The function $T$ given by $T(d)=10 d+20$ can be used to determine the temperature $T$, in degrees Celsius, at a depth $d$, in kilometers, inside the earth. $\\$ a) Find$T(5), T(20)$, and$T(1000)$.$ $b) The radius of the earth is about$5600 $$ \mathrm{~km}$. Use this fact to determine the domain of the function. $$

Write the first six terms of the geometric sequence with the first term, $a_{1}$, and common ratio, r. $a_{1}=2, r=3$

What 2 by 2 matrix P₁ projects the vector (x, y) onto the x axis to produce (x, 0)? What matrix P₂ projects onto the y axis to produce (0, y)? If you multiply (5, 7) by P₁ and then multiply by P₂, you get () and ().

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Determine the horizontal component, $u_B$, of the displacement of point $B$ due to flexure of the curved beam shown in Fig. . Assume that the radius of curvature, $R$, of the centerline of the bar is large relative to the radial depth of the cross section so that the straight-beam elastic flexure formula holds. Express your answer in terms of $P, R, E$, and $I$.

In a study of frost penetration it was found that the temperature T at time t (measured in days) at a depth x (measured in feet) can be modeled by the function T(x,t)=T0+T1e^-λx sin(wt-λx) where w = 2π/365 and λ is a positive constant. Find ∂T/∂t. What is its physical significance?

To fill a child's inflatable wading pool, you use a garden hose with a diameter of $2.9 \mathrm{~cm}$. Water flows from this hose with a speed of $1.3 \mathrm{~m} / \mathrm{s}$. How long will it take to fill the pool to a depth of $26 \mathrm{~cm}$ if the pool is circular and has a diameter of $2.0 \mathrm{~m}$ ?

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What was the first neurotransmitter discovered in the CNS?

Near a buoy, the depth of a lake at the point with coordinates $(x, y)$ is $z = 200 + 0.02x^2 - 0.001y^3,$ where $x, y,$ and $z$ are measured in meters. A fisherman in a small boat starts at the point (80, 60) and moves toward the buoy, which is located at (0, 0). Is the water under the boat getting deeper or shallower when he departs? Explain.

A new store is being built in the shape of a rectangle with a parking lot in the shape of an isosceles trapezoid. The parking lot and the store will share a side. The area of the store is to be 154 square meters. If the depth is given as $\frac{1}{14} x^2+\frac{15}{14} x$, find the value of x.

A 7

B 11

C 14

D 28

At ordinary body temperature $\left(37^{\circ} \mathrm{C}\right)$ the solubility of $\mathrm{N}_2$ in water in contact with air at ordinary atmospheric pressure $(1.0 \mathrm{~atm})$ is $0.015 \mathrm{~g} / \mathrm{L}$. Air is approximately $78 \mathrm{~mol} \% \mathrm{~N}_2$. Calculate the number of moles of $\mathrm{N}_2$ dissolved per liter of blood, which is essentially an aqueous solution. At a depth of $100 \mathrm{ft}$ in water, the pressure is $4.0 \mathrm{~atm}$. What is the solubility of $\mathrm{N}_2$ from air in blood at this pressure? If a scuba diver suddenly surfaces from this depth, how many milliliters of $\mathrm{N}_2$ gas, in the form of tiny bubbles, are released into the bloodstream from each liter of blood?

Why do legislators vote for spending projects in districts that are not their own?

The italicized portion of each sentence below contains some flaw. Select the answer that best corrects the flaw.

Monk Pond is much more shallower than Goodman's Lake.

F. lesser in depth then

G. much less deeper than

H. much more shallow than

J. much less deep than