A key code must contain 6 numerals. There are 10 numerals available. Using these numerals, how many different key codes may be c
1 answer:
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Answer:
1. The sides are: 38.5, 39.5, 40.5 and 41.5
2. Presently, Inzo is 15 years old and Miz is 10 years old
3.
4. Possible pairs are: (12, 14), (16, 18) and (20, 24)
5.
Step-by-step explanation:
The question has lots of missing details. See the comment section for complete question
Solving (a):
Given
Shape: Quadrilateral
Sides: Consecutive
Let one of the sides be x. The other sides will be x + 1, x + 2 and x + 3.
So, the perimeter is:
This gives:
Collect Like Terms
Divide both sides by 4
<em>So, the sides are: 38.5, 39.5, 40.5 and 41.5</em>
<em></em>
Solving (b):
Given
Presently:
Five years ago: --- (Missing from the question)
Required: Determine their present ages
Substitute for Inzo in the second equation
Multiply both sides by 3
Collect Like Terms
Divide both sides by 2
Substitute 10 for Miz in
<em>So presently, Inzo is 15 years old and Miz is 10 years old</em>
Solving (3):
Given
Express Train:
Local Train:
Required: Determine the distance between A and B
Distance is calculated as:
For the express train:
For the local train
Distance between both stations are equal; So,
Collect Like Terms
Divide by 55
Substitute 36.82 for t in
Solving (4):
Let the even numbers be: n and n + 2.
Sum greater than 24:
Sum less than 60:
So, we have:
Collect Like Terms
Collect Like Terms
Divide by 2
So, we have:
and
So, possible pairs are: (12, 14), (16, 18) and (20, 24)
Solving (5):
Given
Required: Find the possible lengths
Let the length be L.
Perimeter is calculated as:
So, we have:
Divide through by 4
Hence, length is less than 38m (e.g. 37m)
Given that , we have
, so that
Take the derivative and find the critical points of :
Take the second derivative and evaluate it at the critical point:
Since is positive for all
, the critical point is a minimum.
At the critical point, we get the minimum value .