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Montano1993 [528]
3 years ago
8

True or False? In Exercises 43 and 44, determine whether each statement is true or false. If a statement is true, give a reason

or cite an appropriate statement from the text. If a statement is false, provide an example that shows the statement is not true in all cases or cite an appropriate statement from the text. 43. (a) If W is a subspace of a vector space V, then it has closure under scalar multiplication as defined in V. (b) If V and W are both subspaces of a vector space U, then the intersection of V and W is also a subspace. (c) If U, V, and W are vector spaces such that W is a subspace of V and U is a subspace of V, then W = U
Physics
1 answer:
rjkz [21]3 years ago
4 0

Answer:

a)True.

b)True.

c)False

Explanation:

a)

Yes it is true because W is also  a vector  and that is why it satisfy all the principle of a vector spacer.

b)

Yes it is true.

Lets take v have two subspace U₁ and U₂ then U₁ ∩ U₂ will be a subset of V.

Lets a , b ∈ U₁ ∩ U₂ and ∝ ∈ F

1)

a , b ∈ U₁  ⇒ a +b ∈ U₁  then ∝a ∈ U₁

2)

a , b ∈ U₂ ⇒ a +b ∈ U₂  then ∝a ∈ U₁

So we can say that

a +b ∈ U₁ ∩ U₂  and ∈ U₁ ∩ U₂  

So  U₁ ∩ U₂  is a subspace.

c)

It is false.

The two subspace W and U of a vector space V can only same when W=U.When dimensions of W and U will be same only when they will be equal.

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5. You're examining some of the tiny printing on one of the newer twenty-dollar bills. A 1.5 mm tall letter appears 3 mm tall an
kow [346]

Answer:

80mm or 8cm

Explanation:

According to the lens formula,

1/f = 1/u+1/v

If the object distance u = 4cm = 40mm

Object height = 1.5mm

Image height = 3mm

First, we need to get the image distance (v) using the magnification formula Magnification = image distance/object distance = Image height/object height

v/40=3/1.5

1.5v = 120

v = 120/1.5

v = 80mm

The image distance is 80mm

To get the focal length, we will substitute the image distance and the object distance in the mirror formula to have;

1/f = 1/40+1/-80

Note that the image formed by the lens is an upright image (virtual), therefore the image distance will be negative.

Also the focal length of the converging lens is positive. Our formula will become;

1/f = 1/40-1/80

1/f = 2-1/80

1/f = 1/80

f = 80mm

The focal length of the lens 80mm or 8cm

5 0
4 years ago
Read 2 more answers
A ping-pong ball is shot straight north from a popgun at 4.0 m/s. The wind is blowing to the west at 3.0 m/s. What is the actual
Vlad1618 [11]

Actual velocity of the ping-pong ball= 5 m/s

Explanation:

velocity of ping pong ball because of the shot gun= 4 m/s North

velocity added to the ping-pong ball due to the wind=3 m/s

These velocities are perpendicular to each other. so we use Pythagoras theorem to find the resultant velocity of the ping- pong ball

so the actual velocity of the ping-pong ball =V= √4²+3²

V= √25

V= 5 m/s

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4 years ago
What theory explains why the Earth is a magnet
LuckyWell [14K]
Hi,Conclusiontime

The Dynamo theory explains why the earth is a magnet.
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4 years ago
Can please someone help me ​
LiRa [457]

Answer:

Hi. can you repost? i cant see the image

Explanation:

7 0
3 years ago
Two identical steel balls, each of mass 67.8 g, are moving in opposite directions at 4.80 m/s.They collide head-on and bounce ap
xz_007 [3.2K]

Answer:

Explanation:

To detrmine the time interval at which the balls are in contact.

<u>Given information</u>

The mass of each steal ball 67.8g. The speed of ball towards each other is 4.80 m/s. The exerted force by each jaw 15.9 kN and the forece reduce the diameter by 0.130 mm.

Expression for the effective spring constant ball is shown below.

K = |F|/|x|

Here,

k is a spring constant

F is the force exerted on the ball

x is dispalcement due force

substitute 15.9 kN for F and 0.130 mm in above equation

<h2>K = (15.9 kN)(1X10³N) / (0.130 mm)(1x10⁻³m/1mm)</h2><h2>122 x 10⁶ N/m</h2>

The spring constant is 122 x 10⁶ N/m

     

4 0
3 years ago
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