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3 years ago

9/35 x 7/16 x 20/21 =show work

1 answer:

5 0

$\frac{9}{35}\cdot\frac{\not7^1}{16}\cdot\frac{20}{\not21_3}=\frac{9}{35}\cdot\frac{1}{\not16_4}\cdot\frac{\not20^5}{3}=\frac{\not9^3}{35}\cdot\frac{1}{4}\cdot\frac{5}{\not3_1}=\frac{3}{\not35_7}\cdot\frac{1}{4}\cdot\frac{\not5^1}{1}\\\\=\frac{3}{7}\cdot\frac{1}{4}\cdot\frac{1}{1}=\frac{3\cdot1\cdot1}{7\cdot4\cdot1}=\frac{3}{28}$

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3 years ago

Approximate the area under the

taurus [48]

Split up the interval [0, 3] into 3 equally spaced subintervals of length $\Delta x = \frac{3-0}3 = 1$ . So we have the partition

[0, 1] U [1, 2] U [2, 3]

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$\ell_i = i - 1$

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Then the area is given by the definite integral and approximated by the left-hand Riemann sum

$\displaystyle \int_0^3 f(x) \, dx \approx \sum_{i=1}^3 f(\ell_i) \Delta x \\\\ ~~~~~~~~~~ = \sum_{i=1}^3 (i-1)^3 \\\\ ~~~~~~~~~~ = \sum_{i=0}^2 i^3 \\\\ ~~~~~~~~~~ = 0^3 + 1^3 + 2^3 = \boxed{9}$

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2 years ago