For the following exercises, determine the function described and then use it to answer the question. 57. An object dropped from a height of 600 feet hasa height, h ( t ) , in feet after tseconds have elapsed,such that h ( t ) = 600 − 16 t 2 . Express t as a functionof height h , and find the time to reach a height of400feet.
For the following exercises, determine the function described and then use it to answer the question. 57. An object dropped from a height of 600 feet hasa height, h ( t ) , in feet after tseconds have elapsed,such that h ( t ) = 600 − 16 t 2 . Express t as a functionof height h , and find the time to reach a height of400feet.
For the following exercises, determine the function described and then use it to answer the question.
57. An object dropped from a height of 600 feet hasa height,
h
(
t
)
,
in feet after tseconds have elapsed,such that
h
(
t
)
=
600
−
16
t
2
.
Express t as a functionof height h, and find the time to reach a height of400feet.
Expression, rule, or law that gives the relationship between an independent variable and dependent variable. Some important types of functions are injective function, surjective function, polynomial function, and inverse function.
Q1: A: Let M and N be two subspace of finite dimension linear space X, show that if M = N
then dim M = dim N but the converse need not to be true.
B: Let A and B two balanced subsets of a linear space X, show that whether An B and
AUB are balanced sets or nor.
Q2: Answer only two
A:Let M be a subset of a linear space X, show that M is a hyperplane of X iff there exists
ƒ€ X'/{0} and a € F such that M = (x = x/f&x) = x}.
fe
B:Show that every two norms on finite dimension linear space are equivalent
C: Let f be a linear function from a normed space X in to a normed space Y, show that
continuous at x, E X iff for any sequence (x) in X converge to Xo then the sequence
(f(x)) converge to (f(x)) in Y.
Q3: A:Let M be a closed subspace of a normed space X, constract a linear space X/M as
normed space
B: Let A be a finite dimension subspace of a Banach space X, show that A is closed.
C: Show that every finite dimension normed space is Banach space.
• Plane II is spanned by the vectors:
P12
P2 = 1
• Subspace W is spanned by the vectors:
W₁ =
-- () ·
2
1
W2 =
0
Three streams - Stream A, Stream B, and Stream C - flow into a lake. The flow rates of these streams are
not yet known and thus to be found. The combined water inflow from the streams is 300 m³/h. The rate of
Stream A is three times the combined rates of Stream B and Stream C. The rate of Stream B is 50 m³/h less
than half of the difference between the rates of Stream A and Stream C.
Find the flow rates of the three streams by setting up an equation system Ax = b and solving it for x.
Provide the values of A and b. Assuming that you get to an upper-triangular matrix U using an elimination
matrix E such that U = E A, provide also the components of E.
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.
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Higher Order Differential Equation with constant coefficient (GATE) (Part 1) l GATE 2018; Author: GATE Lectures by Dishank;https://www.youtube.com/watch?v=ODxP7BbqAjA;License: Standard YouTube License, CC-BY