Suppose that a and b are nonzero vectors that are not parallel and c is any vector in the plane determined by a and b. give a geomatric argument to show that c can be written as c=sa+tb for suitable scalars s and t. then give an argument using components.

You are responsible for designing a new city. you are inspired by pierre charles l'enfant, who laid out the streets of our nation's capital. numbered streets run north and south, and lettered streets run east and west. avenues are named after states, and they intersect the streets on a diagonal. the streets are parallel and the intersections form similar triangles. 18th st. is 454 meters long and the intersection of 18th and k st. is 207 meters from connecticut ave. if 19th st. and k st. is 385 meters from connecticut ave., what is the length of 19th st.?

In a circle, a 45° sector has an area of 32π cm2. what is the radius of this circle? 32 cm 12 cm 16 cm 8 cm

You are standing next to a really big circular lake. you want to measure the diameter of the lake, but you don't want to have to swim across with a measuring tape! you decide to walk around the perimeter of the lake and measure its circumference, and find that it's 400\pi\text{ m}400? m. what is the diameter dd of the lake?