The answer in decimal format is 15.7
Or 7 radical 5
Answer:
Step-by-step explanation:
Area of a trapezium is the average of the parallel sides times the distance between them.
If we subtract 15 units from each of the parallel sides, we end up with a triangle that has two sides of 8 units and one of 10 units. One of the 8 unit sides is the base and we need to find the height h which is perpendicular to this base.
Let the base be split into two segments, call one A, the other will be 8 - A
From Pythagoras.
10² - A² = h² = 8² - (8 - A)²
10² - A² = 8² - (8 - A)²
100 - A² = 64 - (64 - 16A + A²)
100 - A² = 64 - 64 + 16A - A²
100 = 16A
A = 6.25
h = √(10² - 6.25²)
h = √60.9375
A = ½(15 + 23)√60.9375
A = 148.31870246... ≈ 148.3 cm²
Answer:
look at the picture i sent.......
Answer:
Step-by-step explanation:
define the function:

As both
and x are continuous functions,
will also be continuous.
Now, what can we say about
?
we know that
, thus:

thus
is non-negative.
What about
? Again we have:

That means that
is not positive.
Now, we can imagine two cases, either one of
or
is equal to zero, or none of them is. If either of them is equal to zero, we have found a fixed point! In fact, any point
for which
is a fixed point, because:

Now, if
and
, then we have that
and
. And by Bolzano's theorem we can assert that there must exist a point c between a and b for which
. And as we have shown before that point would be a fixed point. This completes the proof.