In cylindrical coordinates, we have , so that
correspond to the upper and lower halves of a sphere with radius . In spherical coordinates, this sphere is .
means our region is between two cylinders with radius 1 and . In spherical coordinates, the inner cylinder has equation
This cylinder meets the sphere when
which occurs at
where . Then .
The volume element transforms to
Putting everything together, we have
The linear form of that equation is y=1/4x+2. Your y-intercept should be 2 and the slope is 1/4.
Answer:
y = 27/7
Step-by-step explanation:
Perform the indicated multiplication:
3(4y-7)=15y+6 becomes:
12y - 21 = 5y + 6
Combining like terms, we get:
7y = 27, so that y = 27/7
Answer:
<u>f(g(x)) = 9x² + 15x + 2</u>
Step-by-step explanation:
- f(x) = x² + 5x + 2
- g(x) = 3x
<u>Solving f(g(x))</u>
- f(g(x))
- f(3x)
- f(3x) = (3x)² + 5(3x) + 2
- f(3x) = 9x² + 15x + 2
- <u>f(g(x)) = 9x² + 15x + 2</u>
Answer:
1200 ml per hour
Step-by-step explanation:
To compute what rate is 300 ml over 15 mins as a rate of ml per hour, we do a rule of 3, using a variable x as that amount of ml we don't know yet. We should have everything in the same units, so instead of writing 1 hour we write 60 minutes:
Now we solve for x:
And so, now that we know the value of x, the rate we wanted to find is
Which is just 1200 ml per hour.