Podcast Beta
Questions and Answers
- If the perimeter and the area of a right-angled triangle are 60 and 150 respectively, find the length of the hypotenuse of the triangle.
$a + b + c = 60$, $ab/2 = 150$, $a^2 + b^2 = c^2$
- If the area and the diagonal of a rectangle are 80 and 4\sqrt{15}, find the perimeter of the rectangle.
$ab = 80$, $a^2 + b^2 = (4\sqrt{15})^2$, $2a + 2b$
- How many numbers from the first 1000 natural numbers that has exactly 3 factors.
Numbers with exactly 3 factors are perfect squares of prime numbers
- If 20221024 is divisible by 2𝑘 , find the maximum value of integer 𝑘.
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- Find the coefficient of 𝑥 2022 in the expansion of (𝑥 100 + 1)4 (𝑥 + 1)23.
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