An element in plane stress is subjected to stresses $\sigma_x=5750\ \mathrm{psi}, \sigma_y=1100\ \mathrm{psi}$. and $\tau_{x y}=750\ \mathrm{psi}$. Determine the principal stresses and show them on a sketch of a properly oriented element.

An element exists in the gaseous state at room temperature and normal atmospheric pressure and is known to be one of the following: hydrogen, helium, nitrogen, oxygen, fluorine, chlorine, or neon. Identify the element based on the electrondot structure at right.

After you fill in the element on the line, write the type of element ( prefix, root, combining form, suffix) you have used below the lines. Fill in the blanks.

Bone cell that lives in a lacuna osteo/________

Identify the group $6 A$ element that best fits each of the following descriptions: (a) Is a metal (b) Is the most abundant element in the human body (c) Is the strongest oxidizing agent (d) Has the most negative electron affinity

Consider the following arrays.

$$\mathbf { A } = \left[ \begin{array} { c c c } { 1 } & { 4 } & { 2 } \\ { 2 } & { 4 } & { 100 } \\ { 7 } & { 9 } & { 7 } \\ { 3 } & { \pi } & { 42 } \end{array} \right] \quad \mathbf { B } = \ln ( \mathbf { A } )$$

Write MATLAB expressions to do the following. a. Select just the second row of B. b. Evaluate the sum of the second row of B. c. Multiply the second column of B and the rst column of A element by element. d. Evaluate the maximum value in the vector resulting from element-byelement multiplication of the second column of B with the rst column of A. e. Use element-by-element division to divide the rst row of A by the rst three elements of the third column of B. Evaluate the sum of the elements of the resulting vector.

(a) Prove by induction that given $n \in \mathbb{Z}_{+}$, every nonempty subset of $\{1, \ldots, n]$ has a largest element. (b) Explain why you cannot conclude from (a) that every nonempty subset of $\mathbb{Z}_{+}$ has a largest element.

List the element in the set.

$\{x \mid x$ is a whole number greater than 5$\}$

The mass of a radioactive element is 35 milligrams. The mass of the element decreases by 12.9% every year. a. Write a function that represents this situation. b. Predict the mass of the elements in 4 years. Round your answer to the nearest tenth.

The heating element of an electric dryer is rated at 4.1 kW when connected to a 240-V line. (a) What is the current in the heating element? Is 12-gauge wire large enough to supply this current? (b) What is the resistance of the dryer’s heating element at its operating temperature? (c) At 11 cents per kWh, how much does it cost per hour to operate the dryer?

A plumb bob does not hang exactly along a line directed to the center of the Earth's rotation. How much does the plumb bob deviate from a radial line at $35.0^{\circ}$ north latitude? Assume that the Earth is spherical.

Prove that every $(n+1)$-element subset of $\{1,2,...,2n\}$ contains two distinct integers $p$ and $q$ such that $p$ divides $q$. Hint: If $X$ is an $(n+1)$-element subset of $\{1,2,...,2n\}$, write the numbers in $X$ in the form $2^mk$, where $k$ is odd.

Provide the combining word element in the following statement.

___________graphy is an x-ray examination.

The useful life of a radial tire is normally distributed with a mean of 30,000 miles and a standard deviation of 5000 miles. The company makes 10,000 tires a month. About how many tires will last more than 40,000 miles?

The useful life of a radial tire is normally distributed with a mean of 30,000 miles and a standard deviation of 5000 miles. The company makes 10,000 tires a month. About how many tires will last between 25,000 and 35,000 miles?