Practice Mathematics I questions with answers and explanations.
An antiderivative is 1/2 x²+4x. At x=2, the value is 10.0.
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The sum is n(n+1)/2=55, so the mean is 55/10.
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There are 4 favourable outcomes out of 10 equally likely outcomes, so P(red)=4/10.
The coordinate differences are 3 and 4, so the distance is √(3²+4²)=5.
f′(x)=9x²+16x. Substituting x=4 gives 208.
An antiderivative is 4/2 x²+3x. At x=5, the value is 65.0.
The dot product is 4×2+4×4=24.
Rewrite the value using base 5: 3125 = 5^5. Matching exponents gives x = 5.
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Use the circle-area formula A = πr². Substituting r = 5 gives A = π × 5² = 25π.
An antiderivative is 3/2 x²+2x. At x=4, the value is 32.0.
The dot product is 3×4+3×3=21.
Rewrite the value using base 4: 256 = 4^4. Matching exponents gives x = 4.
