Answer:
-Exponential Decay
-Decay factor is (1-0.05)
Step-by-step explanation:
-Given that the number decreases by a defined rate each year from the initial size by 5%,
-This is an exponential decay function of the form:
Where:
is the quantity/size after time t
is the initial size
is the rate of decay
-Our function can the be written as
Hence, the decay rate/factor is 0.05
#Alternatively
The exponential decay can be of the form:
Where:
y is the size at time x, a is the initial size, x is time and b is the decay factor.
b is of the form 
Hence, the decay factor is (1-0.05)
Option B:
Solution:
In the given figure 
.
If two triangles are similar, then their corresponding sides and angles are equal.
By CPCTC, in 
,
– – – – (1)
– – – – (2)
– – – – (3)
– – – – (4)
– – – – (5)
– – – – (6)
Option A: 
By CPCTC proved in equation (2) .
Therefore 
. Option A is false.
Option B:
By CPCTC proved in equation (1) .
Therefore Option B is true.
Option C: 
By CPCTC proved in equation (4) .
Therefore 
. Option C is false.
Option D: 
By CPCTC proved in equation (5) .
Therefore 
. Option D is false.
Hence Option B is the correct answer.
Answer: (a) e ^ -3x (b)e^-3x
Step-by-step explanation:
I suggest the equation is:
d/dx[integral (e^-3t) dt
First we integrate e^-3tdt
Integral(e ^ -3t dt) as shown in attachment and then we differentiate the result as shown in the attachment.
(b) to differentiate the integral let x = t, and substitute into the expression.
Therefore dx = dt
Hence, d/dx[integral (e ^-3x dx)] = e^-3x
Answer:
Step-by-step explanation:
Given
Required
Determine x2, y2
Start by splitting the expression
and 
Solving for x2 in
Multiply through by 2
Make x2 the subject;
Similarly:
Multiply through by 2
Make y2 the subject;
Hence:
