The function is (-x+3)/ (3x-2) and we get f(1)=1 and differentiation is f'(x)=-7/ (9x²- 12x+4).
Given that,
The function is (-x+3)/ (3x-2)
We have to find f(1) and f'(x).
Take the function expression
f(x)= (-x+3)/ (3x-2)
Taking x as 1 value
f(1)= (-1+3)/(3(1)-2)
f(1)=2/1
f(1)=1
Now, to get f'(x)
With regard to x, we must differentiate.
f(x) is in u/v
We know
u/v=(vu'-uv')/ v² (formula)
f'(x)= ((3x-2)(-1)- (-x+3)(3))/ (3x-2)²
f'(x)= ((-3x+2)-(-3x+9))/ 9x²- 12x+4
f'(x)=(-3x+2+3x-9)/ 9x²- 12x+4
f'(x)=2-9/ (9x²- 12x+4)
f'(x)=-7/ (9x²- 12x+4)
Therefore, The function is (-x+3)/ (3x-2) and we get f(1)=1 and differentiation is f'(x)=-7/ (9x²- 12x+4).
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The volume of the cylindrical water tank that has a length of 20 feet and a radius of 12 feet is about <u>9,048</u> cubic feet.
The correct option is option <em>d</em>;
d. 9,048
<h3>What is the volume of a solid?</h3>
The volume of a solid indicates the amount of space the solid takes at a location.
The formula for finding the volume of the cylindrical tank is presented as follows;
<em>V</em> = π·r²·L
Where;
r = The radius of the tank
L = The length of the tank
From a similar question on the website, we have;
The length of the tank, <em>L</em> = 20 feet
Therefore;
The volume of the tank, <em>V</em> = π × 12² × 20 ≈ 9048
- The volume of the water tank is about <u>9,048</u> cubic feet
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It will be at point (5,5)
Solution:
Average time per line = total time / total lines
Average time per line = (3x^2 + 2)/(x + 4)
Average time per line = 3x - 12 + (3x^2 + 2)/50 milliseconds