Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used. Match the estimated value of each express
ion with its position on the number line. plz help
1 answer:
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Answer:
a) No
b) No
c) No
d) No
Step-by-step explanation:
Remember, a set V wit the operations addition and scalar product is a vector space if the following conditions are valid for all u, v, w∈V and for all scalars c and d:
1. u+v∈V
2. u+v=v+u
3. (u+v)+w=u+(v+w).
4. Exist 0∈V such that u+0=u
5. For each u∈V exist −u∈V such that u+(−u)=0.
6. if c is an escalar and u∈V, then cu∈V
7. c(u+v)=cu+cv
8. (c+d)u=cu+du
9. c(du)=(cd)u
10. 1u=u
let's check each of the properties for the respective operations:
Let
Observe that
1. u+v∈V
2. u+v=v+u, because the adittion of reals is conmutative
3. (u+v)+w=u+(v+w). because the adittion of reals is associative
4.
5.
then regardless of the escalar product, the first five properties are met for a), b), c) and d). Now let's verify that properties 6-10 are met.
a)
6.
7.
8.
Since 8 isn't satify then V is not a vector space with the addition as in R^3 and the scalar product
b) 6.
7.
8.
9.
10
Since 10 isn't satify then V is not a vector space with the addition as in R^3 and the scalar product
c) Observe that
Since 10 isn't satify then V is not a vector space with the addition as in R^3 and the scalar product .
d) Observe that
Since 10 isn't satify then V is not a vector space with the addition as in R^3 and the scalar product .
Length AC is 12 .
<u>Step-by-step explanation:</u>
We have , △ABC is inscribed in a circle such that vertices A and B lie on a diameter of the circle. If the length of the diameter of the circle is 13 and the length of chord BC is 5 . According to the data given in question we can visualize that triangle must be a right angled triangle where:
AB = hypotenuse = 13
BC = base = 5
Ac = Perpendicular
Now, By Pythagoras Theorem:
⇒
⇒
⇒
⇒
⇒
⇒
⇒
∴ Length AC is 12 .