Answer:
x=
−4
/3
y+5
Step-by-step explanation:
It is hard to comprehend your question. As far as I understand:
f(x,y) = e^(-x)
Find the volume over region R = {(x,y): 0<=x<=ln(6), -6<=y <= 6}.
That is all I understood. It would be easier to understand with a picture or some kind of visual aid.
Anyways, to find the volume between the surface and your rectangular region R, we must evaluate a double integral of f on the region R.

Now evaluate,

which evaluates to, 5/6 if I did the math correct. Correct me if I am wrong.
Now integrate this w.r.t. y:

So,

The sphere has surface are of 900π m².
Step-by-step explanation:
Given,
Diameter = d = 30m
Radius = 
Surface area of sphere = 

The sphere has surface are of 900π m².
Keywords: Surface area, multiplication
Learn more about spheres at:
#LearnwithBrainly
This question is incomplete
Complete Question
Tyler went to the supermarket to buy food for a food pantry. He has $36, and can carry up to 20 pounds of food in his backpack. Pasta costs $1 for a 1-pound package. Pasta sauce costs $3 for a 1.5 pound jar. Let x = the number of packages of pasta and y = the number of jars of pasta sauce. One package of pasta is the right amount to go with one jar of pasta sauce. What is the best numbers of packages of pasta and jars of pasta sauce to buy for the food pantry? Explain your reasoning.
Answer:
Eight is the best numbers of packages of pasta and jars of pasta sauce to buy for the food pantry.
Step-by-step explanation:
Let
x = the number of packages of pasta
y = the number of jars of pasta sauce.
He has $36, and can carry up to 20 pounds of food in his backpack. Pasta costs $1 for a 1-pound package. Pasta sauce costs $3 for a 1.5 pound jar.
x + 1.5y ≤ 20....... Equation 1
x = 20 - 1.5y
x × $1 + y × $3 = $36
x + 3y ≤ 36..... Equation 2
20 - 1.5y + 3y = 36
-1.5y + 3y = 36 - 20
1.5y = 16
y = 16/1.5
y = 8
And x = 8
Therefore,
Eight is the best numbers of packages of pasta and jars of pasta sauce to buy for the food pantry.
Answer
Find out the how long did they rest in 8 hours.
To prove
As given
contestants in a dance-a-thon rest for the same amount of time every hour.
A couple rests for 25 minutes in 5 hours .
As
25 mintues = 5 hours

1 hours = 5 mintues
Thus in 1hours a the dance -a-thon rest for 5 mintues.
Now for 8 hours.
8 hours = 8 × 5 mintues
= 40 mintues
Therefore in 8 hours a dance-a-thon rest for 40 mintues.