Find the approximate side length of a square game board with an area of 105 in2.

Mathematics

1 answer:

aleksley [76]1 year ago

8 0

Answer:

Rounded to the nearest inch: 10

Rounded to the nearest tenth: 10.2

Rounded to the nearest hundredth: 10.25

Step-by-step explanation:

To find the area of a square, we multiply the side length by itself, or in other words, SQUARE the side length!

$A=s^2$

We are given the area, so plugging that into our equation looks like this:

$105=s^2$

To eliminate the exponent, take the square root of both sides of the equation!

$\sqrt{105}=s$

From here, there are a few paths to take, depending on what your teacher is looking for. I will evaluate the approximate of the square root by finding the nearest perfect squares.

The nearest perfect square less than √105 is √100, and the nearest perfect square greater than √105 is √121.

105 is closer to 100 than to 121, so √105 is closer to √100.

√100 is equal to 10, so the √105 is approximately 10 inches!

Using a calculator to check:

$\sqrt{105}=10.247$ inches

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Answer:

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Step-by-step explanation:

The Mean Value Theorem says,

Let be a function that satisfies the following hypotheses:

f is continuous on the closed interval [a, b].
f is differentiable on the open interval (a, b).

Then there is a number c in (a, b) such that

$f'(c)=\frac{f(b)-f(a)}{b-a}$

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By assumption, the car’s speed is continuous and differentiable everywhere. This means we can apply the Mean Value Theorem.

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