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Minchanka [31]
3 years ago
11

Solve this equation for x. Round your answer to the nearest hundredth. 3 = In(x + 9)

Mathematics
1 answer:
Mrac [35]3 years ago
7 0

Answer:

x ≈ 11.09

Step-by-step explanation:

Using the rule of logarithms

log_{b} x = n ⇒ x = b^{n}

Given

ln(x + 9) = 3 , that is

log_{e} (x + 9) = 3 , then

x + 9 = e³ ( subtract 9 from both sides )

x = e³ - 9 ≈ 11.09 ( to the nearest hundredth )

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Let a and b be real numbers satisfying a^3 - 3ab^2 = 47 and b^3 - 3a^2 b = 52. Find a^2 + b^2.
boyakko [2]

Answer: a²+b² = -99/2

Step-by-step explanation:

Since we are given two equations, this equations will be solved simultaneously to get a² and b²

a³ - 3ab² = 47 ... 1

b³ - 3a² b = 52... 2

From 1, a(a² - 3b²) = 47...3

From 2, b(b² - 3a²) = 52... 4

Adding 3 and 4, we have;

a²+b²-3b²-3a² = 99 (note that a and b will no longer be part of the equations as they have been factored out)

a²+b²-(3b²+3a²) = 99

(a²+b²) -3(b²+a²)= 99

Taking the difference we have

- 2(a²+b²) = 99

a²+b² = -99/2

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So the two possible original temperatures would be either -9 or 9.
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morpeh [17]

Answer:

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Step-by-step explanation:

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