what whole number and rational number to the nearest half is 40√ between

Answer 1

To find the whole number and rational number to the nearest half that is between $40$ and $\sqrt{40}$, we need to find the whole number and rational number to the nearest half between $6.32$ and $6$.

Since $6$ is closer to $6.32$ than $6.5$, the whole number and rational number to the nearest half between $40$ and $\sqrt{40}$ is $\boxed{6}$.

Answer 2

The diagonal of a square equals 2–√ times the side length. Using 1.4 for the square root of 2, what is the approximate length in feet from one corner to an opposite corner of a square park that is 700 feet on a side?

Answer 3

If the diagonal of a square is equal to $2 - \sqrt{2}$ times the side length, we can set up the equation:

$\text{diagonal} = (2 - \sqrt{2}) \times \text{side length}$

We are given that the side length is 700 feet, so we substitute that in:

$\text{diagonal} = (2 - \sqrt{2}) \times 700$

Using the given approximation $1.4$ for $\sqrt{2}$, we can simplify the equation:

$\text{diagonal} = (2 - 1.4) \times 700$

$\text{diagonal} = 0.6 \times 700$

$\text{diagonal} = 420$ feet

Therefore, the approximate length from one corner to an opposite corner of the square park is $\boxed{420}$ feet.

Answer 4

The height of an equilateral triangle equals √3/2 times the side length. Using 7/4 for the square root of 3, what is the approximate height in meters of an equilateral triangle with a side length of 8 meters?

Answer 5

If the height of an equilateral triangle is equal to $\sqrt{3}/2$ times the side length, we can set up the equation:

$\text{height} = (\sqrt{3}/2) \times \text{side length}$

We are given that the side length is 8 meters, so we substitute that in:

$\text{height} = (\sqrt{3}/2) \times 8$

Using the given approximation $7/4$ for $\sqrt{3}$, we can simplify the equation:

$\text{height} = (7/4)\times(8) = 7 \, \text{meters}$

Therefore, the approximate height of the equilateral triangle is $\boxed{7}$ meters.

Answer 6

A sign in a gas station advertises gas at the rate of $3.39910 per gallon. How many dollars does a gallon cost, writing the price strictly as a decimal?

Answer 7

To write the price strictly as a decimal, we can remove the dollar sign and only retain the numerical value.

The price of gas is $3.39910 per gallon, so the cost of one gallon is $\boxed{3.39910}$ dollars.

Answer 8

A sign in a gas station advertises gas at the rate of $3.39 9/10 per gallon. How many dollars does a gallon cost, writing the price strictly as a decimal?

Answer 9

To write the price strictly as a decimal, we first need to convert the mixed number $3.39 \frac{9}{10}$ into a decimal.

$3.39 \frac{9}{10}$ can be rewritten as $3.39 + \frac{9}{10}$. To convert $\frac{9}{10}$ into a decimal, we divide 9 by 10:

$\frac{9}{10} = 0.9$

Now we can add $0.9$ to $3.39$ to get the decimal form of the price:

$3.39 + 0.9 = 4.29$

Therefore, a gallon of gas costs $\boxed{4.29}$ dollars.