Answer:
The rhombus ABCD has an area of 22 square units.
Step-by-step explanation:
The coordinates of rhombus ABCD are shown in the image attached below. The area of the rhombus can be found in terms of their diagonals, which are now calculated by Pythagorean Theorem:
![AC = \sqrt{[6-(-4)]^{2}+[8-(-4)]^{2}}](https://tex.z-dn.net/?f=AC%20%3D%20%5Csqrt%7B%5B6-%28-4%29%5D%5E%7B2%7D%2B%5B8-%28-4%29%5D%5E%7B2%7D%7D)
![BD = \sqrt{(4-6)^{2}+[0-(-2)]^{2}}](https://tex.z-dn.net/?f=BD%20%3D%20%5Csqrt%7B%284-6%29%5E%7B2%7D%2B%5B0-%28-2%29%5D%5E%7B2%7D%7D)
The area of the rhombus is: ( and )
The rhombus ABCD has an area of 22 square units.
Answer:
dy/dx = 6x(x²-3)cos2x - 2(x²-3)³sin2x
Step-by-step explanation:
We use the Product Rule:
y= (x²-3)³cos2x
dy/dx = (x²-3)³ d(cos2x)/dx + cos2x * d ((x²-3)³)/dx
= (x²-3)³ * -2sin2x + cos2x * 3(x²-3)*2x
= -2sin2x*(x²-3)³ + 6xcos2x*(x²-3)
= 6x(x²-3)cos2x - 2(x²-3)³sin2x
Answer:
40 degrees
Step-by-step explanation:
The 100 degree angle is supplementary to angle CED. This means CED will end up being 80 degrees. Since the angles in all triangles equate to 180 degrees 80 + 60 + angle D must equal 180 degrees. Therefore, angle D has to be 40 degrees.
Answer:
<u>37.5 parcels </u>in 5 minutes. Round down to 37, if required for the purpose of the calculation.
Step-by-step explanation:
Let M and K be the rates Michael and Kate can pack parcels, in parcels/minute, or p/m.
M = (10/3)p/m
K = (7/2)p/m
When they work together for 5 minutes, we can calculate the numbers of parcels each pack.
Michael: ((10/3)p/m)*(5m) = 20 p
Kate: ((7/2)p/m)*(5m) = 17.5 p
Total = 37.5 parcels
