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3 years ago

Choose the correct ordered pair

Mathematics

2 answers:

VladimirAG [237]3 years ago

8 0

A (8, 1) is your answer.

x + y = 9
x - y = 7

We have to use a system of equations to solve for both x and y

Take equation 1 (x + y = 9)
Solve for x by subtracting y from both sides
x = 9 - y

Plug 9 - y in for x in the second equation.
(9 - y) - y = 7

Solve for y
9 - 2y = 7
2 = 2y
y = 1

Now that we know y = 1, we can plug 1 in for y in the first equation to solve for x.
x + 1 = 9

Solve for x
x = 8

So our coordinate that satisfies the system of equations is (8, 1)

Mars2501 [29]3 years ago

4 0

Your answer will be A. (8,1)

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Step-by-step explanation:

Given definite integral is:

$\int\limits^7_4 {\frac{x}{2}+x^{3}} \, dx \\f(x)=\frac{x}{2}+x^{3}---(1)\\\Delta x=\frac{b-a}{n}\\\\\Delta x=\frac{7-4}{n}=\frac{3}{n}\\\\x_{i}=a+\Delta xi\\a= Lower Limit=4\\\implies x_{i}=4+\frac{3}{n}i---(2)\\\\then\\f(x_{i})=\frac{x_{i}}{2}+x_{i}^{3}$

Substituting (2) in above

$f(x_{i})=\frac{1}{2}(4+\frac{3}{n}i)+(4+\frac{3}{n}i)^{3}\\\\f(x_{i})=(2+\frac{3}{2n}i)+(64+\frac{27}{n^{3}}i^{3}+3(16)\frac{3}{n}i+3(4)\frac{9}{n^{2}}i^{2})\\\\f(x_{i})=\frac{27}{n^{3}}i^{3}+\frac{108}{n^{2}}i^{2}+\frac{3}{2n}i+\frac{144}{n}i+66\\\\f(x_{i})=\frac{27}{n^{3}}i^{3}+\frac{108}{n^{2}}i^{2}+\frac{291}{2n}i+66\\\\f(x_{i})=3[\frac{9}{n^{3}}i^{3}+\frac{36}{n^{2}}i^{2}+\frac{97}{2n}i+22]$

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$= \lim_{n \to \infty} \sum^{n} _{i=1}3[\frac{9}{n^{3}}i^{3}+\frac{36}{n^{2}}i^{2}+\frac{97}{2n}i+22]$

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