CODE/CALC ET 3-HOLE
2nd Edition
ISBN: 9781323178522
Author: Briggs
Publisher: PEARSON
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Chapter 10.1, Problem 7E
To determine
To find: A function
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(x)=2x-x2
2
a=2, b = 1/2, C=0
b) Vertex v
F(x)=ax 2 + bx + c
x=
Za
V=2.0L
YEF(- =) = 4
b
(글)
JANUARY 17, 2025
WORKSHEET 1
Solve the following four problems on a separate sheet. Fully justify your answers to
MATH 122
ล
T
earn full credit.
1. Let f(x) = 2x-
1x2
2
(a) Rewrite this quadratic function in standard form: f(x) = ax² + bx + c
and indicate the values of the coefficients: a, b and c.
(b) Find the vertex V, focus F, focal width, directrix D, and the axis of
symmetry for the graph of y = f(x).
(c) Plot a graph of y = f(x) and indicate all quantities found in part (b)
on your graph.
(d) Specify the domain and range of the function f.
OUR
2. Let g(x) = f(x) u(x) where f is the quadratic function from problem 1
and u is the unit step function:
u(x) = { 0
1 if x ≥0
0 if x<0
y = u(x)
0
(a) Write a piecewise formula for the function g.
(b) Sketch a graph of y = g(x).
(c) Indicate the domain and range of the function g.
X
фирм
where u is the unit step function defined in problem 2.
3. Let…
Question 1
"P3
Question 3: Construct the accessibility matrix Passociated with
the following graphs, and compute P2 and identify each at the
various two-step paths in the graph
Ps
P₁
P₂
Chapter 10 Solutions
CODE/CALC ET 3-HOLE
Ch. 10.1 - Explain how a pair of parametric equations...Ch. 10.1 - Prob. 2ECh. 10.1 - Prob. 3ECh. 10.1 - Give parametric equations that generate the line...Ch. 10.1 - Prob. 5ECh. 10.1 - Prob. 6ECh. 10.1 - Prob. 7ECh. 10.1 - Prob. 8ECh. 10.1 - Prob. 9ECh. 10.1 - Explain how to find points on the curve x = f(t),...
Ch. 10.1 - Prob. 11ECh. 10.1 - Prob. 12ECh. 10.1 - Prob. 13ECh. 10.1 - Prob. 14ECh. 10.1 - Prob. 15ECh. 10.1 - Prob. 16ECh. 10.1 - Prob. 17ECh. 10.1 - Prob. 18ECh. 10.1 - Prob. 19ECh. 10.1 - Prob. 20ECh. 10.1 - Prob. 21ECh. 10.1 - Prob. 22ECh. 10.1 - Prob. 23ECh. 10.1 - Prob. 24ECh. 10.1 - Prob. 25ECh. 10.1 - Prob. 26ECh. 10.1 - Parametric equations of circles Find parametric...Ch. 10.1 - Parametric equations of circles Find parametric...Ch. 10.1 - Parametric equations of circles Find parametric...Ch. 10.1 - Prob. 30ECh. 10.1 - Parametric equations of circles Find parametric...Ch. 10.1 - Prob. 32ECh. 10.1 - Prob. 33ECh. 10.1 - Prob. 34ECh. 10.1 - Prob. 35ECh. 10.1 - Prob. 36ECh. 10.1 - Parametric lines Find the slope of each line and a...Ch. 10.1 - Parametric lines Find the slope of each line and a...Ch. 10.1 - Parametric lines Find the slope of each line and a...Ch. 10.1 - Prob. 40ECh. 10.1 - Prob. 41ECh. 10.1 - Prob. 42ECh. 10.1 - Prob. 43ECh. 10.1 - Prob. 44ECh. 10.1 - Curves to parametric equations Give a set of...Ch. 10.1 - Curves to parametric equations Give a set of...Ch. 10.1 - Prob. 47ECh. 10.1 - Prob. 48ECh. 10.1 - More parametric curves Use a graphing utility to...Ch. 10.1 - More parametric curves Use a graphing utility to...Ch. 10.1 - More parametric curves Use a graphing utility to...Ch. 10.1 - More parametric curves Use a graphing utility to...Ch. 10.1 - More parametric curves Use a graphing utility to...Ch. 10.1 - More parametric curves Use a graphing utility to...Ch. 10.1 - Prob. 55ECh. 10.1 - Beautiful curves Consider the family of curves...Ch. 10.1 - Prob. 57ECh. 10.1 - Prob. 58ECh. 10.1 - Prob. 59ECh. 10.1 - Derivatives Consider the following parametric...Ch. 10.1 - Derivatives Consider the following parametric...Ch. 10.1 - Prob. 62ECh. 10.1 - Derivatives Consider the following parametric...Ch. 10.1 - Prob. 64ECh. 10.1 - Explain why or why not Determine whether the...Ch. 10.1 - Tangent lines Find an equation of the line tangent...Ch. 10.1 - Tangent lines Find an equation of the line tangent...Ch. 10.1 - Tangent lines Find an equation of the line tangent...Ch. 10.1 - Tangent lines Find an equation of the line tangent...Ch. 10.1 - Prob. 70ECh. 10.1 - Prob. 71ECh. 10.1 - Prob. 72ECh. 10.1 - Prob. 73ECh. 10.1 - Prob. 74ECh. 10.1 - Prob. 75ECh. 10.1 - Prob. 76ECh. 10.1 - Prob. 77ECh. 10.1 - Prob. 78ECh. 10.1 - Prob. 79ECh. 10.1 - Prob. 80ECh. 10.1 - Prob. 81ECh. 10.1 - Prob. 82ECh. 10.1 - Eliminating the parameter Eliminate the parameter...Ch. 10.1 - Eliminating the parameter Eliminate the parameter...Ch. 10.1 - Prob. 85ECh. 10.1 - Prob. 86ECh. 10.1 - Prob. 87ECh. 10.1 - Prob. 88ECh. 10.1 - Slopes of tangent lines Find all the points at...Ch. 10.1 - Slopes of tangent lines Find all the points at...Ch. 10.1 - Slopes of tangent lines Find all the points at...Ch. 10.1 - Slopes of tangent lines Find all the points at...Ch. 10.1 - Prob. 93ECh. 10.1 - Prob. 94ECh. 10.1 - Prob. 95ECh. 10.1 - Lissajous curves Consider the following Lissajous...Ch. 10.1 - Lam curves The Lam curve described by...Ch. 10.1 - Prob. 98ECh. 10.1 - Prob. 99ECh. 10.1 - Prob. 100ECh. 10.1 - Prob. 101ECh. 10.1 - Prob. 102ECh. 10.1 - Prob. 103ECh. 10.1 - Air drop A plane traveling horizontally at 80 m/s...Ch. 10.1 - Air dropinverse problem A plane traveling...Ch. 10.1 - Prob. 106ECh. 10.1 - Implicit function graph Explain and carry out a...Ch. 10.1 - Prob. 108ECh. 10.1 - Prob. 109ECh. 10.1 - Prob. 110ECh. 10.2 - Plot the points with polar coordinates (2,6) and...Ch. 10.2 - Prob. 2ECh. 10.2 - Prob. 3ECh. 10.2 - Prob. 4ECh. 10.2 - What is the polar equation of the vertical line x...Ch. 10.2 - What is the polar equation of the horizontal line...Ch. 10.2 - Prob. 7ECh. 10.2 - Prob. 8ECh. 10.2 - Graph the points with the following polar...Ch. 10.2 - Graph the points with the following polar...Ch. 10.2 - Prob. 11ECh. 10.2 - Prob. 12ECh. 10.2 - Prob. 13ECh. 10.2 - Points in polar coordinates Give two sets of polar...Ch. 10.2 - Converting coordinates Express the following polar...Ch. 10.2 - Converting coordinates Express the following polar...Ch. 10.2 - Converting coordinates Express the following polar...Ch. 10.2 - Converting coordinates Express the following polar...Ch. 10.2 - Converting coordinates Express the following polar...Ch. 10.2 - Converting coordinates Express the following polar...Ch. 10.2 - Converting coordinates Express the following...Ch. 10.2 - Converting coordinates Express the following...Ch. 10.2 - Converting coordinates Express the following...Ch. 10.2 - Converting coordinates Express the following...Ch. 10.2 - Converting coordinates Express the following...Ch. 10.2 - Converting coordinates Express the following...Ch. 10.2 - Prob. 27ECh. 10.2 - Prob. 28ECh. 10.2 - Prob. 29ECh. 10.2 - Prob. 30ECh. 10.2 - Prob. 31ECh. 10.2 - Prob. 32ECh. 10.2 - Prob. 33ECh. 10.2 - Prob. 34ECh. 10.2 - Prob. 35ECh. 10.2 - Prob. 36ECh. 10.2 - Prob. 37ECh. 10.2 - Prob. 38ECh. 10.2 - Prob. 39ECh. 10.2 - Prob. 40ECh. 10.2 - Graphing polar curves Graph the following...Ch. 10.2 - Graphing polar curves Graph the following...Ch. 10.2 - Prob. 43ECh. 10.2 - Prob. 44ECh. 10.2 - Graphing polar curves Graph the following...Ch. 10.2 - Graphing polar curves Graph the following...Ch. 10.2 - Graphing polar curves Graph the following...Ch. 10.2 - Graphing polar curves Graph the following...Ch. 10.2 - Prob. 49ECh. 10.2 - Prob. 50ECh. 10.2 - Prob. 51ECh. 10.2 - Prob. 52ECh. 10.2 - Using a graphing utility Use a graphing utility to...Ch. 10.2 - Using a graphing utility Use a graphing utility to...Ch. 10.2 - Prob. 55ECh. 10.2 - Using a graphing utility Use a graphing utility to...Ch. 10.2 - Using a graphing utility Use a graphing utility to...Ch. 10.2 - Using a graphing utility Use a graphing utility to...Ch. 10.2 - Prob. 59ECh. 10.2 - Prob. 60ECh. 10.2 - Prob. 61ECh. 10.2 - Cartesian-to-polar coordinates Convert the...Ch. 10.2 - Cartesian-to-polar coordinates Convert the...Ch. 10.2 - Cartesian-to-polar coordinates Convert the...Ch. 10.2 - Cartesian-to-polar coordinates Convert the...Ch. 10.2 - Prob. 66ECh. 10.2 - Prob. 67ECh. 10.2 - Prob. 68ECh. 10.2 - Prob. 69ECh. 10.2 - Prob. 70ECh. 10.2 - Prob. 71ECh. 10.2 - Prob. 72ECh. 10.2 - Prob. 73ECh. 10.2 - Prob. 74ECh. 10.2 - Circles in general Show that the polar equation...Ch. 10.2 - Prob. 76ECh. 10.2 - Prob. 77ECh. 10.2 - Prob. 78ECh. 10.2 - Prob. 79ECh. 10.2 - Prob. 80ECh. 10.2 - Prob. 81ECh. 10.2 - Equations of circles Find equations of the circles...Ch. 10.2 - Prob. 83ECh. 10.2 - Prob. 84ECh. 10.2 - Prob. 85ECh. 10.2 - Prob. 86ECh. 10.2 - Prob. 87ECh. 10.2 - Prob. 88ECh. 10.2 - Prob. 89ECh. 10.2 - Limiting limaon Consider the family of limaons r =...Ch. 10.2 - Prob. 91ECh. 10.2 - Prob. 92ECh. 10.2 - Prob. 93ECh. 10.2 - The lemniscate family Equations of the form r2 = a...Ch. 10.2 - The rose family Equations of the form r = a sin m...Ch. 10.2 - Prob. 96ECh. 10.2 - Prob. 97ECh. 10.2 - The rose family Equations of the form r = a sin m...Ch. 10.2 - Prob. 99ECh. 10.2 - Prob. 100ECh. 10.2 - Prob. 101ECh. 10.2 - Spirals Graph the following spirals. Indicate the...Ch. 10.2 - Prob. 103ECh. 10.2 - Prob. 104ECh. 10.2 - Prob. 105ECh. 10.2 - Prob. 106ECh. 10.2 - Enhanced butterfly curve The butterfly curve of...Ch. 10.2 - Prob. 108ECh. 10.2 - Prob. 109ECh. 10.2 - Prob. 110ECh. 10.2 - Prob. 111ECh. 10.2 - Cartesian lemniscate Find the equation in...Ch. 10.2 - Prob. 113ECh. 10.2 - Prob. 114ECh. 10.3 - Prob. 1ECh. 10.3 - Prob. 2ECh. 10.3 - Explain why the slope of the line tangent to the...Ch. 10.3 - What integral must be evaluated to find the area...Ch. 10.3 - Slopes of tangent lines Find the slope of the line...Ch. 10.3 - Slopes of tangent lines Find the slope of the line...Ch. 10.3 - Slopes of tangent lines Find the slope of the line...Ch. 10.3 - Slopes of tangent lines Find the slope of the line...Ch. 10.3 - Slopes of tangent lines Find the slope of the line...Ch. 10.3 - Slopes of tangent lines Find the slope of the line...Ch. 10.3 - Slopes of tangent lines Find the slope of the line...Ch. 10.3 - Slopes of tangent lines Find the slope of the line...Ch. 10.3 - Slopes of tangent lines Find the slope of the line...Ch. 10.3 - Slopes of tangent lines Find the slope of the line...Ch. 10.3 - Horizontal and vertical tangents Find the points...Ch. 10.3 - Horizontal and vertical tangents Find the points...Ch. 10.3 - Horizontal and vertical tangents Find the points...Ch. 10.3 - Prob. 18ECh. 10.3 - Prob. 19ECh. 10.3 - Prob. 20ECh. 10.3 - Areas of regions Make a sketch of the region and...Ch. 10.3 - Areas of regions Make a sketch of the region and...Ch. 10.3 - Areas of regions Make a sketch of the region and...Ch. 10.3 - Areas of regions Make a sketch of the region and...Ch. 10.3 - Areas of regions Make a sketch of the region and...Ch. 10.3 - Areas of regions Make a sketch of the region and...Ch. 10.3 - Areas of regions Make a sketch of the region and...Ch. 10.3 - Areas of regions Make a sketch of the region and...Ch. 10.3 - Areas of regions Make a sketch of the region and...Ch. 10.3 - Areas of regions Make a sketch of the region and...Ch. 10.3 - Areas of regions Make a sketch of the region and...Ch. 10.3 - Areas of regions Make a sketch of the region and...Ch. 10.3 - Areas of regions Make a sketch of the region and...Ch. 10.3 - Areas of regions Make a sketch of the region and...Ch. 10.3 - Areas of regions Make a sketch of the region and...Ch. 10.3 - Areas of regions Make a sketch of the region and...Ch. 10.3 - Prob. 37ECh. 10.3 - Prob. 38ECh. 10.3 - Prob. 39ECh. 10.3 - Prob. 40ECh. 10.3 - Prob. 41ECh. 10.3 - Prob. 42ECh. 10.3 - Prob. 43ECh. 10.3 - Prob. 44ECh. 10.3 - Prob. 45ECh. 10.3 - Multiple identities Explain why the point (1, 3/2)...Ch. 10.3 - Area of plane regions Find the areas of the...Ch. 10.3 - Area of plane regions Find the areas of the...Ch. 10.3 - Area of plane regions Find the areas of the...Ch. 10.3 - Area of plane regions Find the areas of the...Ch. 10.3 - Prob. 51ECh. 10.3 - Prob. 52ECh. 10.3 - Regions bounded by a spiral Let Rn be the region...Ch. 10.3 - Area of polar regions Find the area of the regions...Ch. 10.3 - Area of polar regions Find the area of the regions...Ch. 10.3 - Area of polar regions Find the area of the regions...Ch. 10.3 - Prob. 57ECh. 10.3 - Prob. 58ECh. 10.3 - Grazing goat problems Consider the following...Ch. 10.3 - Grazing goat problems Consider the following...Ch. 10.3 - Prob. 61ECh. 10.3 - Tangents and normals Let a polar curve be...Ch. 10.3 - Prob. 63ECh. 10.4 - Give the property that defines all parabolas.Ch. 10.4 - Prob. 2ECh. 10.4 - Give the property that defines all hyperbolas.Ch. 10.4 - Prob. 4ECh. 10.4 - Prob. 5ECh. 10.4 - What is the equation of the standard parabola with...Ch. 10.4 - Prob. 7ECh. 10.4 - Prob. 8ECh. 10.4 - Given vertices (a, 0) and eccentricity e, what are...Ch. 10.4 - Prob. 10ECh. 10.4 - What are the equations of the asymptotes of a...Ch. 10.4 - Prob. 12ECh. 10.4 - Graphing parabolas Sketch a graph of the following...Ch. 10.4 - Prob. 14ECh. 10.4 - Prob. 15ECh. 10.4 - Prob. 16ECh. 10.4 - Prob. 17ECh. 10.4 - Graphing parabolas Sketch a graph of the following...Ch. 10.4 - Prob. 19ECh. 10.4 - Equations of parabolas Find an equation of the...Ch. 10.4 - Equations of parabolas Find an equation of the...Ch. 10.4 - Prob. 22ECh. 10.4 - Prob. 23ECh. 10.4 - Equations of parabolas Find an equation of the...Ch. 10.4 - From graphs to equations Write an equation of the...Ch. 10.4 - From graphs to equations Write an equation of the...Ch. 10.4 - Prob. 27ECh. 10.4 - Prob. 28ECh. 10.4 - Prob. 29ECh. 10.4 - Prob. 30ECh. 10.4 - Prob. 31ECh. 10.4 - Prob. 32ECh. 10.4 - Equations of ellipses Find an equation of the...Ch. 10.4 - Equations of ellipses Find an equation of the...Ch. 10.4 - Equations of ellipses Find an equation of the...Ch. 10.4 - Prob. 36ECh. 10.4 - Prob. 37ECh. 10.4 - Prob. 38ECh. 10.4 - Prob. 39ECh. 10.4 - Prob. 40ECh. 10.4 - Prob. 41ECh. 10.4 - Prob. 42ECh. 10.4 - Prob. 43ECh. 10.4 - Prob. 44ECh. 10.4 - Equations of hyperbolas Find an equation of the...Ch. 10.4 - Equations of hyperbolas Find an equation of the...Ch. 10.4 - Equations of hyperbolas Find an equation of the...Ch. 10.4 - Prob. 48ECh. 10.4 - From graphs to equations Write an equation of the...Ch. 10.4 - From graphs to equations Write an equation of the...Ch. 10.4 - Eccentricity-directrix approach Find an equation...Ch. 10.4 - Eccentricity-directrix approach Find an equation...Ch. 10.4 - Eccentricity-directrix approach Find an equation...Ch. 10.4 - Eccentricity-directrix approach Find an equation...Ch. 10.4 - Prob. 55ECh. 10.4 - Prob. 56ECh. 10.4 - Prob. 57ECh. 10.4 - Prob. 58ECh. 10.4 - Prob. 59ECh. 10.4 - Prob. 60ECh. 10.4 - Tracing hyperbolas and parabolas Graph the...Ch. 10.4 - Tracing hyperbolas and parabolas Graph the...Ch. 10.4 - Tracing hyperbolas and parabolas Graph the...Ch. 10.4 - Tracing hyperbolas and parabolas Graph the...Ch. 10.4 - Prob. 65ECh. 10.4 - Hyperbolas with a graphing utility Use a graphing...Ch. 10.4 - Prob. 67ECh. 10.4 - Prob. 68ECh. 10.4 - Tangent lines Find an equation of the tine tangent...Ch. 10.4 - Tangent lines Find an equation of the tine tangent...Ch. 10.4 - Tangent lines Find an equation of the tine tangent...Ch. 10.4 - Prob. 72ECh. 10.4 - Prob. 73ECh. 10.4 - Prob. 74ECh. 10.4 - Prob. 75ECh. 10.4 - The ellipse and the parabola Let R be the region...Ch. 10.4 - Tangent lines for an ellipse Show that an equation...Ch. 10.4 - Prob. 78ECh. 10.4 - Volume of an ellipsoid Suppose that the ellipse...Ch. 10.4 - Area of a sector of a hyperbola Consider the...Ch. 10.4 - Volume of a hyperbolic cap Consider the region R...Ch. 10.4 - Prob. 82ECh. 10.4 - Prob. 83ECh. 10.4 - Golden Gate Bridge Completed in 1937, San...Ch. 10.4 - Prob. 85ECh. 10.4 - Prob. 86ECh. 10.4 - Prob. 87ECh. 10.4 - Prob. 88ECh. 10.4 - Shared asymptotes Suppose that two hyperbolas with...Ch. 10.4 - Focal chords A focal chord of a conic section is a...Ch. 10.4 - Focal chords A focal chord of a conic section is a...Ch. 10.4 - Focal chords A focal chord of a conic section is a...Ch. 10.4 - Prob. 93ECh. 10.4 - Prob. 94ECh. 10.4 - Confocal ellipse and hyperbola Show that an...Ch. 10.4 - Approach to asymptotes Show that the vertical...Ch. 10.4 - Prob. 97ECh. 10.4 - Prob. 98ECh. 10.4 - Prob. 99ECh. 10 - Explain why or why not Determine whether the...Ch. 10 - Prob. 2RECh. 10 - Prob. 3RECh. 10 - Prob. 4RECh. 10 - Prob. 5RECh. 10 - Prob. 6RECh. 10 - Prob. 7RECh. 10 - Prob. 8RECh. 10 - Eliminating the parameter Eliminate the parameter...Ch. 10 - Prob. 10RECh. 10 - Parametric description Write parametric equations...Ch. 10 - Parametric description Write parametric equations...Ch. 10 - Prob. 13RECh. 10 - Prob. 14RECh. 10 - Parametric description Write parametric equations...Ch. 10 - Parametric description Write parametric equations...Ch. 10 - Tangent lines Find an equation of the line tangent...Ch. 10 - Prob. 18RECh. 10 - Prob. 19RECh. 10 - Sets in polar coordinates Sketch the following...Ch. 10 - Prob. 21RECh. 10 - Prob. 22RECh. 10 - Polar conversion Write the equation...Ch. 10 - Polar conversion Consider the equation r = 4/(sin ...Ch. 10 - Prob. 25RECh. 10 - Prob. 26RECh. 10 - Prob. 27RECh. 10 - Slopes of tangent lines a. Find all points where...Ch. 10 - Slopes of tangent lines a. Find all points where...Ch. 10 - Slopes of tangent lines a. Find all points where...Ch. 10 - Prob. 31RECh. 10 - The region enclosed by all the leaves of the rose...Ch. 10 - The region enclosed by the limaon r = 3 cosCh. 10 - The region inside the limaon r = 2 + cos and...Ch. 10 - Prob. 35RECh. 10 - Prob. 36RECh. 10 - The area that is inside the cardioid r = 1 + cos ...Ch. 10 - Prob. 38RECh. 10 - Prob. 39RECh. 10 - Prob. 40RECh. 10 - Conic sections a. Determine whether the following...Ch. 10 - Prob. 42RECh. 10 - Prob. 43RECh. 10 - Prob. 44RECh. 10 - Tangent lines Find an equation of the line tangent...Ch. 10 - Prob. 46RECh. 10 - Tangent lines Find an equation of the line tangent...Ch. 10 - Tangent lines Find an equation of the line tangent...Ch. 10 - Prob. 49RECh. 10 - Prob. 50RECh. 10 - Prob. 51RECh. 10 - Prob. 52RECh. 10 - Prob. 53RECh. 10 - Prob. 54RECh. 10 - Eccentricity-directrix approach Find an equation...Ch. 10 - Prob. 56RECh. 10 - Prob. 57RECh. 10 - Prob. 58RECh. 10 - Prob. 59RECh. 10 - Prob. 60RECh. 10 - Prob. 61RECh. 10 - Prob. 62RECh. 10 - Prob. 63RECh. 10 - Prob. 64RECh. 10 - Prob. 65RECh. 10 - Prob. 66RECh. 10 - Prob. 67RECh. 10 - Prob. 68RECh. 10 - Prob. 69RECh. 10 - Prob. 70RECh. 10 - Prob. 71RE
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- A cable television company estimates that with x thousand subscribers, its monthly revenue and cost (in thousands of dollars) are given by the following equations. R(x) = 45x - 0.24x2 C(x) = 257 + 13xarrow_forwardx³-343 If k(x) = x-7 complete the table and use the results to find lim k(x). X-7 x 6.9 6.99 6.999 7.001 7.01 7.1 k(x) Complete the table. X 6.9 6.99 6.999 7.001 7.01 7.1 k(x) (Round to three decimal places as needed.)arrow_forward(3) (4 points) Given three vectors a, b, and c, suppose: |bx c = 2 |a|=√√8 • The angle between a and b xc is 0 = 135º. . Calculate the volume a (bxc) of the parallelepiped spanned by the three vectors.arrow_forward
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