How many solutions does the following equation have? -2z+10+7z=16z+7
2 answers:
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Answer:
3π square units.
Step-by-step explanation:
We can use the disk method.
Since we are revolving around AB, we have a vertical axis of revolution.
So, our representative rectangle will be horizontal.
R₁ is bounded by y = 9x.
So, x = y/9.
Our radius since our axis is AB will be 1 - x or 1 - y/9.
And we are integrating from y = 0 to y = 9.
By the disk method (for a vertical axis of revolution):
So:
Simplify:
Integrate:
Evaluate (I ignored the 0):
The volume of the solid is 3π square units.
Note:
You can do this without calculus. Notice that R₁ revolved around AB is simply a right cone with radius 1 and height 9. Then by the volume for a cone formula:
We acquire the exact same answer.
Answer:
A. at (8,7) the maximum value is 98
Step-by-step explanation:
First draw the region, that is bounded by all
inequalities. This is the triangle with vertices
(6,1), (2,5) and (8,7).
Now you can see where the line f(x,y)=7x+6y
intersect this region. The maximum value will be
at endpoints of this region:
• at (6,1), f(6,1)=7-6+6-1=42+6=48;
·
at (2,5), f(2,5)=7·2+6.5=14+30=44;
• at (8,7), f(8,7)=7.8+6-7=56+42=98.
Thus, the maximum value of the function is 98 at
the point (8,7).
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