The height of an equilateral triangle equals 3√2 times the side length. Using 74 for the square root of 3, what is the approximate height in meters of an equilateral triangle with a side length of 8 meters?(1 point).
The height of an equilateral triangle equals 3√2 times the side length.
Given that the side length is 8 meters, we can substitute this value into the equation:
Height = 3√2 * Side length
Height = 3√2 * 8
Now, we just need to substitute the value of √2 with the given value of 74:
Height = 3 * (74) * 8
Height = 222 * 8
Height = 1776
Therefore, the approximate height of an equilateral triangle with a side length of 8 meters is 1776 meters.
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?(1 point)
Given that the square root of 3 is represented as 7/4, we can substitute this value into the equation:
Height = 3√2 * Side length
Height = 3 * (7/4) * 8
To simplify the equation, we can first multiply 3 and 8:
Height = 24 * (7/4)
Next, we can simplify the expression (7/4):
Height = (24 * 7) / 4
Height = 168 / 4
Height = 42
Therefore, the approximate height of an equilateral triangle with a side length of 8 meters, using 7/4 for the square root of 3, is 42 meters.
Using a number line, what whole number and rational number to the nearest half is 40−−√ between?(1 poi
To determine which whole number and rational number to the nearest half the square root of 40 lies between, we can look at the number line.
By calculating the square root of 40, we find that it is approximately 6.32456.
On the number line, we can see that 6 is the whole number right before 6.32456, and 7 is the whole number right after it.
To find the nearest half, we can divide the interval between 6 and 7 into halves:
6 ------------ 6.5 ------------ 7
Since 6.32456 is closer to 6.5 than it is to 6, the square root of 40, rounded to the nearest half, is between 6 and 6.5.
Therefore, the whole number to the nearest half is 6, and the rational number to the nearest half is 6.5.
Using rational approximations, what is an inequality statement comparing 81−−√ and 8–√8? Enter <, >, or =.
To compare 81−−√ and 8–√8 using rational approximations, we can find their decimal approximations.
The square root of 81 is exactly 9.
The square root of 8 is approximately 2.82843.
Comparing these decimal approximations, we can see that 9 is greater than 2.82843.
Therefore, the inequality statement comparing 81−−√ and 8–√8 is:
81−−√ > 8–√8
Monique measured the widths of several stamps in her collection of world stamps. The measurements are 1 5/8in., 1 11/16in., 1 1 1 1 3/4in., and 1 1/2in. What is the width of the widest stamp?(1 point)
To find the width of the widest stamp among the given measurements, we need to compare the measurements and determine the largest one.
The given measurements are:
1 5/8in.
1 11/16in.
1 1 1 1 3/4in.
1 1/2in.
To facilitate the comparison, it can be helpful to convert all the measurements to the same denominator:
1 5/8in. = (8 + 5)/8 = 13/8in.
1 11/16in. = (16 + 11)/16 = 27/16in.
1 1 1 1 3/4in. = (4 x 16 + 3)/16 = 67/16in.
1 1/2in. = (2 + 1)/2 = 3/2in.
Now, we can determine which fraction is the largest.
Comparing the fractions, we can see that 67/16in. is the largest among them.
Therefore, the width of the widest stamp is 67/16in.
What is the circumference of a circle with a diameter of 4.5 miles? Estimate the circumference to the hundredths place using 3.14 for π
.