Triangle D E F is shown. Angle D E F is 90 degrees and angle F D E is 42 degrees. The length of D E is 7.2 and the length of E F
is d. What is the value of d to the nearest hundredth? d ≈
2 answers:
The value of the d is 6.48, if the angle D E F is 90 degrees and angle F D E is 42 degrees and the length of D E is 7.2 and the length of E F is d.
Step-by-step explanation:
The given is,
Angle D E F is 90 degrees
Angle F D E is 42 degrees
The length of D E is 7.2
The length of E F is d
Step:1
For the given values,
Triangle DEF is right angle triangle,
Ref the attachment,
Angle FDE, ∅ = 42°
DE = 7.2
EF = d
Trigonometric ratio for the given right angle triangle,
∅ =
∅ =
( the value of tan 42° = 0.900404 )
EF = d = 6.48
Result:
The value of the d is 6.48, if the angle D E F is 90 degrees and angle F D E is 42 degrees and the length of D E is 7.2 and the length of E F is d.
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If x is strictly negative (x < 0), then |x| = -x, and d|x|/dx = d(-x)/dx = -1.
But if x = 0, the derivative doesn't exist!
In order for the derivative of a function f(x) to exist at x = c, the limit
must exist. This limit does not exist for f(x) = |x| and c = 0 because the value of the limit depends on which way x approaches 0.
If x approaches 0 from below (so x < 0), we have
whereas if x approaches 0 from above (so x > 0), we have
But 1 ≠ -1, so the limit and hence derivative doesn't exist at x = 0.
Putting everything together, you can define the derivative of |x| as