The assignment is to draw a contour diagram of an ordinary object of your choosing. the object should be somewhat a) the diagram should show the origin and at least 10 b) pick a point and calculate/estimate a directional irregularly shaped. contours. derivative in a direction of your choosing. while you are doing this, contemplate the thought that calculus is largely about how to measure quantitative change, and be sure to use units in your calculations. c) attach a photograph of the object. d) calculate/estimate the gradient at the same point. how does the gradient compare numerically to your directional derivative? how are the gradient and the level curve positioned with respect to each other? strive for accuracy, clarity, and focus. hopefully, this exercise will reveal a deep and technical understanding of the directional derivative. also, the word "slant" may come to have an enhanced meaning: that our understanding of it depends in large part on the direction in which we are looking. finally, try to enjoy the process of measuring, drawing, and thinking in this mathematical way!

What is the relationship between the wavelength of a wave and it's energy?

Explain to someone who knows nothing about fossils the study of invertebrate paleontology and how it scientists understand the history of the earth. be sure your explanation contains a minimum of two complete sentences.

The particle in a two-dimensional well is a useful model for the motion of electrons around the indole ring (3), the conjugated cycle found in the side chain of tryptophan. we may regard indole as a rectangle with sides of length 280 pm and 450 pm, with 10 electrons in the conjugated p system. as in case study 9.1, we assume that in the ground state of the molecule each quantized level is occupied by two electrons. (a) calculate the energy of an electron in the highest occupied level. (b) calculate the frequency of radiation that can induce a transition between the highest occupied and lowest unoccupied levels. 9.27 electrons around the porphine ring (4), the conjugated macrocycle that forms the structural basis of the heme group and the chlorophylls. we may treat the group as a circular ring of radius 440 pm, with 20 electrons in the conjugated system moving along the perimeter of the ring. as in exercise 9.26, assume that in the ground state of the molecule quantized each level is occupied by two electrons. (a) calculate the energy and angular momentum of an electron in the highest occupied level. (b) calculate the frequency of radiation that can induce a transition between the highest occupied and lowest unoccupied levels.