The area calculation for the shaded section, as seen in the attached diagram, involves subtracting the area of the kite from that of the rectangle. The area of the rectangle is calculated as (3x+x)*(x+x), which simplifies to 4x*2x, equating to 8x². The area of the kite is determined using the formula (1/2)*[d1*d2], where d1 and d2 represent the diagonals, specifically d1=4x and d2=2x. Therefore, the area of the kite becomes (1/2)*[4x*2x], leading to 4x². Consequently, the area of the shaded region can be computed as 8x²-4x², resulting in 4x². Thus, the solution is 4x².
Answer:
24
Step-by-step explanation:
Based on the logarithmic expressions given
, we need to identify the value of 
By substituting x = a³, y = a⁷, and z = a⁻² into the logarithmic function
, we will derive;

Therefore, the result of the logarithmic expression is 24
Take note of the image below
the riverbank requires no fencing due to the river's presence
so the pen's perimeter can be calculated as 2w + l, or w + w + l
thus

derive P(w), set it to zero, locate any critical points, and perform a first-derivative test for minimum values.
Response:1 and 2
Step-by-step Explanation:
Provided data
Volume required 
For the initial cylinder





For the second cylinder





For the third cylinder





For the fourth cylinder





Thus, cylinders
and
meet the requirement as they remain under 