Answer:
AFCE = 30
P+Q = 11
Step-by-step explanation:
From the picture, you can see the figure can be decomposed into two identical large triangles with area 20, and 4 identical longer ones, that have to cover the remaining area 40, thus 10 each.
From that you can count the area.
Second puzzle is just trial and error.
Answer:
Step-by-step explanation:
separate with like terms
the first fraction can be left alone as it can't be simplified any further
the second fraction can be written as w⁹ ÷ w¹ , when the bases are the same and division is involved subtract the powers: 9 - 1 = 8, so it's simplified to w⁸
the third fraction can be written as m⁵ ÷ m⁹, subtract the powers: 5 - 9 = -4, so it's simplified to m⁻⁴
putting it together:
Answer:
--- Objective function
Interval =
Step-by-step explanation:
Given
Represent the number with x
The required sum can be represented as:
Hence, the objective function is:
To get the the interval, we start by differentiating w.r.t x
<em>Using first principle, this gives:</em>
Equate S'(x) to 0 in order to solve for x
Subtract 1 from both sides
Multiply both sides by -1
Cross Multiply
Take positive square root of both sides because x is positive
Representing x using interval notation, we have
Interval =
To get the smallest sum, we substitute 1 for x in
<em>Hence, the smallest sum is 2</em>