Isolating a variable in the formula - practice problems
Work with mathematical expressions. Expressions are mathematical objects where some numbers are replaced by letters - variables. For example, the area of a circle is S = π r2, where r is a variable, the radius of the circle, and S is also a variable, the area. This is how we can describe the relationship between area and radius for all circles, generally. We can modify expressions, simplify, multiply, divide, add, etc. Expressing from a formula means putting some variable on the left side. For example, the radius of a circle r = √ (S/π). For completeness, let us add that the symbol π is a constant, Ludolf's number = 3.14159.... A constant is like a variable, but always with the same value.Number of problems found: 2866
- GP - negative term
The first term of a GP is -3 and the square of the second term is equal to its 4th term. Find the 7th term of the GP. - Three in a ratio
If A is 40% more than B, B is 20% less than C then, find the ratio A : C. - School - boys:girls
In a school 10% of boy is equal to the 1/4 of number of girls and 10% of the number of girls is equal to the 1/25 of boys. Find the ratio between the number of boys and girls. - The sum 53 The sum ofthree numbers of a GP series is 35 and their product is 1000. Find the numbers.
- The centroid
The centroid of a triangle ABC is at the point (3,3,3). If the coordinates of A and B are (3, –5, 7) and (–1, 7, – 6) respectively, find the coordinates of the point C. - The surface 5
The surface area of a cylinder is 6140 cm², and the radius is 25 cm. What is the height? - A rope for cow
Find the length of a rope by which a cow must be tethered in order that it may be able to graze an area of 154 sq m .
- The average 19 The average age of a class was 15 years. When 5 boys whose average age was 12 years 6 months were admitted in the class, the average was reduced by 6 months. How many students were there in the class originally?
- Cu ore
An ore contains 5% copper. How much ore is required to obtain 400 grams of copper? - The Earth and Moon
The diameter of the Moon is approximately 1/4 of the diameter of the Earth. What fraction of the volume of the Earth is the volume of the Moon? - Salaries - ratio3
The salaries A, B, C are in the ratio 2 : 3 : 5. If the increments of 15%, 10% and 20% are allowed respectively in their salaries, then what will be new ratio of their salaries? - Goods train
A goods train runs at the speed of 72 kmph and crosses a 250 m long platform in 26 seconds. What is the length of the goods train? - Angle of inclination
Find the angle of inclination of a ramp that rise for 80 cm and is 200 cm long. - Tower + pole
On the horizontal plane, there is a vertical tower with a flag pole on its top. At a point 9 m away from the foot if the tower, the angle of elevation of the top and bottom of the flag pole are 60°and 30° respectively. Find the height of the flag pole. - A rectangle 15
A rectangle is 5 cm longer its width. It areas is 6 cm square. What are the dimensions of the rectangle.
- Rhombus = area, diagonal
The area of a rhombus is 144 sq cm. One of its diagonals is twice the other. How long is the shorter diagonal? - The rhombus (a,d) Find the area of a rhombus, one side of which measures 20 cm, and one diagonal 24 cm.
- The length 20
The length and breadth of a rectangular park are in the ratio 8:5. A path,1.5 m wide, running all around the outside of the park has an area of 594 sq m. Find the dimensions of the park. - A field
A field is in the shape of a trapezium whose parallel sides are 25 m and 10 m and the non parallel sides are 14 m and 13 m. Find the area of the field. - The average 17
The average monthly salary of 20 workers in an office is $4590 . If the manage's salary is added, the average salary becomes $ 4920 per month What's the manager's monthly salary?
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