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1 answer:
Answer:
An artist use 51.9 feet of string for constructing a piece of art in the shape of rectangle
Step-by-step explanation:
Here an artist is constructing a piece of art in the shape of rectangle having length 12 feet & width of 7 feet
Since the artist wants to use string to tightly tie each vertex of rectangle to the other three vertices. Hence one string will tie in a diagonal way
Hence total length of string will be
Total length = Perimeter of rectangle + length of diagonal
Perimeter of rectangle = 2( length + width ) = 2 ( 12 + 7 ) = 2 x 19 = 38 feet
Length of diagonal given by Pythagoras theorem
Hence
Total length = Perimeter of rectangle + length of diagonal
Total length = 38 feet + 13.89244 feet = 51.9 feet
Hence an artist use 51.9 feet of string for constructing a piece of art in the shape of rectangle
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Answer:
There is not root of the function on the interval [0, 1].
Step-by-step explanation:
The Intermediate Value Theorem says:
<em>If f(x) is a continuous function on [a, b], then for every d between f(a) and f(b), there exists a value c in between a and b such that f(c) = d.</em>
This means that whenever we can show that:
- there is a point above some line
- and a point below that line, and
- that the curve is continuous,
we can then safely say yes, there is a value somewhere in between that is on the line.
To show that there is solution between x = 0 and x = 1.
We evaluate the function at x = 0 and x = 1
We know that
at x = 0, the line is above zero and
at x = 1 the line is above zero.
We also know that the function is continuous but because the line is always above zero there is no solution at the interval (0, 1).
We can check our work with the graph of the function.
