=3$$ $$-4x+2y-6z=2$$ $$4x+3z=0$$

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ANSWERED ### Transform the given differential equation or system into an equivalent system of first-order differential equations.

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ANSWERED ### One cake recipe calls for $$\displaystyle{\frac{{{2}}}{{{3}}}}$$ cup of sugar. Another recipe calls for $$\displaystyle{1}{\frac{{{1}}}{{{4}}}}$$ cups of sugar. How many cups of sugar are needed to make both cakes?

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ANSWERED ### Tooth decay occurs when tooth enamel wears away over time. It exponential decay models the change in the number of dentists in the United States over time, do you think the number of dentists in the United States is increasing or decreasing?

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ANSWERED ### A motorcycle is traveling at 42 miles per hour on tires that measure 1.2 feet in diameter. Find the approximate angular speed of the tires in radians per minute.

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ANSWERED ### A scatterplot shows a moderately strong negative linear relationship. Use your calculator or software to find the equation of the least-squares regression line.

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ANSWERED ### Overproduction of uric acid in the body can be an indication of cell breakdown. This may be an advance indication of illness such as gout, leukemia, or lymphoma. Over a period of months, an adult male patient has taken eight blood tests for uric acid. The mean concentration was x¯=5.35mg/dl. The distribution of uric acid in healthy adult males can be assumed to be normal with σ=1.85mg/dlσ=1.85mg/dl. Give a brief interpretation of your results in the context of this problem.

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ANSWERED ### A chef has one cheese that contains 45% fat and another cheese that contains 20% fat. How many grams of each cheese should she use in order to obtain 30 grams of a cheese mixture that is 30% fat?

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ANSWERED ### Penguins spend almost 75% of their lives in the sea. An Emperor Penguin in the wild has a life span of about 18 years. About how many years does this penguin spend In the sea?

Matrices
ANSWERED ### A matrix is defined as ''a rectangular array of numbers''. Many of the arrays that you have worked have additional features, such as labels on the rows and columns or entries that are numbers with units. An array with additional features is technically not a matrix, instead we would call it a table. The difference between a matrix and a table is not vitally important in this unit, so we have worked with the underlying array of numbers and not worried about this technical detail. In more advanced courses in mathematics, like Linear Algebra, it will be important to be very precise about matrices. For now, describe and give examples of some of the ways a table can be different from a matrix. In your description and examples, be sure to include differences related to at least these three characteristics: entries, labels, and operations.

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ANSWERED ### How close to 0 do we need to take x so that $$(x^{2}+6x+9)<9.001?$$

Matrices
ANSWERED ### One of the five given matrices represents an orthogonal projection onto a line and another represents a reflection about line. Identify both and briefly justify your choice. ANSWERED 