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erastova [34]
2 years ago
12

Approximate the area under the

Mathematics
1 answer:
taurus [48]2 years ago
4 0

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]

The left endpoint of the i-th subinterval is

\ell_i = i - 1

where i\in\{1,2,3\}.

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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If m∠4 = 35, find m∠2. Explain.
Bad White [126]

Answer:

Option (1)

Step-by-step explanation:

From the picture attached,

Triangle CAB is a right triangle.

Therefore, m∠1 = 90°

Similarly, m∠ACD = 90°

m∠ACD = m∠ACB + m∠BCD = 90°

             = m∠3 + m∠4 = 90°

Since m∠4 = 35°,

m∠3 + 35° = 90°

m∠3 = 90° - 35°

        = 55°

In the triangle ABC,

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55° + m∠2 + 90° = 180°

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Option (1) is the correct option.

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