Consider a right circular cone with given height h . The volume of the cone as a function of its radius r is given by V ( r ) = 1 3 π r 2 h . Consider a right circular cone with fixed height h = 6 in. a. Write the diameter d of the cone as a function of the radius r . b. Write the radius r as a function of the diameter d . c. Find ( V ∘ r ) ( d ) and interpret its meaning. Assume that h = 6 in.
Consider a right circular cone with given height h . The volume of the cone as a function of its radius r is given by V ( r ) = 1 3 π r 2 h . Consider a right circular cone with fixed height h = 6 in. a. Write the diameter d of the cone as a function of the radius r . b. Write the radius r as a function of the diameter d . c. Find ( V ∘ r ) ( d ) and interpret its meaning. Assume that h = 6 in.
Consider a right circular cone with given height h. The volume of the cone as a function of its radius r is given by
V
(
r
)
=
1
3
π
r
2
h
. Consider a right circular cone with fixed height
h
=
6
in.
a. Write the diameter d of the cone as a function of the radius r.
b. Write the radius r as a function of the diameter d.
c. Find
(
V
∘
r
)
(
d
)
and interpret its meaning. Assume that
h
=
6
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Unit Test
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Which statement is true about the graph of the equation y = csc¯¹(x)?
There is a horizontal asymptote at y = 0.
उद
There is a horizontal asymptote at y = 2.
There is a vertical asymptote at x = 0.
O There is a vertical asymptote at x=-
R
Mark this and return
C
Save and Exit
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ے ملزمة احمد
Q (a) Let f be a linear map from a space X into a space Y and (X1,X2,...,xn) basis for X, show that fis one-to-
one iff (f(x1),f(x2),...,f(x) } linearly independent.
(b) Let X= {ao+ax₁+a2x2+...+anxn, a;ER} be a vector space over R, write with prove a hyperspace and a
hyperplane of X.
مبر خد احمد
Q₂ (a) Let M be a subspace of a vector space X, and A= {fex/ f(x)=0, x E M ), show that whether A is
convex set or not, affine set or not.
Write with prove an
application of Hahn-Banach theorem.
Show that every singleton set in a normed space X is closed and any finite set in X is closed (14M)
Let M be a proper subspace of a finite dimension vector space X over a field F show that
whether: (1) If S is a base for M then S base for X or not, (2) If T base for X then base for M
or not.
(b) Let X-P₂(x) be a vector space over polynomials a field of real numbers R, write with L
prove convex subset of X and hyperspace of X.
Q₂/ (a) Let X-R³ be a vector space over a over a field of real numbers R and
A=((a,b,o), a,bE R), A is a subspace of X, let g be a function from A into R such that
gla,b,o)-a, gEA, find fe X such that g(t)=f(t), tEA.
(b) Let M be a non-empty subset of a space X, show that M is a hyperplane of X iff there
Xiff there
exists fE X/10) and tE F such that M=(xE X/ f(x)=t).
(c) Show that the relation equivalent is an equivalence relation on set of norms on a space
X.
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