Question

Hi could you please answer the following questions on upper and lower bounds. Please provide full working out for each answer. Thanks, 36 points are available.
1. The width and length of a rectangle was measured. The length was 645mm to the nearest 5mm, and the width was 400mm to the nearest 5mm.

Calculate the lower bound for the area of this rectangle, give your answer correct to 3 significant figures.

2. A rectangle has a width of 28 metres to the nearest metre, work out the upper bound of this width.

3. The length of a rectangle is 145 metres measured to the nearest 5 metres and the width is 28 to the nearest metre. Calculate the upper bound for the perimeter of this rectangle.

4. The length of a rectangle is 35cm to the nearest cm, the width is 26cm to the nearest cm. Calculate the upper bound for the area of this rectangle. Write down all the figures on your calculator display.

5. The length of a rectangle is 30 correct to 2 significant figures, the width is 18cm correct to 2 significant figures. Write down the upper bound of the width and the upper bound of the area of the triangle.

Thanks

Please answer Asap

Answer 1

Ok so I will do only one and only put the answer for the others
ok so nearest xmm means that you havet o find teh smalles then largest so



1. legnth times width=area
so find max and min area
5 mm eror
legnth=645
width=400
so the legnth and witdth could be area
640 (subtract 5 for rerror) and 395 (subtract 5 for error
or
650 (add 5 for error) and 405 (add 5 for error)

so areas could be
640 times 395=252800
650 times 405=263250
upper bound=263250 mm^2
lower bound=252800 mm^2
so basically subtract the error to find minimum possible area and then add error to original measues to find max possible area


2. upper bound=29 m
 lower bound=27 m


3. perimiter=2(L+W)
2((145-5)+(28-1))=lower bound=334 m
2((145+5)+(28+1))=upper bound=358 m


4. (35-1)(26-1)=lower bound=850 cm^2
(35+1)(26+1)=upper bound=972 cm^2


5. 2 sig figs (not sure about this question as much)
nonzeros are significant
30 is 1 sig fig since 0 is not significant
therfor
30.9 to 30.0
18=2 sig figs so that is alreight
upper bound of width=18
30.9 times 18=upper bound=556.2 cm^2
30.0 times 18=lower bound=540 cm^2


ANSWERS


1. upper bound=263250 mm^2
lower bound=252800 mm^2


2. upper bound=29 m
 lower bound=27 m


3. lower bound=334 m
upper bound=358 m


4. lower bound=850 cm^2
upper bound=972 cm^2



5. upper and lower bound o 18=18

upper bound=556.2 cm^2
lower bound=540 cm^2