a) Let $\mathcal{R}$ be the region consisting of the points $(x,y)$ that satisfy \[-6 \le 3x - 5y \le 6\]and \[-3 \le x + 2y \le
3.\]Plot the region $\mathcal{R},$ and identify the vertices of polygon $\mathcal{R}.$ (b) Find the maximum value of $x + y$ among all points $(x,y)$ in $\mathcal{R}.$
2 answers:
First, we can solve the inequalities as if they were equalities, so we solve the equation 3x - 5y = -6 and x + 2y = 3. Eliminating y, we get x = 3/11. Then y = 15/11, so (x,y) = (3/11, 15/11) is one corner of the region R. The inequalities are symmetric around the origin, so the region R is also symmetric around the region. So R is the rectangle with vertices (-3/11, 15/11), (3/11, 15/11), (-3/11, 15/11), and (-3/11, -15/11).
The maximum value of x + y is then given by the corners of the rectangle R, so the maximum is 3/11 + 15/11 = 18/11.
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Answer:
The population will be 896 turtles 6 years later ⇒ B
Step-by-step explanation:
The exponential increasing formula is y = a, where
- y is the new value
- a is the initial value
- r is the rate of increase in decimal
- x is the time in years
∵ There are 300 turtles
∴ a = 300
∵ The population of the turtles exponentially increases 20% each year
∴ r = 20%
→ Divide it by 100 to change it to decimal
∵ 20% = 20 ÷ 100 = 0.2
∴ r = 0.2
∵ The time is 6 years
∴ x = 6
→ Substitute these values in the exponential formula above
∵ y = 300
∴ y = 300
∴ y = 895.7952
→ Round it to the nearest whole number
∴ y = 896
∴ The population will be 896 turtles 6 years later