Hello :
v . w = <span>| | v | | × </span><span>| | w | | cos(</span><span>θ) ....(1)
v(2,0,1) w(0,1,-3)
</span>v . w = (2)(0)+(0)(1)+(1)(-3) = - 3
| | v | | = √((2)²+(0)²+(1)²) = <span>√5
</span>| | w | = √((0)²+(1)²+(-3)²) = √10
by (1) :
cos(θ) = (v . w ) / | | v | | × | | w | |
cos(θ) = = - 3/√50
θ =..... calculate by 2ind function ( calculator)
An undefined slope is NOT the same as y= 0, since it is a vertical line. The x-coordinate never changes even if the y-coordinate is different. There is no run.
Possibly A)249.6
Explanation
The name of an item that a person can only buy once in one's lifetime are:
- A strong quality outdoor trash can.
- A high-quality knife set.
- Can opener.
- Corkscrew.
- Measuring cups, etc.
<h3>What are lifetime products?</h3>
These are known to be a product that one can buy and a person can use for a lifetime until they grow tired of using it.
Note that not all product can or need to last forever but there are a lot of products that can actually do. some of which are:
- A strong quality outdoor trash can.
- A high-quality knife set.
- Can opener.
- Corkscrew.
- Measuring cups, etc.
Learn more about products from
brainly.com/question/27487922
#SPJ1
Step-by-step explanation:
a = age of Alex
l = age of Lucy
m = age of Megan
a + l + m = 126
l = 3a
l = m + 7
=>
a = l/3
m = l - 7
we are using that in the first equation :
l/3 + l + l - 7 = 126
l + 3l + 3l - 21 = 378
7l = 357
l = 357/7 = 51
a = l/3 = 51/3 = 17
m = l - 7 = 51 - 7 = 44
the ratio of the age of Lucy to Alex to Megan is
51 : 17 : 44
