Answer:
Step-by-step explanation:
The equation of the line that is parallel to the line we are trying to find is
We can recall that when two lines are parallel it means that they have the same slope. Therefore the slope of the line we are trying to find is also -4. We now know that:
Therefore the equation of the line is:
Answer:
-a(a+4)/(16 - a²)
Step-by-step explanation:
a/(a - 4) Multiply by (a + 4)/(a + 4)
= a(a + 4)/[(a – 4)(a + 4)] Multiply the denominatorator terms
= a(a + 4)/(a² - 16) Multiply by -1/(-1)
= -a(a+4)/(-a² + 16) Reorder terms in denominator
= -a(a+4)/(16 - a²)
Answer:
2.29 ft of side length and 1.14 height
Step-by-step explanation:
a) Volume V = x2h, where x is side of square base and h is hite.
Then surface area S = x2 + 4xh because box is open.
b) From V = x2h = 6 we have h = 6/x2.
Substitude in formula for surface area: S = x2 + 4x·6/x2, S = x2 + 24/x.
We get S as function of one variable x. To get minimum we have to find derivative S' = 2x - 24/x2 = 0, from here 2x3 - 24 = 0, x3 = 12, x = (12)1/3 ≅ 2.29 ft.
Then h = 6/(12)2/3 = (12)1/3/2 ≅ 1.14 ft.
To prove that we have minimum let get second derivative: S'' = 2 + 48/x3, S''(121/3) = 2 + 48/12 = 6 > 0.
And because by second derivative test we have minimum: Smin = (12)2/3 + 4(12)1/3(12)1/3/2 = 3(12)2/3 ≅ 15.72 ft2
The distance between the two adjacent gas stations will be 5 miles.
<h3>What is the difference between a ratio and a proportion?</h3>
A ratio is an ordered pair of integers a and b expressed as a/b, with b never equaling 0. A percentage is a mathematical expression in which two ratios are specified to be equal.
Distance between city airport and the train station = 45 miles
Stations equally spaced between the airport and train station=9
Let the space between two gas stations will be x;
x = 45/9
x=5 mile.
Hence, the distance between the two adjacent gas stations will be 5 miles.
To learn more about the ratio, refer to the link;
brainly.com/question/14335762
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