******* Calculus************
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Let P1 be the plane defined by the equation...
******* Calculus************
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+
=
~.~
Let P1 be the plane defined by the equation 2x−8y+5z = 2 and
let P2 be the plane defined by the equation 3x + 2y − z = 7. Find
the equation for a new plane, P3, which is perpendicular to both P1
and P2, and also which passes through the point (-3,1,2). HINT: If
P3 is perpendicular to P1 and P2, then the normal vector for P3
should be perpendicular to the normal vectors of P1 and
P2.
PLEASE GRAPH P1, P2, and P3 on the same set of axes.
please explain as much as you can thank you :)))
Solutions
Expert Solution
However, To graph 3D planes P1, P2, P3 it will be best to use
some 3D graphing calculator or software. Graph will look like this
:
I hope it helps. Please feel free to revert back with further
queries (if any) in comments. Thanks!
Let 2a > -1, If the area of the region of the plane defined
by {(x,y) : x ≥ 0, 2y-x ≥ 0, ax+y-3 ≤ 0} is equal to 3, then the
value of a, lies in
Answer key: (0.75, 1.5)
Let f(x, y) = 2x^3 − 6xy + 3y^2 be a function defined on
xy-plane
(a) Find first and second partial derivatives of.
(b) Determine the local extreme points of f (max., min., saddle
points) if there are any.
(c) Find the absolute max. and absolute min. values of f over
the closed region bounded by the lines x = 2, y = 0, and y = x
We can define the plane of incidence as the plane defined by the
incident beam and the normal to the surface of the transparent
chamber. Based on your observations, is the reflected beam also in
this plane? Explain how you reached your conclusion.
A projective plane is a plane (S,L ) satisfying the following
four axioms. P1. For any two distinct points P and Q there is one
and only one line containing P and Q. P2. For any two distinct
lines l and m there exists one and only one point P belonging to
l∩m. P3. There exist three noncollinear points. P4. Every line
contains at least three points.
Let π be a projective plane. Using P1 − P4, show that π...
Let S be the surface with equation x2+y2-z2=1. (a) In a single
xy-plane, sketch and label the trace curves z=k for k =
-2,-1,0,1,2. In words describe what types of curves these are and
how they change. (b) In a single yz-plane, sketch and label the
trace curves x=k for k= -2,-1,0,1,2. In other words, describe what
types of curves these are and how they change as k varies.
a. consider the plane with equation -x+y-z=2, and let p be the
point (3,2,1)in R^3. find the distance from P to the plane.
b. let P be the plane with normal vector n (1,-3,2) which passes
through the point(1,1,1). find the point in the plane which is
closest to (2,2,3)
Applied Math
Let T be the operator on P2 defined by the equation
T(f)=f+(1+x)f'
(a) Show T i linear operator from P2 into
P2!
(b) Give matrix reppressentaion in base vectorss
B={1,x,x2}!
(c) Give a diagonal matrix representing T
(d) Give a diagonal matrix representing T
Where P2 is ppolynomials with degree less then or
equal to 2 and f' is the derivative of polynomial f.
Let a < c < b, and let f be defined on [a,b]. Show that f
∈ R[a,b] if and only if f ∈ R[a, c] and f ∈ R[c, b]. Moreover,
Integral a,b f = integral a,c f + integral c,b f .
Let X be the exam grade of a student taking Calculus 1 with
Professor Smith. The professor believes that X has a mean of 76 and
a standard deviation of 12.5. Suppose there are 100 students in
Professor Smith's class. Approximate the probability that X is
between 73.8 and 77.8.