Algebra and Trigonometry
1st Edition
ISBN: 9781938168376
Author: Jay Abramson
Publisher: OpenStax
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Textbook Question
Chapter 12.1, Problem 19SE
For the following exercises, write the equation of an ellipse in standard form, and identify the end points of the major and minor axes as well as the foci.
19.
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d₁ ≥ ≥ 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.
T2.4: Let d₁
T2.3: 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.
Chapter 12 Solutions
Algebra and Trigonometry
Ch. 12.1 - What is the standard form equation of the ellipse...Ch. 12.1 - What is the standard form equation of the ellipse...Ch. 12.1 - Graph the ellipse given by the equation x236+y24=1...Ch. 12.1 - Graph the ellipse given by the equation...Ch. 12.1 - Graph the ellipse given by the equation...Ch. 12.1 - Express the equation of the ellipse given in...Ch. 12.1 - Suppose a whispering chamber is 480 feet long and...Ch. 12.1 - Define an ellipse in terms of its foci.Ch. 12.1 - Where must the foci of an ellipse lie?Ch. 12.1 - What special case of the ellipse do we have when...
Ch. 12.1 - For the special case mentioned in the previous...Ch. 12.1 - What can be said about the symmetry of the graph...Ch. 12.1 - For the following exercises, determine whether the...Ch. 12.1 - For the following exercises, determine whether the...Ch. 12.1 - For the following exercises, determine whether the...Ch. 12.1 - For the following exercises, determine whether the...Ch. 12.1 - For the following exercises, determine whether the...Ch. 12.1 - For the following exercises, write the equation of...Ch. 12.1 - For the following exercises, write the equation of...Ch. 12.1 - For the following exercises, write the equation of...Ch. 12.1 - For the following exercises, write the equation of...Ch. 12.1 - For the following exercises, write the equation of...Ch. 12.1 - For the following exercises, write the equation of...Ch. 12.1 - For the following exercises, write the equation of...Ch. 12.1 - For the following exercises, write the equation of...Ch. 12.1 - For the following exercises, write the equation of...Ch. 12.1 - For the following exercises, write the equation of...Ch. 12.1 - For the following exercises, write the equation of...Ch. 12.1 - For the following exercises, write the equation of...Ch. 12.1 - For the following exercises, write the equation of...Ch. 12.1 - For the following exercises, write the equation of...Ch. 12.1 - For the following exercises, write the equation of...Ch. 12.1 - For the following exercises, write the equation of...Ch. 12.1 - ALGEBRAIC For the following exercises, find the...Ch. 12.1 - For the following exercises, find the foci for the...Ch. 12.1 - For the following exercises, find the foci for the...Ch. 12.1 - For the following exercises, find the foci for the...Ch. 12.1 - For the following exercises, find the foci for the...Ch. 12.1 - For the following exercises, graph the given...Ch. 12.1 - For the following exercises, graph the given...Ch. 12.1 - For the following exercises, graph the given...Ch. 12.1 - For the following exercises, graph the given...Ch. 12.1 - For the following exercises, graph the given...Ch. 12.1 - For the following exercises, graph the given...Ch. 12.1 - For the following exercises, graph the given...Ch. 12.1 - For the following exercises, graph the given...Ch. 12.1 - For the following exercises, graph the given...Ch. 12.1 - For the following exercises, graph the given...Ch. 12.1 - For the following exercises, graph the given...Ch. 12.1 - For the following exercises, graph the given...Ch. 12.1 - For the following exercises, graph the given...Ch. 12.1 - For the following exercises, graph the given...Ch. 12.1 - For the following exercises, graph the given...Ch. 12.1 - For the following exercises, graph the given...Ch. 12.1 - For the following exercises, use the given...Ch. 12.1 - For the following exercises, use the given...Ch. 12.1 - For the following exercises, use the given...Ch. 12.1 - For the following exercises, graph the given...Ch. 12.1 - For the following exercises, given the graph of...Ch. 12.1 - For the following exercises, given the graph of...Ch. 12.1 - For the following exercises, given the graph of...Ch. 12.1 - For the following exercises, given the graph of...Ch. 12.1 - For the following exercises, given the graph of...Ch. 12.1 - For the following exercises, find the area of the...Ch. 12.1 - For the following exercises, find the area of the...Ch. 12.1 - For the following exercises, find the area of the...Ch. 12.1 - For the following exercises, find the area of the...Ch. 12.1 - For the following exercises, find the area of the...Ch. 12.1 - Find the equation of the ellipse that will just...Ch. 12.1 - Find the equation of the ellipse that will just...Ch. 12.1 - An arch has the shape of a semi-ellipse (the top...Ch. 12.1 - An arch has the shape of a semi-ellipse. The arch...Ch. 12.1 - A bridge is to be built in the shape of a...Ch. 12.1 - A person in a whispering gallery standing at one...Ch. 12.1 - A person is standing 8 feet from the nearest wall...Ch. 12.2 - Identify the vertices and foci of the hyperbola...Ch. 12.2 - What is the standard form equation of the...Ch. 12.2 - What is the standard form equation of the...Ch. 12.2 - Graph the hyperbola given by the equation...Ch. 12.2 - Graph the hyperbola given by the standard form of...Ch. 12.2 - A design for a cooling tower project is shown in...Ch. 12.2 - Define a hyperbola in terms of its foci.Ch. 12.2 - What can we conclude about a hyperbola if its...Ch. 12.2 - What must be true of the foci of a hyperbola?Ch. 12.2 - If the transverse axis of a hyperbola is vertical,...Ch. 12.2 - Where must the center of hyperbola be relative to...Ch. 12.2 - For the following exercises, determine whether the...Ch. 12.2 - For the following exercises, determine whether the...Ch. 12.2 - For the following exercises, determine whether the...Ch. 12.2 - For the following exercises, determine whether the...Ch. 12.2 - For the following exercises, determine whether the...Ch. 12.2 - For the followung exericses, write the equation...Ch. 12.2 - For the following exercises, write the equation...Ch. 12.2 - For the following exercises, write the equation...Ch. 12.2 - For the following exercises, write the equation...Ch. 12.2 - For the following exercises, write the equation...Ch. 12.2 - For the following exercises, write the equation...Ch. 12.2 - For the following exercises, write the equation...Ch. 12.2 - For the following exercises, write the equation...Ch. 12.2 - For the following exercises, write the equation...Ch. 12.2 - For the following exercises, write the equation...Ch. 12.2 - For the following exercises, write the equation...Ch. 12.2 - For the following exercises, write the equation...Ch. 12.2 - For the following exercises, write the equation...Ch. 12.2 - For the following exercises, write the equation...Ch. 12.2 - For the following exercises, write the equation...Ch. 12.2 - For the following exercises, find the equations of...Ch. 12.2 - For the following exercises, find the equations of...Ch. 12.2 - For the following exercises, find the equations of...Ch. 12.2 - For the following exercises, find the equations of...Ch. 12.2 - For the following exercises, find the equations of...Ch. 12.2 - For the following exercise, sketch a graph of the...Ch. 12.2 - For the following exercise, sketch a graph of the...Ch. 12.2 - For the following exercise, sketch a graph of the...Ch. 12.2 - For the following exercise, sketch a graph of the...Ch. 12.2 - For the following exercise, sketch a graph of the...Ch. 12.2 - For the following exercise, sketch a graph of the...Ch. 12.2 - For the following exercise, sketch a graph of the...Ch. 12.2 - For the following exercise, sketch a graph of the...Ch. 12.2 - For the following exercise, sketch a graph of the...Ch. 12.2 - For the following exercise, sketch a graph of the...Ch. 12.2 - For the following exercise, sketch a graph of the...Ch. 12.2 - For the following exercise, sketch a graph of the...Ch. 12.2 - For the following exercise, sketch a graph of the...Ch. 12.2 - For the following exercise, sketch a graph of the...Ch. 12.2 - For the following exercise, given information...Ch. 12.2 - For the following exercise, given information...Ch. 12.2 - For the following exercise, given information...Ch. 12.2 - For the following exercise, given information...Ch. 12.2 - For the following exercise, given information...Ch. 12.2 - For the following exercise, given information...Ch. 12.2 - For the following exercise, given information...Ch. 12.2 - For the following exercise, given information...Ch. 12.2 - For the following exercise, given information...Ch. 12.2 - For the following exercise, given information...Ch. 12.2 - For the following exercise, given information...Ch. 12.2 - For the following exercises, express the equation...Ch. 12.2 - For the following exercises, express the equation...Ch. 12.2 - For the following exercises, express the equation...Ch. 12.2 - For the following exercises, express the equation...Ch. 12.2 - For the following exercises, express the equation...Ch. 12.2 - For the following exercises, a hedge is to be...Ch. 12.2 - For the following exercises, a hedge is to be...Ch. 12.2 - For the following exercises, a hedge is to be...Ch. 12.2 - For the following exercises, a hedge is to be...Ch. 12.2 - For the following exercises, a hedge is to be...Ch. 12.2 - For the following exercises, assume an object...Ch. 12.2 - For the following exercises, assume an object...Ch. 12.2 - For the following exercises, assume an object...Ch. 12.2 - For the following exercises, assume an object...Ch. 12.2 - For the following exercises, assume an object...Ch. 12.3 - Graph y2=16x . Identify and label the focus,...Ch. 12.3 - Graph x2=8y . Identify and label the focus,...Ch. 12.3 - What is the equation for the parabola with focus...Ch. 12.3 - Graph (y+1)2=4(x8) . Identify and label the...Ch. 12.3 - Graph (x+2)2=20(y3) . Identify and label the...Ch. 12.3 - Balcony-sized solar cookers have been designed for...Ch. 12.3 - Define a parabola in terms of its focus and...Ch. 12.3 - If the equation of a parabola is written in...Ch. 12.3 - If the equation of a parabola is written in...Ch. 12.3 - What is the effect on the graph of a parabola if...Ch. 12.3 - As the graph of a parabola becomes wider, what...Ch. 12.3 - For the following exercises, determine whether the...Ch. 12.3 - For the following exercises, determine whether the...Ch. 12.3 - For the following exercises, determine whether the...Ch. 12.3 - For the following exercises, determine whether the...Ch. 12.3 - For the following exercises, determine whether the...Ch. 12.3 - For the following exercises, determine whether the...Ch. 12.3 - For the following exercises, rewrite the given...Ch. 12.3 - For the following exercises, rewrite the given...Ch. 12.3 - For the following exercises, rewrite the given...Ch. 12.3 - For the following exercises, rewrite the given...Ch. 12.3 - For the following exercises, rewrite the given...Ch. 12.3 - For the following exercises, rewrite the given...Ch. 12.3 - For the following exercises, rewrite the given...Ch. 12.3 - For the following exercises, rewrite the given...Ch. 12.3 - For the following exercises, rewrite the given...Ch. 12.3 - For the following exercises, rewrite the given...Ch. 12.3 - For the following exercises, rewrite the given...Ch. 12.3 - For the following exercises, rewrite the given...Ch. 12.3 - For the following exercises, rewrite the given...Ch. 12.3 - For the following exercises, rewrite the given...Ch. 12.3 - For the following exercises, rewrite the given...Ch. 12.3 - For the following exercises, rewrite the given...Ch. 12.3 - For the following exercises, rewrite the given...Ch. 12.3 - For the following exercises, rewrite the given...Ch. 12.3 - For the following exercises, rewrite the given...Ch. 12.3 - For the following exercises, graph the parabola,...Ch. 12.3 - For the following exercises, graph the parabola,...Ch. 12.3 - For the following exercises, graph the parabola,...Ch. 12.3 - For the following exercises, graph the parabola,...Ch. 12.3 - For the following exercises, graph the parabola,...Ch. 12.3 - For the following exercises, graph the parabola,...Ch. 12.3 - For the following exercises, graph the parabola,...Ch. 12.3 - For the following exercises, graph the parabola,...Ch. 12.3 - For the following exercises, graph the parabola,...Ch. 12.3 - For the following exercises, graph the parabola,...Ch. 12.3 - For the following exercises, graph the parabola,...Ch. 12.3 - For the following exercises, graph the parabola,...Ch. 12.3 - For the following exercises, graph the parabola,...Ch. 12.3 - For the following exercises, graph the parabola,...Ch. 12.3 - For the following exercises, find the equation of...Ch. 12.3 - For the following exercises, find the equation of...Ch. 12.3 - For the following exercises, find the equation of...Ch. 12.3 - For the following exercises, find the equation of...Ch. 12.3 - For the following exercises, find the equation of...Ch. 12.3 - For the following exercises, find the equation of...Ch. 12.3 - For the following exercises, determine the...Ch. 12.3 - For the following exercises, find the equation of...Ch. 12.3 - For the following exercises, find the equation of...Ch. 12.3 - For the following exercises, find the equation of...Ch. 12.3 - For the following exercises, find the equation of...Ch. 12.3 - For the following exercises, the vertex and...Ch. 12.3 - For the following exercises, the vertex and...Ch. 12.3 - For the following exercises, the vertex and...Ch. 12.3 - For the following exercises, the vertex and...Ch. 12.3 - For the following exercises, the vertex and...Ch. 12.3 - The mirror in an automobile headlight has a...Ch. 12.3 - If we want to construct the mirror from the...Ch. 12.3 - A satellite dish is shaped like a paraboloid of...Ch. 12.3 - Consider the satellite dish from the previous...Ch. 12.3 - A searchlight is shaped like a paraboloid of...Ch. 12.3 - If the searchlight from the previous exercise has...Ch. 12.3 - An arch is in the shape of a parabola. It has a...Ch. 12.3 - If the arch from the previous exercise has a span...Ch. 12.3 - An object is projected so as to follow a parabolic...Ch. 12.3 - For the object from the previous exercise, assume...Ch. 12.4 - Identify the graph of each of the following...Ch. 12.4 - Rewrite the 13x263xy+7y2=16 in the x’y’system...Ch. 12.4 - Identify the conic for each of the following...Ch. 12.4 - What effect does the xyterm have on the graph of a...Ch. 12.4 - If the equation of a conic section is written in...Ch. 12.4 - If the equation of a conic section is written in...Ch. 12.4 - Given the equation ax2+4x+3y212=0 , what can we...Ch. 12.4 - For the equation Ax2+Bxy+Cy2+Dx+Ey+F=0 , the value...Ch. 12.4 - For the following exercises, determine which conic...Ch. 12.4 - For the following exercises, determine which conic...Ch. 12.4 - For the following exercises, determine which conic...Ch. 12.4 - For the following exercises, determine which conic...Ch. 12.4 - For the following exercises, determine which conic...Ch. 12.4 - For the following exercises, determine which conic...Ch. 12.4 - For the following exercises, determine which conic...Ch. 12.4 - For the following exercises, determine which conic...Ch. 12.4 - For the following exercises, determine which conic...Ch. 12.4 - or the following exercises, determine which conic...Ch. 12.4 - For the following exercises, determine which conic...Ch. 12.4 - For the following exercises, determine which conic...Ch. 12.4 - For the following exercises, find a new...Ch. 12.4 - For the following exercises, find a new...Ch. 12.4 - For the following exercises, find a new...Ch. 12.4 - For the following exercises, find a new...Ch. 12.4 - For the following exercises, find a new...Ch. 12.4 - For the following exercises, determine the angle ...Ch. 12.4 - For the following exercises, determine the angle ...Ch. 12.4 - For the following exercises, determine the angle ...Ch. 12.4 - For the following exercises, determine the angle ...Ch. 12.4 - For the following exercises, determine the angle ...Ch. 12.4 - For the following exercises, determine the angle ...Ch. 12.4 - For the following exercises determine the angle ...Ch. 12.4 - For the following exercises determine the angle ...Ch. 12.4 - For the following exercises, rotate through the...Ch. 12.4 - For the following exercises, rotate through the...Ch. 12.4 - For the following exercises, rotate through the...Ch. 12.4 - For the following exercises, rotate through the...Ch. 12.4 - For the following exercises, rotate through the...Ch. 12.4 - For the following exercises, rotate through the...Ch. 12.4 - For the following exercises, rotate through the...Ch. 12.4 - For the following exercises, rotate through the...Ch. 12.4 - For the following exercises, graph the equation...Ch. 12.4 - For the following exercises, graph the equation...Ch. 12.4 - For the following exercises, graph the equation...Ch. 12.4 - For the following exercises, graph the equation...Ch. 12.4 - For the following exercises, graph the equation...Ch. 12.4 - For the following exercises, graph the equation...Ch. 12.4 - For the following exercises, graph the equation...Ch. 12.4 - For the following exercises, graph the equation...Ch. 12.4 - For the following exercises, graph the equation...Ch. 12.4 - For the following exercises, graph the equation...Ch. 12.4 - For the following exercises, graph the equation...Ch. 12.4 - For the following exercises. determine the angle...Ch. 12.4 - For the following exercises, determine the angle...Ch. 12.4 - For the following exercises, determine the angle...Ch. 12.4 - For the following exercises, determine the angle...Ch. 12.4 - For the following exercises, determine the angle...Ch. 12.4 - For the following exercises, determine the angle...Ch. 12.4 - For the following exercises, determine the value...Ch. 12.4 - For the following exercises, determine the value...Ch. 12.4 - For the following exercises, determine the value...Ch. 12.4 - For the following exercises, determine the value...Ch. 12.4 - For the following exercises, determine the value...Ch. 12.5 - Identify the conic with focus at the origin, the...Ch. 12.5 - Graph r=24cosCh. 12.5 - Find the polar form of the conic given a focus at...Ch. 12.5 - Convert the conic r=21+2cos to rectangular form.Ch. 12.5 - Explain how eccentricity determines which conic...Ch. 12.5 - If a conic section is written as a polar equation,...Ch. 12.5 - If a conic section is written as a polar equation,...Ch. 12.5 - If the directrix of a conic section is...Ch. 12.5 - What do we know about the focus/foci of a conic...Ch. 12.5 - For the following exercises, identity the conic...Ch. 12.5 - For the following exercises, identity the conic...Ch. 12.5 - For the following exercises, identity the conic...Ch. 12.5 - For the following exercises, identity the conic...Ch. 12.5 - For the following exercises, identity the conic...Ch. 12.5 - For the following exercises, identity the conic...Ch. 12.5 - For the following exercises, identity the conic...Ch. 12.5 - For the following exercises, identity the conic...Ch. 12.5 - For the following exercises, identity the conic...Ch. 12.5 - For the following exercises, identity the conic...Ch. 12.5 - For the following exercises, identity the conic...Ch. 12.5 - For the following exercises, identity the conic...Ch. 12.5 - For the following exercises, convert the polar...Ch. 12.5 - For the following exercises, convert the polar...Ch. 12.5 - For the following exercises, convert the polar...Ch. 12.5 - For the following exercises, convert the polar...Ch. 12.5 - For the following exercises, convert the polar...Ch. 12.5 - For the following exercises, convert the polar...Ch. 12.5 - For the following exercises, convert the polar...Ch. 12.5 - For the following exercises, convert the polar...Ch. 12.5 - For the following exercises, convert the polar...Ch. 12.5 - For the following exercises, convert the polar...Ch. 12.5 - For the following exercises, convert the polar...Ch. 12.5 - For the following exercises, convert the polar...Ch. 12.5 - For the following exercises, convert the polar...Ch. 12.5 - For the following exercises, graph the given conic...Ch. 12.5 - For the following exercises, graph the given conic...Ch. 12.5 - For the following exercises, graph the given conic...Ch. 12.5 - For the following exercises, graph the given conic...Ch. 12.5 - For the following exercises, graph the given conic...Ch. 12.5 - For the following exercises, graph the given conic...Ch. 12.5 - For the following exercises, graph the given conic...Ch. 12.5 - For the following exercises, graph the given conic...Ch. 12.5 - For the following exercises, graph the given conic...Ch. 12.5 - For the following exercises, graph the given conic...Ch. 12.5 - For the following exercises, graph the given conic...Ch. 12.5 - For the following exercises, graph the given conic...Ch. 12.5 - For the following exercises, find the polar...Ch. 12.5 - For the following exercises, find the polar...Ch. 12.5 - For the following exercises. find the polar...Ch. 12.5 - For the following exercises. find the polar...Ch. 12.5 - For the following exercises. find the polar...Ch. 12.5 - For the following exercises. find the polar...Ch. 12.5 - For the following exercises. find the polar...Ch. 12.5 - For the following exercises. find the polar...Ch. 12.5 - For the following exercises. find the polar...Ch. 12.5 - For the following exercises. find the polar...Ch. 12.5 - For the following exercises. find the polar...Ch. 12.5 - For the following exercises. find the polar...Ch. 12.5 - For the following exercises. find the polar...Ch. 12.5 - Recall from Rotation of Axes that equations of...Ch. 12.5 - Recall from Rotation of Axes that equations of...Ch. 12.5 - Recall from Rotation of Axes that equations of...Ch. 12.5 - Recall from Rotation of Axes that equations of...Ch. 12.5 - Recall from Rotation of Axes that equations of...Ch. 12 - For the following exercises. write the equation of...Ch. 12 - For the following exercises, write the equation of...Ch. 12 - For the following exercises, write the equation of...Ch. 12 - For the following exercises, write the equation of...Ch. 12 - For the following exercises, graph the ellipse,...Ch. 12 - For the following exercises, graph the ellipse,...Ch. 12 - For the following exercises, graph the ellipse,...Ch. 12 - For the following exercises, graph the ellipse,...Ch. 12 - For the following exercises, use the given...Ch. 12 - For the following exercises, use the given...Ch. 12 - For the following exercises, use the given...Ch. 12 - For the following exercises. write the equation of...Ch. 12 - For the following exercises, write the equation of...Ch. 12 - For the following exercises. write the equation of...Ch. 12 - For the following exercises, write the equation of...Ch. 12 - For the following exercises, graph the hyperbola,...Ch. 12 - For the following exercises, graph the hyperbola,...Ch. 12 - For the following exercises, graph the hyperbola,...Ch. 12 - For the following exercises, graph the hyperbola,...Ch. 12 - For the following exercises, find the equation of...Ch. 12 - For the following exercises, find the equation of...Ch. 12 - For the following exercises, write the equation of...Ch. 12 - For the following exercises, write the equation of...Ch. 12 - For the following exercises, write the equation of...Ch. 12 - For the following exercises, write the equation of...Ch. 12 - For the following exercises, graph the parabola....Ch. 12 - For the following exercises, graph the parabola....Ch. 12 - For the following exercises, graph the parabola....Ch. 12 - For the following exercises, graph the parabola....Ch. 12 - For the following exercises, write the equation of...Ch. 12 - For the following exercises, write the equation of...Ch. 12 - For the following exercises, write the equation of...Ch. 12 - For the following exercises, determine which of...Ch. 12 - For the following exercises, determine which of...Ch. 12 - For the following exercises, determine which of...Ch. 12 - For the following exercises, determine the angle ...Ch. 12 - For the following exercises,determine the angle ...Ch. 12 - For the following exercises, graph the equation...Ch. 12 - For the following exercises, graph the equation...Ch. 12 - For the following exercises, graph the equation...Ch. 12 - For the following exercises, given the polar...Ch. 12 - For the following exercises, given the polar...Ch. 12 - For the following exercises, given the polar...Ch. 12 - For the following exercises, given the polar...Ch. 12 - For the following exercises, graph the conic given...Ch. 12 - For the following exercises, graph the conic given...Ch. 12 - For the following exercises, graph the conic given...Ch. 12 - For the following exercises, graph the conic given...Ch. 12 - For the following exercises, given information...Ch. 12 - For the following exercises, given information...Ch. 12 - For the following exercises, write the equation in...Ch. 12 - For the following exercises, write the equation in...Ch. 12 - For the following exercises, sketch the graph,...Ch. 12 - For the following exercises, sketch the graph....Ch. 12 - For the following exercises, sketch the graph....Ch. 12 - For the following exercises, sketch the graph,...Ch. 12 - For the following exercises, write the equation of...Ch. 12 - For the following exercises, write the equation of...Ch. 12 - For the following exercises, graph the hyperbola,...Ch. 12 - For the following exercises, graph the hyperbola....Ch. 12 - For the following exercises, graph the hyperbola,...Ch. 12 - For the following exercises. write the equation of...Ch. 12 - For the following exercises, write the equation of...Ch. 12 - For the following exercises, graph the parabola,...Ch. 12 - For the following exercises, graph the parabola,...Ch. 12 - For the following exercises, graph the parabola,...Ch. 12 - For the following exercises, graph the parabola,...Ch. 12 - For the following exercises, determine which conic...Ch. 12 - For the following exercises, determine which conic...Ch. 12 - For the following exercises, rewrite in the x’y’...Ch. 12 - For the following exercises, rewrite in the x’y’...Ch. 12 - For the following exercises, identify the conic...Ch. 12 - For the following exercises. identify the conic...Ch. 12 - For the following exercises, graph the given conic...Ch. 12 - For the following exercises, graph the given conic...Ch. 12 - For the following exercises, graph the given conic...
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- T2.2 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_forward= == T2.1: Prove that the necessary conditions for a degree sequence of a tree are sufficient by showing that if di 2n-2 there is a caterpillar with these degrees. Start the construction as follows: if d1, d2,...,d2 and d++1 = d = 1 construct a path v1, v2, ..., vt and add d; - 2 pendent edges to v, for j = 2,3,..., t₁, d₁ - 1 to v₁ and d₁ - 1 to v₁. Show that this construction results vj in a caterpillar with degrees d1, d2, ..., dnarrow_forward4 sin 15° cos 15° √2 cos 405°arrow_forward
- 2 18-17-16-15-14-13-12-11-10 -9 -8 -6 -5 -4-3-2-1 $ 6 8 9 10 -2+ The curve above is the graph of a sinusoidal function. It goes through the points (-10, -1) and (4, -1). Find a sinusoidal function that matches the given graph. If needed, you can enter π-3.1416... as 'pi' in your answer, otherwise use at least 3 decimal digits. f(x) = > Next Questionarrow_forwardketch a graph of the function f(x) = 3 cos (표) 6. x +1 5 4 3 3 80 9 2+ 1 -9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 -1 -2 -3+ -4 5 -6+ Clear All Draw: пи > Next Questionarrow_forwardDraw the following graph on the interval πT 5π < x < 2 2 y = 2 sin (2(x+7)) 6. 5. 4 3 3 2 1 +3 /2 -π/3 -π/6 π/6 π/3 π/2 2π/3 5π/6 π 7π/6 4π/3 3π/2 5π/311π/6 2π 13π/67π/3 5π Clear All Draw:arrow_forward
- ketch a graph of the function f(x) = 3 cos (표) 6. x +1 5 4 3 3 80 9 2+ 1 -9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 -1 -2 -3+ -4 5 -6+ Clear All Draw: пи > Next Questionarrow_forward3 2 20-10-18-17-16-15-14-13-12-11-10-9 -8 -7 -6 -$4-3-2-1 -1 -2 -3 4- -5+ The curve above is the graph of a sinusoidal function. It goes through the points (-8, -4) and (6,-4). Find a sinusoidal function that matches the given graph. If needed, you can enter π=3.1416... as 'pi' in your answer, otherwise use at least 3 decimal digits. f(x) = > Next Question Barrow_forwardX Grades for X Assignmen X A-Z Datab XE Biocultural X EBSCO-Ful X Review es/119676/assignments/3681238 Review Quiz 8.1-p2 points possible Answered: 3/5 ● Question 1 4+ 3. 2 1 13 /12-11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 -1 -2 -3 -4- 5 2 6 The curve above is the graph of a sinusoidal function. It goes through the points (-7,0) and (3,0). Find a sinusoidal function that matches the given graph. If needed, you can enter π=3.1416... as 'pi' in your answer, otherwise use at least 3 decimal digits. f(x) = > Next Question 申 J % F 刀 Q Search S € t ח Y 7 I * 00 J ப I Darrow_forward
- 2 d) Draw the following graph on the interval k 5π Next Questionarrow_forwardDraw the following graph on the interval 5л Next Questionarrow_forwardDraw the following graph on the interval πT 5π < x < x≤ 2 2 y = 2 cos(3(x-77)) +3 6+ 5 4- 3 2 1 /2 -π/3 -π/6 Clear All Draw: /6 π/3 π/2 2/3 5/6 x 7/6 4/3 3/2 5/311/6 2 13/67/3 5 Question Help: Video Submit Question Jump to Answerarrow_forward
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