A pediatrician's office has two doors that are similar rectangles: one for adults and one for children. The larger door has a base of 4 ft and a height of 6.5 ft. The smaller door has a base of 3 ft. Which of the following best represents the length of a diagonal on the smaller door? C. 5.1 ft, D. 5.7 ft.

Hot coffee is contained in a cylindrical thermos bottle that is of length L=0.3 m and is lying on its side (horizontally). The coffee container consists of a glass flask of diameter $D_{1}=0.07 \mathrm{m}$, separated from an aluminum housing of diameter $D_{2}=0.08 \mathrm{m}$ by air at atmospheric pressure. The outer surface of the flask and the inner surface of the housing are silver coated to provide emissivities of $\varepsilon_{1}=\varepsilon_{2}=0.25$. If these surface temperatures are $T_{1}=75^{\circ} \mathrm{C}$ and $T_{2}=35^{\circ} \mathrm{C}$, what is the heat loss from the coffee?

A polynomial p(x) is even if p(-x)=p(x) and odd if p(-x)=-p(x). Let

$$E_n$$

and

$$O_n$$

denote the sets of even and odd polynomials in

$$P_n$$

. (a) Show that

$$E_n$$

is a subspace of

$$P_n$$

and find dim

$$E_n$$

. (b) Show that

$$O_n$$

is a subspace of

$$P_n$$

and find dim

$$O_n$$

.

A student claims that h(x) = 3x and j(x) = -3x are inverse functions. Is the student correct? Justify your answer.

Solve the matrix equation for X. [1 -1 1, 2 3 0, 0 2 -1] X = [2 - 1 5 7 8, 4 0 -3, 0 1, 3 5 -7 2 1]

Write the number in scientific notation. −5,222,145

Find the time required, to the nearest 0.1 year, for the investment to reach the desired goal. $2,000 invested at 6.75%, compounded daily; goal:$3,000.

Which compound gives a molecular ion at m/z = 122:

$$\mathrm { C } _ { 6 } \mathrm { H } _ { 5 } \mathrm { CH } _ { 2 } \mathrm { CH } _ { 2 } \mathrm { CH } _ { 3 }, \mathrm { C } _ { 6 } \mathrm { H } _ { 5 } \mathrm { COCH } _ { 2 } \mathrm { CH } _ { 3 } , \text { or } \mathrm { C } _ { 6 } \mathrm { H } _ { 5 } \mathrm { OCH } _ { 2 } \mathrm { CH } _ { 3 } ?$$

Write each set in set-builder notation.

$$M = \{ 1,3,5,7,9,11,13,17,19 \}$$

A vitreous silica optical fiber of diameter $100 \mu \mathrm{m}$ is used to send optical signals from a sensor placed deep inside a hydrogen chamber. The hydrogen is at a pressure of 20 bars. The mass diffusivity and solubility of the hydrogen in the glass fiber are $D_{\mathrm{AB}}=2.88 \times 10^{-15}\mathrm{m}^{2} / \mathrm{s}$ and $S=4.15 \times 10^{-3} \mathrm{kmol} / \mathrm{m}^{3} \cdot \mathrm { bar }$, respectively. Hydrogen diffusion into the fiber is undesirable, since it changes the spectral transmissivity and refractive index of the glass and can lead to failure of the detection system. (a) Determine the average hydrogen concentration in an uncoated optical fiber, $\bar{C}$, after 100 h of operation in the hydrogen environment. Determine the corresponding change in the refractive index, $\Delta n$, of the fiber. For vitreous silica, $\Delta n=\left(1.6 \times 10^{-3} \mathrm{m}^{3} / \mathrm{kmol}\right) \times \bar{C}$. (b) Determine the average hydrogen concentration and change in refractive index after 1 h and 10 h of operation in the hydrogen environment.

A man owns two building supply stores, one on the east side and one on the west side of a city. Two customers order some $\frac{1}{2}$-inch plywood. Customer A needs 50 sheets, and customer B needs 70 sheets. The east-side store has 80 sheets, and the west-side store has 45 sheets of this plywood in stock. The east-side store’s delivery costs per sheet are $0.50 to customer A and$0.60 to customer B. The west-side store’s delivery costs per sheet are $0.40 to customer A and$0.55 to customer B. How many sheets should be shipped from each store to each customer to minimize delivery costs?

r(t) is the position vector of a moving particle. Graph the curve and the velocity and acceleration vectors at the indicated time. Find the speed at that time. $\mathbf{r}(t)=-\cosh 2 t \mathbf{i}+\sinh 2 t \mathbf{j} ; t=0$

Give the name or condensed structural formula, as appropriate: 2,3-dimethylhexane

Solve the equation algebraically without using a calculator.

$$3x-4=6x+5$$