Micah is thinking of a 2-digit number. It is a multiple of 6 and 12. It is a factor of 108. The sum of its digits is 9. What num
1 answer:
You might be interested in
Answer:
- Base Length of 84cm
- Height of 42 cm.
Step-by-step explanation:
Given a box with a square base and an open top which must have a volume of 296352 cubic centimetre. We want to minimize the amount of material used.
Step 1:
Let the side length of the base =x
Let the height of the box =h
Since the box has a square base
Volume,
Surface Area of the box = Base Area + Area of 4 sides
Step 2: Find the derivative of A(x)
Step 3: Set A'(x)=0 and solve for x
Step 4: Verify that x=84 is a minimum value
We use the second derivative test
Since the second derivative is positive at x=84, then it is a minimum point.
Recall:
Therefore, the dimensions that minimizes the box surface area are:
- Base Length of 84cm
- Height of 42 cm.
Answer: (12,9), (6,9), (12,-6) and (6,-6)
Step-by-step explanation:
Given: The coordinates of the original rectangle are (8, 6), (4, 6), (8, −4), and (4, −4). We know that the coordinates of the image after dilation from the origin by a scale factor of k is given by:_
Then, the coordinates of the image after dilation from the origin by a scale factor of 1.5 are given by:_
(8, 6)→
(4, 6)→
(8, −4) →
(4, −4)→
Hence, the coordinates of the image after dilation from the origin by a scale factor of 1.5 are (12,9), (6,9), (12,-6) and (6,-6).