question 1 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. Question 2 The sides of an equilateral triangle are 9.4 cm, correct to the nearest millimetre. Work out the upper bound of the perimeter of this triangle Question 3 A metal pole is 500cm long, correct to the nearest centimetre. The pole is cut into rods each of length 5.8 cm, correct to the nearest millimetre. Calculate the largest number of rods that the pole can be cut into. Question 4 A rectangle has length 5.8 cm and width 2.4 cm, both correct to 1 decimal place. Calculate the lower bound and the upper bound of the perimeter of this rectangle Question 5 One year ago Ahmed’s height was 114 cm. Today his height is 120 cm. Both measurements are correct to the nearest centimetre. Work out the upper bound for the increase in Ahmed’s height. Question 6 6 The length, l metres, of a football pitch, is 96m, correct to the nearest metre. Complete the statement about the length of this football pitch. Question 7 7 The length, p cm, of a car is 440 cm, correct to the nearest 10 cm. Complete the statement about p. Question 8 9 An equilateral triangle has sides of length 16.1cm, correct to the nearest millimetre. Find the lower and upper bounds of the perimeter of the triangle. Question 9 A large water bottle holds 25 litres of water correct to the nearest litre. A drinking glass holds 0.3 litres correct to the nearest 0.1 litre. Calculate the lower bound for the number of glasses of water which can be filled from the bottle. Question 10 A carton contains 250 ml of juice, correct to the nearest millilitre. Complete the statement about the amount of juice, j ml, in the carton. Question 13 4 The cost of making a chair is $28 correct to the nearest dollar. Calculate the lower and upper bounds for the cost of making 450 chairs.
Answers
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–√
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