A kilogram of water on the side of Earth nearest the moon is gravitationally attracted to the moon with a greater force is gravitationally attracted to the moon with a greater force than a kilogram of water on the side of Earth farthest from the moon. The difference in force per mass, the tidal force, is approximated by

$$F _ { T } = \frac { 4 G M R } { d ^ { 3 } }$$

where G is the gravitational constant, M is the mass of the moon, R is the radius of Earth, and d is the distance between the centers of the moon and Earth. Even a 1-kg melon held above your head exerts a tidal force on you. The above equation, however, is a good approximation only when d is much larger than R. The distance d between the center of the melon and your center is only about twice R. So the general tidal force equation (the source of the above equation) must be used, which is

$$F _ { \mathrm { T } } = ( 4 G M d R ) / \left( d ^ { 2 } - R ^ { 2 } \right) ^ { 2 }$$

Use this to calculate the melon‘s

$$F_T$$

on you. Here M = 1 kg, and if you’re 2 m tall, R = 1 m, and d = 2 m. How does this compare with the tidal force of the moon on you?

Which provisions of the Constitution provide for checks and balances between the branches of government 1. Legislative Branch 2. Executive Branch 3. Judicial Branch.

A kilogram of water on the side of Earth nearest the moon is gravitationally attracted to the moon with a greater force than a kilogram of water on the side of Earth farthest from the moon. The difference in force per mass, the tidal force, is approximated by

$$F _ { \mathrm { T } } = \frac { 4 G M R } { d ^ { 3 } }$$

where G is the gravitational constant, M is the mass of the moon, R is the radius of Earth, and d is the distance between the centers of the moon and Earth. Calculate

$$F_T$$

of the moon on Earth in units

$$\mathrm { N } / \mathrm { kg } . ( M = 7.35 \times 10 ^ { 22 } \mathrm { kg } , R = 6.4 \times 10 ^ { 6 } \mathrm { m }, \text {and} d = 3.85 \times 10 ^ { 8 } \mathrm { m } )$$

Use a ruler to draw ray diagrams to locate the images of the following objects: (a) an object that is 30 cm from a convex lens of $+10-\mathrm{cm}$ focal length, (b) an object that is 14 cm from the same lens, and (c) an object that is 5 cm from the same lens. (Choose a scale so that your drawing fills a significant portion of the width of a paper.) Measure the image locations on your drawings and indicate if they are real or virtual,upright or inverted.

Solve. Use substitution to check. $\frac { 3 } { 7 } = - \frac { 9 } { 14 } d$

How would you say 'the princess that was jealous (imperfect) of the mirror' in Spanish?

Find k in the expansion $(m-2 n)^{10}=m^{10}-20 m^{9} n+k m^{8} n^{2}-\ldots+1024 n^{10}$.

A kilogram of water on the side of Earth nearest the moon is gravitationally attracted to the moon with a greater force than a kilogram of water on the side of Earth farthest from the moon. The difference in force per mass, the tidal force, is approximated by

$$F _ { \mathrm { T } } = \frac { 4 G M R } { d ^ { 3 } }$$

where G is the gravitational constant, M is the mass of the moon, R is the radius of Earth, and d is the distance between the centers of the moon and Earth. If you stand on Earth directly under the moon, the moon’s tidal pull will slightly stretch you, pulling harder on your head than on your feet. Your head and feet are not part apart like Earth’s oceans are, so R in the tidal force equation is only about half your height rather than half Earth’s diameter. Approximately the

$$F_T$$

of the moon on you.

A sleeping bag weighs 8 pounds. Your backpack and sleeping bag together weigh 31 pounds. Write an equation to determine whether the backpack without the sleeping bag weighs 25 or 23 pounds .

Two sides and an angle are given. Determine whether the given information results in one triangle, two triangles, or no triangle at all. Solve any triangle(s) that results. $a=3, b=2, A=50^{\circ}$

Determine whether the Mean Value Theorem applies for the functions over the given interval [a, b]. Justify your answer.

$$y=5+|x| \text { over }[-1,1]$$

The number N of bacteria present in a culture at time t (in hours) obeys the law of uninhibited growth $N(t)=1000 e^{0.01 t}.$ What is the growth rate of the bacteria?

Determine whether the given function is linear, exponential, or neither. For those that are linear functions, find a linear function that models the data; for those that are exponential, find an exponential function that models the data.

$$\begin{array}{|cc|}\hline x & {g(x)} \\ \hline-1 & {6} \\ 0 & {1} \\ {1} & {0} \\ {2} & {3} \\ {3} & {10} \\ \hline\end{array}$$

An industrial load consumes 44 kW at 0.82 pf lagging from a 240$\angle 0^{\circ}$-V rms 60-Hz line. A bank of capacitors totaling 600 $\mu$F is available. If these capacitors are placed in parallel with the load, what is the new power factor of the total load?