Apet-store supply truck moves at 25.0 m/s north along a highway. inside, a dog moves at 1.75 m/s at an angle of 35.0 degrees east of north. what is the velocity of the dog relative to the road?
i did all of my math, but i somehow got a negative number for the resultant vector, but if i'm not mistaken, the resultant vector is going in a positive direction, so something is not adding i guess the only thing i need with is figuring out what angle i'm supposed to use for the law of cosine formula?

Along, straight wire with 3.0 a current flowing through it produces magnetic field strength 1.0 t at its surface. if the wire has a radius r, where within the wire is the field strength equal to 36.0% of the field strength at the surface of the wire? assume that the current density is uniform throughout the wire

Comedians like to joke that the reason we haven’t been visited by intelligent life from elsewhere in the universe is that aliens have been monitoring earth’s broadcasts of intellectually embarrassing tv programs, like gilligan’s island, fear factor, the jersey shore, and the jerry springer showand so consider us far too primitive to merit a visit. let’s check the assertion that aliens could have been receiving them. tv programs are broadcast at a frequency of about 100mhz with about 100kw of total power in 30frames per second, which emanatesroughly uniformly in all directions. assume that interstellar space transmits these broadcasts without attenuation. no matter how smart they are, aliens would require at least one photon per frame to interpret our signals. findthe number of photons per unit time per unit area reaching a receiver on a possible planet in the nearest star system, which is about 4 light-years away (a light-year is the distance light travels in a year). if aliens aimed a receiver or detector directly at earth, how big (in diameter) would it have to be to receive a photon per frame

The radius of a sphere is increasing at a rate of 9 cm/ sec. find the radius of the sphere when the volume and the radius of the sphere are increasing at the same numerical rate.