Page 11 - SM inner class 7.cdr

Ex am ple 11. A freez ing sys tem starts cool ing Rate of cooling = °4 C per hour
the room at the rate of 4°C per hour. If at the \ number of hours required
beginning, the temperature of the room is -32
30°C, find the num ber of hours it takes to lower =
down the room tem per a ture to - °2 C. -4
[Negative sign ( )- indicates the temperature
So lu tion : To tal tem per a ture to be low ered down has lowered down]
= Final temperature - Initial temperature 32
= = 8 hours
= - °C -30 °C = -32 °C 4
2
E xercise 1.4

1. A man trav elled 60 km to the east of Delhi and then 100 km to the west of it. How far from Delhi was he
fi nally?
2. A bomb dis places the oil in a well from 975 m deep and raises it to a de posit place 48 m above ground
level. How far does the oil dis place?
3. What is the change in tem per a ture a cus tomer in a gro cery store ex pe ri ences when they walk from the
chilled veg e ta ble sec tion at 4°C to the frozen fish sec tion which is set to -18 °C?
4. The air tem per a ture in the at mo sphere de creases at the rate of 9 °C ev ery 300 me ters. What height
would a plain have to fly to ex pe ri ence a tem per a ture of - °81 C? The tem per a ture is 0 °C at sea level.
5. In a well there is 800 li ters of wa ter. At the top there is a pipe that de pos its 25 l per min ute into the well,
and at the bot tom there is an other pipe which with draws 30 l per min ute from the same well. How many
li ters of wa ter will there be in the well af ter 15 min utes of the pipes func tion ing?

Summary
m The whole numbers 0,1,2,….. together with the negative numbers –1, –2, –3 ….. are called integers.

m Integers are also known as directed numbers.
m Integers can be represented by using a number line.
m The numerical value of an integer is a distance from zero to that number on the number line.
m Numerical value of an integer is also known as its absolute value.
m Addition of integers

(i) In case of like signs, add the absolute values of integers and common sign is written with the sum.
(ii) In case of unlike signs, subtract the smaller absolute value from the larger absolute value and the sign of
integer of larger absolute value is written with the resulting value.
m Subtraction of integers
m Subtract one integer from the other by changing the sign of the integer being subtracted and adding according
to the rules for addition of integers.
m Multiplication of integers

(i) The product of two integers of like signs is a positive integer.
(ii) The product of two integers of unlike signs is a negative integer.
m Division of integers

(i) If both the integers have like signs the quotient is positive.
(ii) If both the integers have unlike signs the quotient is negative.

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Mathematics In Focus - 7