Find an equation of a line through (-2, 4) and perpendicular to -x+8y=16
2 answers:
Answer:
Step-by-step explanation:
The equation of the line has the form:
Where m is the slope and b is the y-intercept.
Let's find the slope of the given line. Solve for y:
Then m=1/8
By definition the slopes of perpendicular lines are negative reciprocals, therefore the slope of the other line is:
m=-8
Substitute the slope and the point given into the equation of the line to calculate b:
Then the equation is:
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Answer:
Where 0 < x < 3
The location of the local minimum, is (2, 0)
The location of the local maximum is at (0, 16)
Step-by-step explanation:
The given function is f(x) = (x + 2)⁴
The range of the minimum = 0 < x < 3
At a local minimum/maximum values, we have;
∴ (-x + 2)³ = 0
x = 2
When x = 2, f''(2) = -12×(-2 + 2)² = 0 which gives a local minimum at x = 2
We have, f(2) = (-2 + 2)⁴ = 0
The location of the local minimum, is (2, 0)
Given that the minimum of the function is at x = 2, and the function is (-x + 2)⁴, the absolute local maximum will be at the maximum value of (-x + 2) for 0 < x < 3
When x = 0, -x + 2 = 0 + 2 = 2
Similarly, we have;
-x + 2 = 1, when x = 1
-x + 2 = 0, when x = 2
-x + 2 = -1, when x = 3
Therefore, the maximum value of -x + 2, is at x = 0 and the maximum value of the function where 0 < x < 3, is (0 + 2)⁴ = 16
The location of the local maximum is at (0, 16).
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What is the value of this expression when c = -4 and d = 10 ? (c³ + d²)
(c³ + d²) where c = -4 and d = 10
The value of the expression (c³ + d²)
(c³ + d²) [Given expression]
Now, putting the value of c = -4 and d = 10 , we get,
{ (-4)³ + (10)² }
( -64 + 100 )
( 36 )
× 36