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 =?

What is the shape of the height and weight distribution

The amount of calories consumed by customers at the chinese buffet is normally distributed with mean 2743 and standard deviation 652. one randomly selected customer is observed to see how many calories x that customer consumes. round all answers to 4 decimal places where possible. a. what is the distribution of x? x ~ n(correct,correct) b. find the probability that the customer consumes less than 2355 calories. incorrect c. what proportion of the customers consume over 3026 calories? incorrect d. the piggy award will given out to the 1% of customers who consume the most calories. what is the fewest number of calories a person must consume to receive the piggy award? incorrect calories. (round to the nearest calorie)

The equation m = 19.32v can be used to find the mass m in grams of a pure gold coin with volume v in cubic centimeters. carl has a coin with a mass of 37.8 grams. the coun's volume is 2.1 cubic centimeters. could the coin be pure gold? explain your reasoning. whoever answers this correctly gets marked brainliest! this is also worth a decent amount of points than normal questions!