There is 2 ways to solve this type of question.
Method 1
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Formula
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a² + b² = c²
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Apply the formula
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(7√2)² + (7√2)² = c²
c² = 98 + 98
c² = 196
c = √196
c = 14
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Ans: The diagonal length is 14cm
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Method 2
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Identify the triangle
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This is a special triangle
45° - 45° - 90°
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Property of the Angles
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x - x - x√2
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Find hypotenuse
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Given that the non-hypotenuse is 7√2
Hypotenuse = (7√2)(√2)
Hypotenuse = 7 x 2
Hypotenuse = = 14cm
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Ans: The diagonal length is 14cm
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Answer:The amount of paint that was sold altogether is 173.36 litres
Step-by-step explanation:
The total amount of paint that the paint shop stocks is 1800 litres.
24% of the paint is white. It means that the amount of white paint would be
24/100 × 1800 = 0.24 × 1800 = 432 litres.
The amount of the remaining paint other than white would be
1800 - 432 = 1368 litres
The shops sells 18% of the white paint. This means that the amount of white paint sold by the shop will be
18/100 × 432 = 0.18 × 432 = 77.6 litres.
The shops sells 7% of the rest of the paint.
This means that the amount of the rest paint sold by the shop will be
7/100 × 1368 = 0.07 × 1368 = 95.76 litres.
The amount of paint that was sold altogether would be
77.6 + 95.76 = 173.36 litres
The answer is: The first triangle. The reasons are shown below:
1. All the triangles are rigth triangles, because they have an angle of 90°. So, let's calculate the others angles of the first one:
Tan(α)^-1= opposite leg/adjacent leg
Opposite leg=5
Adjacent leg=5√3
Tan(α)^-1= 5/5√3
Tan(α)^-1=30°
2. Let's calculate the other angle:
Tan(α)^-1= opposite leg/adjacent leg
Now, the opposite leg will be 5√3 and the adjacent leg will be 5. Then:
Tan(α)^-1= 5√3/5
Tan(α)^-1=60°
As you can see, the angles of first triangle are: 30°,60° and 90°.
5 million x 3% = 150,000
1 Year = 5,150,000
5.15 million x 3% = 154,500
2 Years = 5,304,500
5,304,500 x 3% = 159,135
3 Years = 5,463,635
5,463,635 x 3% = 163,909.05
4 Years = 5,627,544.05
5,627,544.05 x 3% = 168,826.322
5 Years = 5,796,370.37
After 5 years, the population will be 5,796,370.37
The equation: 6r-3=45
6r=48
Answer: r=8
