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Salsk061 [2.6K]
3 years ago
12

Can someone please help me with this geometry proof? It needs to get done ASAP and I'm really struggling.

Mathematics
1 answer:
zhenek [66]3 years ago
6 0

One way to prove that the triangles are congruent is to show that the three pairs of sides have the same length.

For side BD, this is easy, since it is shared by the two triangles, so it is obviously equal.

On the other hand, we know that the given figure is a parallelogram, the opposite sides are equal in length. Particularly, it means that:

AB = CD \quad\textrm{and}\quad BC = AD.

Thus, we have shown that each pair of sides have the same length, which means that:

\triangle ABD \equiv \triangle CDB.

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Answer:

7

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Because 6+7= 13 and 7 times -7 = -14

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express the limit as a definite integral on the given interval. lim n → [infinity] n ∑ i = 1 cos x i x i δ x , [ 2 π , 4 π ]
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The limit as a definite integral on the interval $\lim _{n \rightarrow \infty} \sum_{i=1}^n \frac{\cos x_i}{x_i} \Delta x$ on [2π , 4π] is $\int_{2\pi}^{4 \pi} \frac{\cos x}{x} d x$$.

<h3>What is meant by definite integral?</h3>

A definite integral uses infinitesimal slivers or stripes of the region to calculate the area beneath a function. Integrals can be used to represent a region's (signed) area, the cumulative value of a function changing over time, or the amount of a substance given its density.

Definite integral, a term used in mathematics. is the region in the xy plane defined by the graph of f, the x-axis, and the lines x = a and x = b, where the area above the x-axis adds to the total and the area below the x-axis subtracts from the total.

If an antiderivative F exists for the interval [a, b], the definite integral of the function is the difference of the values at points a and b. The definite integral of any function can also be expressed as the limit of a sum.

Let the equation be

$\int_a^b f(x) d x=\lim _{n \rightarrow \infty} \sum_{i=1}^n f\left(x_i\right) \Delta x$

substitute the values in the above equation, we get

= $\lim _{n \rightarrow \infty} \sum_{i=1}^n \frac{\cos x_i}{x_i} \Delta x$ on [2π, 4π],

simplifying the above equation

$\int_{2\pi}^{4 \pi} \frac{\cos x}{x} d x$$

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