Bring it to the form ax + by = c, where a is positive, and there are no fractions in the equation.
Here, we need to add 2/5x to both sides:
2/5x + y = 0
Then multiply everything by 5 to get rid of the fraction
2x + 5y = 0 <==
The dimensions of the garden that will require the least amount of fencing are 450 m and 900 m and the perimeter of the area is 1800 m.
<h3>What is the area of the rectangle?</h3>
It is defined as the area occupied by the rectangle in two-dimensional planner geometry.
The area of a rectangle can be calculated using the following formula:
Rectangle area = length x width
Let's suppose x and y are the sides of the rectangular garden and y is the parallel to the river.
Then according to the problem:
2x + y = P ..(1)
P is the perimeter of the rectangle.
xy = 405000 (area of the rectangle)
Plug the value of y in the equation (1) from the above equation.
P(x) = 2x + 405000/x
P'(x) = x—405000/x² = 0
x = 450 m
P''(x) > 0 hence at x = 450 the value of P(x) is minimum.
y = 405000/450
y = 900 m
P(min) = 1800 m
Thus, the dimensions of the garden that will require the least amount of fencing are 450 m and 900 m and the perimeter of the area is 1800 m.
Learn more about the rectangle here:
brainly.com/question/15019502
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Answer:
b) The measure of angle B is 117°.
Step-by-step explanation:
Angles A and C are vertical angles, so are congruent. Angles C and 27° total 90°, so ...
∠C = 90° -27° = 63° . . . . . not 53°
The measure of angle B is the supplement of angle A or C, so is ...
∠B = 180° -∠C = 180° -63°
∠B = 117°
Only choice B is correct.
DB/dt = 1/5(100 - B)
5/(100 - B) dB = dt
-5 ln (100 - B) = t + C
Since B(0) = 20, then
-5 ln (100 - 20) = C
i.e. C = -5 ln 80
Thus -5 ln (100 - B) = t - 5 ln 80
or t = 5 ln 80 - 5 ln (100 - B) = 5 ln (80 / (100 - B))
When the weight = 40 grams
t = 5 In (80 / 100 - 40) = 5 In (80 / 60) = 5 ln (4/3) = 1.438 days
Rate of weight gain = 40 / 1.438 = 27.8 grams per day
When the weight = 70 grams
t = 5 ln (80 / 100 - 70) = 5 ln (80 / 30) = 5 ln (8/3) = 4.9 days
Rate of weight gain = 70/4.9 = 14.27 grams per day.
Therefore, the duck gains weight faster when it weighs 40 grams.
