Advertisements
Advertisements
प्रश्न
A solution is to be kept between 86° and 95°F. What is the range of temperature in degree Celsius, if the Celsius (C)/ Fahrenheit (F) conversion formula is given by\[F = \frac{9}{5}C + 32\]
Advertisements
उत्तर
Suppose the temperature of the solution is x degree Celsius.
∴ x in Fahrenheit = \[\frac{9}{5}x + 32\]
Then, as per the given condition:
\[86 < \frac{9}{5}x + 32 < 95\]
\[ \Rightarrow 86 - 32 < \frac{9}{5}x < 95 - 32 (\text{ Subtratcting 32 throughout })\]
\[ \Rightarrow 54 < \frac{9}{5}x < 63\]
\[ \Rightarrow \frac{5}{9} \times 54 < \frac{5}{9} \times \frac{9}{5}x < \frac{5}{9} \times 63 (\text{ Multiplying by } \frac{5}{9} \text{ throughout })\]
\[ \Rightarrow 30 < x < 35\]
Hence, the range of the temperature in degree Celsius is between 30° C and 35° C
APPEARS IN
संबंधित प्रश्न
Solve the following system of inequalities graphically: 3x + 2y ≤ 12, x ≥ 1, y ≥ 2
Solve the following system of inequalities graphically: 2x + y≥ 6, 3x + 4y ≤ 12
Solve the following system of inequalities graphically: x + y≥ 4, 2x – y > 0
Solve the following system of inequalities graphically: x + y ≤ 6, x + y ≥ 4
Solve the following system of inequalities graphically: 2x + y≥ 8, x + 2y ≥ 10
Solve the following system of inequalities graphically: x + y ≤ 9, y > x, x ≥ 0
Solve the following system of inequalities graphically: 3x + 4y ≤ 60, x + 3y ≤ 30, x ≥ 0, y ≥ 0
Solve the following system of inequalities graphically: x + 2y ≤ 10, x + y ≥ 1, x – y ≤ 0, x ≥ 0, y ≥ 0
A solution is to be kept between 30°C and 35°C. What is the range of temperature in degree Fahrenheit?
A company manufactures cassettes and its cost and revenue functions for a week are \[C = 300 + \frac{3}{2}x \text{ and } R = 2x\] respectively, where x is the number of cassettes produced and sold in a week. How many cassettes must be sold for the company to realize a profit?
How many litres of water will have to be added to 1125 litres of the 45% solution of acid so that the resulting mixture will contain more than 25% but less than 30% acid content?
A solution of 8% boric acid is to be diluted by adding a 2% boric acid solution to it. The resulting mixture is to be more than 4% but less than 6% boric acid. If there are 640 litres of the 8% solution, how many litres of 2% solution will have to be added?
Write the set of values of x satisfying the inequation (x2 − 2x + 1) (x − 4) < 0.
Write the solution set of the equation |2 − x| = x − 2.
Write the set of values of x satisfying |x − 1| ≤ 3 and |x − 1| ≥ 1.
Write the solution set of the inequation \[\left| \frac{1}{x} - 2 \right| > 4\]
Write the set of values of x satisfying the inequations 5x + 2 < 3x + 8 and \[\frac{x + 2}{x - 1} < 4\]
Write the solution of set of\[\left| x + \frac{1}{x} \right| > 2\]
Find the graphical solution of the following system of linear inequations:
2x + 3y ≥ 12, – x + y ≤ 3, x ≤ 4, y ≥ 3
Find the graphical solution of the following system of linear inequations:
3x + 2y ≤ 1800, 2x + 7y ≤ 1400
Solve the following system of inequalities `(2x + 1)/(7x - 1) > 5, (x + 7)/(x - 8) > 2`
Find the linear inequalities for which the shaded region in the given figure is the solution set.
Solve the following system of linear inequalities:
3x + 2y ≥ 24, 3x + y ≤ 15, x ≥ 4
Show that the solution set of the following system of linear inequalities is an unbounded region 2x + y ≥ 8, x + 2y ≥ 10, x ≥ 0, y ≥ 0.
Solution set of x ≥ 0 and y ≤ 0 is
Solution set of x ≥ 0 and y ≤ 1 is
