Because I've gone ahead with trying to parameterize directly and learned the hard way that the resulting integral is large and annoying to work with, I'll propose a less direct approach.
Rather than compute the surface integral over straight away, let's close off the hemisphere with the disk of radius 9 centered at the origin and coincident with the plane . Then by the divergence theorem, since the region is closed, we have
where is the interior of . has divergence
so the flux over the closed region is
The total flux over the closed surface is equal to the flux over its component surfaces, so we have
Parameterize by
with and . Take the normal vector to to be
Then the flux of across is
<h2><u>Question</u><u>:</u><u>-</u></h2>
A fruitseller bought 50kg of the fruits. He sold 30kg of fruits for the cost price of 35kg of fruits and he sold the remaining quantity for the cost Price of 18kg of fruits. calculate his profit or loss percent in the total transaction.
<h2><u>Answer</u><u>:</u><u>-</u></h2>
let the cost price be 50x
→he sells 30kg of fruits on it's CP of 35 kg
→CP of 30kg fruits = 30x
→SP of 35kg fruits = 35x
→remaing fruits are 20kg
→he sells 20kg of fruits on CP of 16kg
→CP of 20kg fruits = 20x
→SP of 20kg fruits = 16x
→total CP is = 50x
→total SP is = (35 + 16) = 51x
→SP > CP (it means profit)
→profit = SP-CP
→ 51-50
→ 1
<h2 /><h2><u>Now,</u></h2>
→ Profit% = gain/CP × 100
→ Profit% = 1/50 × 100
→ 2%
Hence the fruit seller had a profit% of 2%.
Y=x+10
y is the total cost
x is the number of toppings times $1
10 is the cost of the pizza
If the price of paper increases by a lot, then book producers would respond by supplying less books.