Michael is 4 times as old as Brandon and is also 27 years older than Brandon. How old is Michael?
2 answers:
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Answer:
Dimensions: 125 m x 250 m
Area: 31,250 m²
Step-by-step explanation:
Given information:
- Total amount of fencing = 500m
- Only 3 sides of the land need to be fenced
First, let us assume that the land is <u>rectangular</u> in shape.
Let = length of the side opposite the river
Let = length of the other 2 sides of the land
Therefore, we can create two equations from the given information:
<u>Area of land</u>:
<u>Perimeter of fence</u>:
Rearrange the equation for the perimeter of the fence to make y the subject:
Substitute this into the equation for Area:
To find the value of x that will make the area a <em>maximum</em>, <u>differentiate</u> A with respect to x:
Set it to zero and solve for x:
Substitute the found value of x into the original equation for the perimeter and solve for y:
Therefore, the dimensions that will give Christine the maximum area are:
125 m x 250 m (where 250 m is the side opposite the river)
The maximum area is:
Answer:
a) 2b = 3g
b) 3p = b
Step-by-step explanation:
Given:
Fire hydrant with a blue cap, b, provides water at a rate = 1500 gallons per min
Fire hydrant with a green cap, g, provides water at a rate = 1000 gallons per min
Fire hydrant with a purple cap, p, provides water at a rate = ½g =
a) The equation to relate the flow of water from the blue hydrant, b, to the flow from the green hydrant, g.
Given flow of blue hydrant, b = 500
Simplifying, we have:
b = 3*500
Since the flow rate of green hydrant, g, is 1000, let's replace 1000 with g above.
Therefore,
Cross multuply
The equation to relate the flow of water from the blue hydrant, b, to the flow from the green hydrant, g is 2b=3g.
b) An equation to relate the flow of water from the purple hydrant, p, to the flow from the blue hydrant, b.
Given flow rate of purple hydrant, p = 500
It could also be re-written as:
Since the flow rate of blue hydrant, b, is 1500, let's replace 1500 with b above.
Cross multiply
3p = b
Usually one will differentiate the function to find the minimum/maximum point, but in this case differentiating yields:
which contains multiple solution if one tries to solve for x when the differentiated form is 0.
I would, though, venture a guess that the minimum value would be (approaching) 5, since the function would be undefined in the vicinity.
If, however, the function is
Then differentiating and equating to 0 yields:
which gives:
or 
We reject x=5 as it is when it ix the maximum and thus,
, for 
which contains multiple solution if one tries to solve for x when the differentiated form is 0.
I would, though, venture a guess that the minimum value would be (approaching) 5, since the function would be undefined in the vicinity.
If, however, the function is
Then differentiating and equating to 0 yields:
which gives:
We reject x=5 as it is when it ix the maximum and thus,