HELP WITH MATH PLEASE! ASAP!!! Annika borrowed a book from the library and forgot to return it on time. The library charges $0.2
2 answers:
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Answer:
The visitor should run approximately 14.96 mile to minimize the time it takes to reach the island
Step-by-step explanation:
From the question, we have;
The distance of the island from the shoreline = 1 mile
The distance the person is staying from the point on the shoreline = 15 mile
The rate at which the visitor runs = 6 mph
The rate at which the visitor swims = 2.5 mph
Let 'x' represent the distance the person runs, we have;
The distance to swim =
The total time, 't', is given as follows;
The minimum value of 't' is found by differentiating with an online tool, as follows;
At the maximum/minimum point, we have;
Simplifying, with a graphing calculator, we get;
-4.72·x² + 142·x - 1,070 = 0
From which we also get x ≈ 15.04 and x ≈ 0.64956
x ≈ 15.04 mile
Therefore, given that 15.04 mi is 0.04 mi after the point, the distance he should run = 15 mi - 0.04 mi ≈ 14.96 mi
Therefore, the distance to run, x ≈ 14.96 mile
Answer:
Please refer to the attached graph for the graph of linear inequality:
Step-by-step explanation:
Method to draw graph of inequality:
<u>1. First of all replace the inequality sign with equality.</u>
Now the equation is:
Now, find point and plot them.
Let us put x = 0, we get y = -1. So one point is <em>(0, -1)</em>
Let us put y = 0, we get x = 2. So one point is <em>(2,0)</em>
Now, plot both the point and join with straight line on xy coordinate axis.
2. Now, try to find a random point and put in the inequality.
If the point satisfies the inequality shade the region moving from the line towards that point.
For example:
Taking a point (4, 2)
Putting in the inequality:
So, (4, 2) satisfies the inequality.
Now, shade the region moving from the line towards the point (4,2).
We get the shaded region as shown in the attached figure in the answer area.
