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I am having difficulties understanding the set-up (of the integrals) in evaluating the area between these two curves given below. Since the question asks ...
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$$\frac{\cos(2x)+\cos(2y)}{\sin(x)+\cos(y)} = 2\cos(y)-2\sin(x)$$ The question asks to prove the identity. I tried simplifying the first half, thought may...
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The modern definition of topology is 'a family of subsets of a set $X$ containing the empty set and $X$, closed under unions and finite intersections...
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How many solutions are there to the equation $x + y + z + w = 17$ for non-negative integers $w, x, y, z$ ? I don't know if I'm doing this right,...
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I am given two sequences: $\{a_n\}$ which converges towards 0 and $\{b_n\}$ which is a bounded sequence. I have to show that $\{b_na_n\}$ is converging to...
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I have an urn with 10 balls: 4 red and 6 white. What is the probability that the first two drawn balls have the same color? Approach No. 1: $|U| = 10! = 3...
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Triangle $ABC$ has 2 given vertices, $A(1,1)$ and $B(5,3)$. Also, AC=BC and $\angle ACB = \,^{\circ}\mathrm{90}$. The triangle is in the first quadrant en...
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The following is a problem in my book that I don't really understand: We take a random sample: $x_1,x_2,\ldots,x_n$ from a population that is $N(μ,σ)...
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I was wondering if a dot product is technically a term used when discussing the product of $2$ vectors is equal to $0$. And would anyone agree that an inn...
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I have 3 known matrices A B and C and wish to find X. My question here is why AXB = C ⇔ XB = A^-1 *C and not AXB = C ⇔ XB = C*A^-1 The A^-1 matrix is of s...
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