wire was bent into the shape of a rectangle with width 5 and length 7. If this wire is bent into shape of a square, what is the length of a side of the square

Given that:

Rectangular wire with the following dimension :

Width = 5

Length = 7

To obtain the total length of the wire :

Perimeter of rectangle :

2 (length + Width)

2 (5 + 7)

2(12)

= 24 cm

The length of each side of the square will be :

Number of sides = 4

Length of each side :

24 / 4 = 6 cm

6 0

2 years ago

If u, v, and w are nonzero vectors in r 2 , is w a linear combination of u and v?

Tju [1.3M]

Not necessarily. $\mathbf u$ and $\mathbf v$ may be linearly dependent, so that their span forms a subspace of $\mathbb R^2$ that does not contain every vector in $\mathbb R^2$ .

For example, we could have $\mathbf u=(0,1)$ and $\mathbf v=(0,-1)$ . Any vector $\mathbf w$ of the form $(r,0)$ , where $r\neq0$ , is impossible to obtain as a linear combination of these $\mathbf u$ and $\mathbf v$ , since

$c_1\mathbf u+c_2\mathbf v=(0,c_1)+(0,-c_2)=(0,c_1-c_2)\neq(r,0)$

unless $r=0$ and $c_1=c_2$ .

8 0

3 years ago