Answer:
The similar triangles are 
and 
and 
Step-by-step explanation:
Given
See attachment for the required figure
Solving (a): The similar triangles
The similar triangles are and
Solving (b): Why they are similar
Both triangles are similar because is dilated (i.e. enlarged) and then reflected to give .
Solving (c): Calculate BE and PE
The following are equivalent ratios
and
Solving for BE, we have:
Substitute the known values
Express as fraction
Multiply both sides by 450
-- approximated
Solving for PE, we have:
Substitute known values
Express as fraction
Multiply both sides by 400
Use This Since You provided no context:
The fundamental theorem of calculus is a theorem that links the concept of differentiating a function (calculating the gradient) with the concept of integrating a function (calculating the area under the curve). ... This implies the existence of antiderivatives for continuous functions.
I'm pretty sure you are looking for factored forms as an equivalent equation, so here is how you do it.
This equation would be solved by difference of squares. 16, x^4, and 81 are all perfect squares ( which means that it is a number multiplied by itself, 16 is 4 x4 for example). So the first thing you want to do is recall the formula which is
(a^2 - b^2) = (a - b)*(a + b)
(16x^4 - 81)= 0
Find the sq. root of 16 which is 4, and of x^4 which is x^2, and 81 which is 9. Now re write it in the (a - b)*(a + b) format. ----> (4x^2 - 9)*(4x^2 + 9) = 0
