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vazorg [7]
3 years ago
5

\sqrt{7+\sqrt{2+\sqrt{x+1} } } =3

Mathematics
1 answer:
Mice21 [21]3 years ago
6 0

First make note of the domain of the left hand side.

• √(x + 1) is defined for x + 1 ≥ 0, or x ≥ -1.

• √(2 + √(x + 1)) is defined for 2 + √(x + 1) ≥ 0. If x ≥ -1, then this condition is satisfied.

• √(7 + √(2 + √(x + 1))) is defined for 7 + √(2 + √(x + 1)) ≥ 0. This condition is also satisified automatically if x ≥ -1.

Now solve the equation. Taking the square of both sides of

√(7 + √(2 + √(x + 1))) = 3

yields

7 + √(2 + √(x + 1)) = 3² = 9

√(2 + √(x + 1)) = 2

Squaring both sides again gives

2 + √(x + 1) = 2² = 4

√(x + 1) = 2

And once more,

x + 1 = 2² = 4   ⇒   x = 3

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Answer is c. -2 (cannot be in the solution set of w/-2)

because.

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but

c) -2/-2 = 1 and 1 = 1




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How do you these two questions?
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Answer:

dy/dx = e⁻²ᵗ (1 − t)

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(1.5, ∞)

Step-by-step explanation:

x = eᵗ

y = te⁻ᵗ

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dy/dx = (dy/dt) / (dx/dt)

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dy/dx = e⁻²ᵗ (1 − t)

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d²y/dx² = (-e⁻²ᵗ − 2(1 − t) e⁻²ᵗ) / eᵗ

d²y/dx² = -e⁻²ᵗ (1 + 2(1 − t)) / eᵗ

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8 0
4 years ago
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