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Amanda [17]
3 years ago
9

What two numbers have a product of -2 and a sum of 7

Mathematics
1 answer:
Citrus2011 [14]3 years ago
7 0

<em>Greetings from Brasil...</em>

According to the statement of the question, we can assemble the following system of equation:

X · Y = - 2      i

X + Y = 7       ii

isolating X from i and replacing in ii:

X · Y = - 2

X = - 2/Y

X + Y = 7

(- 2/Y) + Y = 7     <em>multiplying everything by Y</em>

(- 2Y/Y) + Y·Y = 7·Y

- 2 + Y² = 7X     <em> rearranging everything</em>

Y² - 7X - 2 = 0      <em>2nd degree equation</em>

Δ = b² - 4·a·c

Δ = (- 7)² - 4·1·(- 2)

Δ = 49 + 8

Δ = 57

X = (- b ± √Δ)/2a

X' = (- (- 7) ± √57)/2·1

X' = (7 + √57)/2

X' = (7 - √57)/2

So, the numbers are:

<h2>(7 + √57)/2</h2>

and

<h2>(7 - √57)/2</h2>
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75 points. Will give certified if work is shown and the answer is correct.
Svetach [21]
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So difference between the volumes is:

V_1-V_2\approx7.679\cdot10^8\pi-7.5963\cdot10^8\pi=0.0827\cdot10^8\pi=\boxed{8270000\pi\,\text{mi}^3}

or if we want exact value (we use (a³-b³) = (a-b)(a²+ab+b²) ):

V_1-V_2=\dfrac{4}{3}\cdot\pi\cdot r_1^3-\dfrac{4}{3}\cdot\pi\cdot r_2^3=\dfrac{4}{3}\pi(r_1^3-r_2^3)=\dfrac{4}{3}\pi(832^3-829^3)=\\\\\\=\dfrac{4}{3}\pi(832-829)(832^2+832\cdot829+829^2)=\\\\\\=\dfrac{4}{3}\pi\cdot3(692224+689728+687241)=4\pi\cdot2069193=\boxed{8276772\pi\,\text{mi}^3}
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Answer:

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Step-by-step explanation:

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