Question

the length of a car is 4.2 m , correct to 1 decimal place
write down the upper bound and the lower bound of the length of this car

Answer 1

Answer:

Step-by-step explanation:

The upper bound for the length of 370 mm of a rectangle is as follows.

Upper and lower bounds are used to describe all the possible values that a rounded number could be.

Lower Bounds - The lower bound is the smallest value that would be used to round up a number to the previously estimated value.

Upper Bounds - The upper bound is the smallest value that would be used to round up a number to the next estimated value.

For example, 140 cm measured to nearest 10 cm.

10/2 = 5

Upper bound 140 + 5 = 145

Lower bound 140 - 5 = 135

Similarly for  

370 = 100

100/2 = 50

Upper bound for the length of a rectangle = 370 + 50 = 420 mm

Lower bound for the length of a rectangle = 370 - 50 = 320 mm

The upper bound is 8.35 cm because anything less than 8.35 will round to 8.3, but anything 8.35 or greater will round to 8.4. 8.35 itself does not round to 8.3, but it is the smallest such number, or the least upper bound.

Similarly, the lower bound is 8.25 because anything less than 8.25 rounds to 8.2, and 8.25 rounds to 8.3, so 8.25 is the lower bound (And also the minimum).

Also, your question about 8.25 and 8.249˙ doesn't really make much sense -- those two decimals represent the same real number.

To calculate the height, the length of a perpendicular bisector must be determined. If a perpendicular bisector is drawn in an equilateral triangle, the triangle is divided in half, and each half is a congruent 30-60-90 right triangle. This type of triangle follows the equation below.

a2+b2=c2→(a)2+(a3–√)2=(2a)2

The length of the hypotenuse will be one side of the equilateral triangle.

2a=10.

The side of the equilateral triangle that represents the height of the triangle will have a length of a3–√ because it will be opposite the 60o angle.

a=5→a3–√=53–√

To calculate the area of the triangle, multiply the base (one side of the equilateral triangle) and the height (the perpendicular bisector) and divide by two.

A=12bh=12(10)(53–√)=253–√