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Nat2105 [25]
3 years ago
11

Area for rectangle in the coordinate plane. IXL Geometry help pls !

Mathematics
1 answer:
Sidana [21]3 years ago
5 0

Answer:

Step-by-step explanation:

The co-ordinates of the rectangle are:

A (8, 6)

B (-4, -10)

C (-8, -7)

D (4, 9)

The Area of Rectangle is Given by: <em>length x breadth </em>= AB x BC

Lengths of AB and BC can be found by distance formula

<em>length</em>(AB) = \sqrt{(x_{2} - x_{1} )^{2} + (y_{2} - y_{1} )^{2}} = \sqrt{(-4-8)^{2} + (-10-6)^{2}} = 20

Similarly,

<em>length</em>(BC) = 5

Area of Rectangle = AB x BC = 20 x 5 = 100 square units

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\large\begin{array}{l} \mathsf{\displaystyle\int\!3^{2x-1}\,dx}\\\\ =\mathsf{\displaystyle\int\!\frac{1}{2}\cdot 2\cdot 3^{2x-1}\,dx}\\\\ =\mathsf{\displaystyle\frac{1}{2}\int\!3^{2x-1}\cdot 2\,dx\qquad(i)} \end{array}


\large\begin{array}{l} \textsf{Substitute}\\\\ \mathsf{2x-1=u\quad\Rightarrow\quad 2\,dx=du}\\\\\\ \textsf{so (i) becomes}\\\\ =\mathsf{\displaystyle\frac{1}{2}\int\!3^u\,du}\\\\ =\mathsf{\dfrac{1}{2}\cdot \dfrac{1}{\ell n\,3}\,3^u+C}\\\\ =\mathsf{\dfrac{1}{2\,\ell n\,3}\,3^{2x-1}+C} \end{array}


\large\begin{array}{l} \boxed{\begin{array}{c}\mathsf{\displaystyle\int\!3^{2x-1}\,dx=\frac{1}{2\,\ell n\,3}\,3^{2x-1}+C} \end{array}}\qquad\checkmark \end{array}


<span>If you're having problems understanding this answer, try seeing it through your browser: brainly.com/question/2154165


\large\textsf{I hope it helps. :-)}
</span>

Tags: <em>integrate indefinite integral substitution exponential base logarithm log ln composite integral calculus

</em>
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