Use the Fundamental Theorem of Line Integrals to calculate ∫C∇ϕ⋅dr⃗ exactly, if ϕ(x, y)=3yln(x)+5x2−5y, and C is the curve parametrized by r⃗ (t)=⟨t4+1,2t11⟩ where 0≤t≤1. ∫C∇ϕ⋅dr⃗ = ?

(B) (6 pts.) Calculate the following line integral, if L is the line segment from (1,0) to (3,0).

∫L(3yx+10x+4xx2+1+ln(y2+1))dx+(3ln( x)−5+xarctan(y4+4))dy =?

During your cycling trip, you and your friends often stayed in hostels. the prices of these are listed below. hostel standard room (price per night) with breakfast (price per night) super sleep hostels £22.45 £28.65 normandy nights £18.55 £25 zzzola hostels £24.50 £30.99 belgian beds £11.20 £18.55 night-time rest days ? £33 what is the range in cost for a single night, including both standard room prices and with breakfast prices?

Will give brainliest plz hurry lexie surveyed 4 teenagers to find out approximately how many hours, per week, they read for fun, and how many siblings they have. brooke said she reads about 10 h a week for fun, and that she has 5 siblings. celia said she has 1 brother and 1 sister and reads for fun about 3 h each week. henry said he has 2 brothers and reads for fun about 30 min each week. jude said he doesn't read for fun and has 3 brothers and 3 sisters. use this information to complete the data table. express your answers as whole numbers or decimals. name hours of fun number of siblings brooke celia __ henry jude

Askyscraper is 396 meters tall. at a certain time of day, it casts a shadow that is 332 meters long. at what angle is the sun above the horizon at that time?