Answer:
The lines a and b are parallel
Step-by-step explanation:
When we will translate line a, then the new line b will be formed.
Now, as translation preserves orientation each point on line a will be equidistant from line b , thus holding the condition and satisfying the property of two parallel lines.
Hence, line a and line b are parallel to each other.
Answer:
Step-by-step explanation:
Represent the volume of the box with V and the dimensions with l, b and h.
The volume (V) is:
Make h the subject of the formula
The surface area (S) of the aquarium is:
Where lb represents the area of the base (i.e. slate):
The cost (C) of the surface area is:
Substitute for h in the above equation
Differentiate with respect to l and with respect to b
To solve for b and l, we equate both equations and set l to b (to minimize the cost)
By comparison:
becomes
Cross Multiply
Solve for l
Recall that:
Also recall that:
Apply law of indices
The dimension that minimizes the cost of material of the aquarium is:
Answer:
The Point C shows the location of 5-2i in the complex plane: 5 points to the right of the origin and 2 points down from the origin.
Step-by-step explanation:
We have the complex number 5-2i and we have to show the location of the point that represents that number in the complex plane
In the complex plane the real numbers are located in the horizontal axis, increasing to the right. The positives real numbers are at the right of the origin and the negatives to the left.
The complex numbers are located in the vertical axis, with the positives over the origin and the negatives below the origin.
This complex number 5-2i is the sum of a real part (5) and a imaginary part (-2i), so the point will be 5 units rigth on the horizontal axis (for the real part) and 2 units down in the vertical axis (for the imaginary part).
