What is the area of rhombus ABCD ? Enter your answer in the box. Do not round at any steps. units² Rhombus A B C D on a coordina
te plane with vertex A at negative 1 comma 4, vertex B at 3 comma 2, vertex C at negative 1 comma 0, and vertex D at negative 5 comma 2. Point P is at negative 3.4 comma negative 1.2. Dashed segments join point P to point D and point P to point C, forming right angle D P C.
1 answer:
Answer:
16 units²
Step-by-step explanation:
Diagonal AC is a vertical line extending from y=0 to y=4, so is 4 units long.
Diagonal BD is a horizontal line extending from x=-5 to x=3, so is 8 units long.
The area of a rhombus is half the product of the lengths of the diagonals, so ...
A = (1/2)(4 units)(8 units) = 16 units²
The area of rhombus ABCD is 16 units².
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Answer:
volume V of the solid
Step-by-step explanation:
The situation is depicted in the picture attached
(see picture)
First, we divide the segment [0, 5] on the X-axis into n equal parts of length 5/n each
[0, 5/n], [5/n, 2(5/n)], [2(5/n), 3(5/n)],..., [(n-1)(5/n), 5]
Now, we slice our solid into n slices.
Each slice is a quarter of cylinder 5/n thick and has a radius of
-k(5/n) + 5 for each k = 1,2,..., n (see picture)
So the volume of each slice is
for k=1,2,..., n
We then add up the volumes of all these slices
Notice that the last term of the sum vanishes. After making up the expression a little, we get
But
we also know that
and
so we have, after replacing and simplifying, the sum of the slices equals
Now we take the limit when n tends to infinite (the slices get thinner and thinner)
and the volume V of our solid is
