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Solar Eclipse on Mars (Refer to Exercise 69.) The sun’s distance from the surface of Mars is approximately 142,000,000 mi. One of Mars’ two moons, Phobos, has a maximum diameter of 17.4 mi. (Source: World Almanac and Book of Facts.)
Calculate the maximum distance, to the nearest hundred miles, that the moon Phobos can be from Mars for a total eclipse of the sun to occur on Mars.
Phobos is approximately 5800 mi from Mars. Is it possible for Phobos to cause a total eclipse on Mars?
Solar Eclipse on Earth The sun has a diameter of about 865,000 mi with a maximum distance from Earth's surface of about 94,500,000 mi. The moon has a smaller diameter of 2159 mi. For a total solar eclipse to occur, the moon must pass between Earth and the sun. The moon must also be close enough to Earth for the moon’s umbra (shadow) to reach the surface of Earth. (Source: Karttunen, H., P. Kröger, H. Oja, M. Putannen, and K. Donners, Editors, Fundamental Astronomy, Fourth Edition, Springer-Verlag.)
Calculate the maximum distance, to the nearest thousand miles, that the moon can be from Earth and still have a total solar eclipse occur. (Hint: Use similar
The closest approach of the moon to Earth’s surface was 225,745 mi and the farthest was 251,978 mi. (Source: World Almanac and Book of Facts.) Can a total solar eclipse occur every time the moon is between Earth and the sun?
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Chapter 1 Solutions
Trigonometry plus MyLab Math with Pearson eText -- Access Card Package (11th Edition)
- Solve for theta 3 and 4arrow_forwardC III https://www-awu.aleks.com/alekscgi/x/Isl.exe/1o_u-IgNslkr7j8P3jH-li-WkWxK Zm85LW27IRVU66k591 O Trigonometric Functions Sketching the graph of y = a sin(x) or y = a cos(x) Graph the trigonometric function. 3 =sin.x 2 Plot all points corresponding to x-intercepts, minima, and maxima within one cycle. Then cli Explanation Check Esc F1 Search F2 #3 72 F3 4 F4 DII F5 % 5 A G F6 لarrow_forwardIf 0 = 0 = 10元 3 10元 then find exact values for the following. If the trigonometric function is undefined fo enter DNE. > 3 sec(0) equals csc(0) equals tan(0) equals cot (0) equals من Question Help: Video B من B Submit Question Jump to Answerarrow_forward
- Question 9 1 5 4 3 2 1 -8 -7 -05 -4 -3 -2 1 1 2 3 4 5 6 7 8 -1 7 -2 -3 -4 -5+ 1-6+ For the graph above, find the function of the form -tan(bx) + c f(x) =arrow_forwardQuestion 8 5 4 3 2 1 -8 -7 -6 -5/-4 -3 -2 -1, 1 2 3 4 5 6 7/8 -1 -2 -3 -4 -5 0/1 pt 3 98 C -6 For the graph above, find the function of the form f(x)=a tan(bx) where a=-1 or +1 only f(x) = = Question Help: Video Submit Question Jump to Answerarrow_forward6+ 5 -8-7-0-5/-4 -3 -2 -1, 4 3+ 2- 1 1 2 3/4 5 6 7.18 -1 -2 -3 -4 -5 -6+ For the graph above, find the function of the form f(x)=a tan(bx) where a=-1 or +1 only f(x) =arrow_forward
- Question 10 6 5 4 3 2 -π/4 π/4 π/2 -1 -2 -3- -4 -5- -6+ For the graph above, find the function of the form f(x)=a tan(bx)+c where a=-1 or +1 only f(x) = Question Help: Videoarrow_forwardThe second solution I got is incorrect. What is the correct solution? The other thrree with checkmarks are correct Question 19 Score on last try: 0.75 of 1 pts. See Details for more. Get a similar question You can retry this question below Solve 3 sin 2 for the four smallest positive solutions 0.75/1 pt 81 99 Details T= 1.393,24.666,13.393,16.606 Give your answers accurate to at least two decimal places, as a list separated by commas Question Help: Message instructor Post to forum Submit Questionarrow_forwardd₁ ≥ ≥ dn ≥ 0 with di even. di≤k(k − 1) + + min{k, di} vi=k+1 T2.5: Let d1, d2,...,d be integers such that n - 1 Prove the equivalence of the Erdos-Gallai conditions: for each k = 1, 2, ………, n and the Edge-Count Criterion: Σier di + Σjeл(n − 1 − d;) ≥ |I||J| for all I, JC [n] with In J = 0.arrow_forward
- T2.4: Let d₁arrow_forwardT2.3: Prove that there exists a connected graph with degrees d₁ ≥ d₂ >> dn if and only if d1, d2,..., dn is graphic, d ≥ 1 and di≥2n2. That is, some graph having degree sequence with these conditions is connected. Hint - Do not attempt to directly prove this using Erdos-Gallai conditions. Instead work with a realization and show that 2-switches can be used to make a connected graph with the same degree sequence. Facts that can be useful: a component (i.e., connected) with n₁ vertices and at least n₁ edges has a cycle. Note also that a 2-switch using edges from different components of a forest will not necessarily reduce the number of components. Make sure that you justify that your proof has a 2-switch that does decrease the number of components.arrow_forwardT2.2 Prove that a sequence s d₁, d₂,..., dn with n ≥ 3 of integers with 1≤d; ≤ n − 1 is the degree sequence of a connected unicyclic graph (i.e., with exactly one cycle) of order n if and only if at most n-3 terms of s are 1 and Σ di = 2n. (i) Prove it by induction along the lines of the inductive proof for trees. There will be a special case to handle when no d₂ = 1. (ii) Prove it by making use of the caterpillar construction. You may use the fact that adding an edge between 2 non-adjacent vertices of a tree creates a unicylic graph.arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
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