anonymous
  • anonymous
let f(t) be the area of the parallelogram with vertices v=(1,2t), w=(2t,1), (0,0) and v+w=(2t+1,2t+1). find a formula for f(t)
Mathematics
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
schrodinger
  • schrodinger
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anonymous
  • anonymous
emt16, you can make a plot of this thing like I have attached.
1 Attachment
anonymous
  • anonymous
There are a couple of ways of going about it. The easiest is to use the fact that the magnitude of the vector cross product gives the area of a parallelogram. Another way is to find the equation of the line for the base, say, and then use the slope of that base line to determine the slope of a line that is perpendicular to that line and cuts the point, (1,2t), say. I think it's easier to use vectors. The vector of AB is given by B - A => (1-0,2t-10) = (1,2t) The vector AD is D - A => (2t-0,1-0) = (2t,1)
anonymous
  • anonymous
The cross product is then AB x AD = (4t^2-1) in the direction perpendicular to the x-y plane. The area is the magnitude of this vector, which is f(t) = 4t^2-1

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

anonymous
  • anonymous
Are vectors your thing or not?
anonymous
  • anonymous
ok. i can see now how it works. vectors aren't my strongest point but this helps a lot. thanks
anonymous
  • anonymous
Good. It's easier than using coordinate geometry. You'd have to find equations of lines and distances and everything...would take forever.

Looking for something else?

Not the answer you are looking for? Search for more explanations.