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Jobisdone [24]
2 years ago
6

Congruency please help!

Mathematics
1 answer:
expeople1 [14]2 years ago
5 0
The triangles are not congruent as one angle is 67 degrees and the other is 65 degrees. Even if the side is in between the angles it does not matter as it falls under the congruency condition SAS (side, angle, side)
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Step-by-step explanation:

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For the function given below, find a formula for the Riemann sum obtained by dividing the interval (0, 3) into n equal subinterv
Viktor [21]

Splitting up [0, 3] into n equally-spaced subintervals of length \Delta x=\frac{3-0}n = \frac3n gives the partition

\left[0, \dfrac3n\right] \cup \left[\dfrac3n, \dfrac6n\right] \cup \left[\dfrac6n, \dfrac9n\right] \cup \cdots \cup \left[\dfrac{3(n-1)}n, 3\right]

where the right endpoint of the i-th subinterval is given by the sequence

r_i = \dfrac{3i}n

for i\in\{1,2,3,\ldots,n\}.

Then the definite integral is given by the infinite Riemann sum

\displaystyle \int_0^3 2x^2 \, dx = \lim_{n\to\infty} \sum_{i=1}^n 2{r_i}^2 \Delta x \\\\ ~~~~~~~~ = \lim_{n\to\infty} \frac6n \sum_{i=1}^n \left(\frac{3i}n\right)^2 \\\\ ~~~~~~~~ = \lim_{n\to\infty} \frac{54}{n^3} \sum_{i=1}^n i^2 \\\\ ~~~~~~~~ = \lim_{n\to\infty} \frac{54}{n^3}\cdot\frac{n(n+1)(2n+1)}6 = \boxed{18}

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2 years ago
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Vilka [71]
Just answer some questions
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3 years ago
Find the value of a and of b for which<br>(a) the solution of x2 + ax &lt; b is<br>-2&lt;x &lt; 4​
KengaRu [80]

Answer: a = -2

b = 8

Step-by-step explanation:

Given :

x^{2} +ax

re - writing the equation , we have

x^{2} +ax-b

we need to find the value of a and b for which -2<x < 4 , this means that the roots of the quadratic equation are -2<x < 4.

The formula for finding the quadratic equation when the roots are known is :

x^{2} - sum of roots(x) + product of root = 0

sum of roots = -2 + 4 = 2

product of roots = -2 x 4 = -8

substituting into the formula , we have:

x^{2} -2x-8=0 , which could be written in inequality form as

x^{2} -2x-8

comparing with x^{2} +ax-b , it means that :

a = -2

b = 8

3 0
3 years ago
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