The minimum value for g(x)=x² - 10x + 16 is -9
<h3>How to determine the minimum value?</h3>
The function is given as:
g(x)=x² - 10x + 16
Differentiate the function
g'(x) = 2x - 10
Set the function 0
2x - 10 = 0
Add 10 to both sides
2x = 10
Divide by 2
x = 5
Substitute 5 for x in g(x)
g(5)=5² - 10*5 + 16
Evaluate
g(5) = -9
Hence, the minimum value for g(x)=x² - 10x + 16 is -9
Read more about quadratic functions at:
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Answer:
312π mm³
Step-by-step explanation:
Given:
Oblique cone height, h = 14 mm
radius of half sphere = base radius of cone, r = 6 mm
Recall the volume of 1/2 - sphere
= 1/2 x volume of sphere
= 1/2 x (4π/3) r³
= 1/2 x (4π/3) (6)³
= 144π
Also volume of an oblique cone =
=volume of a right cone
= (π/3) r²h
= (π/3) 6²(14)
=168π
Volume of composite figure = 144π + 168π = 312π mm³
Rotation
It’s rotating 90 degrees counterclockwise
Answer:
x = - 2, x = 6
Step-by-step explanation:
Given f(x) = 18 we require to solve
3 | x - 2 | + 6 = 18 ( subtract 6 from both sides )
3 | x - 2 | = 12 ( divide both sides by 3 )
| x - 2 | = 4
The absolute value function always returns a positive value, however, the expression inside can be positive or negative, thus
x - 2 = 4 ( add 2 to both sides )
x = 6
OR
- (x - 2) = 4
- x + 2 = 4 ( subtract 2 from both sides )
- x = 2 ( multiply both sides by - 1 )
x = - 2
As a check substitute these values into the left side of the equation and if equal to the right side then they are the solutions
x = 6 → 3|6 - 2| + 6 = 3|4| + 6 = 3(4) + 6 = 12 + 6 = 18 ← True
x = - 2 → 3|- 2 - 2| + 6 = 3|-4| + 6 = 3(4) + 6 = 12 + 6 = 18 ← True
Hence solutions are x = - 2, x = 6
The answers are as follows:
Box 1) D
Box 2) .02D
Box 3) D + .02D
