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2 answers:
Answer:
Option A is correct.
-2 is the rate of change for the interval between –6 and –3 on the x-axis
Step-by-step explanation:
Average rate of change(A(x)) of function f(x) over the interval [a, b] is given by:
.....[1]
As per the statement:
To find the rate of change for the interval between –6 and –3 on the x-axis.
At x = -6
From the graph:
f(-6) = 6
At x = -3
then;
f(-3) = 0
Substitute these in [1] we have;
Therefore, the rate of change for the interval between –6 and –3 on the x-axis is, -2
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The length of the KN is 4.4
Step-by-step explanation:
We know from Pythagoras theorem
In a right angle ΔLMN
Base² + perpendicular² = hypotenuse ²
From the properties of triangle we also know that altitudes are ⊥ on the sides they fall.
Hence ∠LKM = ∠NKM = 90 °
Given values-
LM=12
LK=10
Let KN be “s”
⇒LN= LK + KN
⇒LN= 10+x eq 1
Coming to the Δ LKM
⇒LK²+MK²= LM²
⇒MK²= 12²-10²
⇒MK²= 44 eq 2
Now in Δ MKN
⇒MK²+ KN²= MN²
⇒44+s²= MN² eq 3
In Δ LMN
⇒LM²+MN²= LN²
Using the values of MN² and LN² from the previous equations
⇒12² + 44+s²= (10+s) ²
⇒144+44+s²= 100+s²+20s
⇒188+s²= 100+s²+20s cancelling the common term “s²”
⇒20s= 188-100
∴ s= 4.4
Hence the value of KN is 4.4
