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PSYCHO15rus [73]
3 years ago
14

How do you eliminate the natural log?​

Mathematics
1 answer:
denis23 [38]3 years ago
8 0

You make both sides exponent of e: since we have

e^{\ln(x)}=x

we also have

\ln(X)=\ln(Y) \iff e^{\ln(X)}=e^{\ln(Y)}\iff X=Y

where X and Y can be any expression.

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If x^2+y^2=1, what is the largest possible value of |x|+|y|?
Marianna [84]

If <em>x</em>² + <em>y</em>² = 1, then <em>y</em> = ±√(1 - <em>x</em>²).

Let <em>f(x)</em> = |<em>x</em>| + |±√(1 - <em>x</em>²)| = |<em>x</em>| + √(1 - <em>x</em>²).

If <em>x</em> < 0, we have |<em>x</em>| = -<em>x</em> ; otherwise, if <em>x</em> ≥ 0, then |<em>x</em>| = <em>x</em>.

• Case 1: suppose <em>x</em> < 0. Then

<em>f(x)</em> = -<em>x</em> + √(1 - <em>x</em>²)

<em>f'(x)</em> = -1 - <em>x</em>/√(1 - <em>x</em>²) = 0   →   <em>x</em> = -1/√2   →   <em>y</em> = ±1/√2

• Case 2: suppose <em>x</em> ≥ 0. Then

<em>f(x)</em> = <em>x</em> + √(1 - <em>x</em>²)

<em>f'(x)</em> = 1 - <em>x</em>/√(1 - <em>x</em>²) = 0   →   <em>x</em> = 1/√2   →   <em>y</em> = ±1/√2

In either case, |<em>x</em>| = |<em>y</em>| = 1/√2, so the maximum value of their sum is 2/√2 = √2.

6 0
3 years ago
The coefficient of 2(3)(6)Q is ___.
nlexa [21]
The answers is 2 x 3 x 6 = 36
4 0
3 years ago
A scale on a blue print drawing of a house shows that 6 centimeters represents 3 meters. What number of centimeters on the blue
Tema [17]

Answer:

  54 cm

Step-by-step explanation:

Measures are proportional on a scale drawing:

  drawing measure : actual measure = 6 cm : 3 m = x : 27 m

The value on the right of the x ratio, 27, is 9 times 3, so the value of x will be 9 times 6 cm.

54 cm on the blueprint represents an actual distance of 27 meters.

5 0
3 years ago
3601-589= What strategy did you use?
Anton [14]

Answer:

3601

-589

———-

To

359(11)

-589

———-

3012

Step-by-step explanation:

3 0
2 years ago
What type of transformation moves P(3,-6) to
mr Goodwill [35]
I don’t know but I’ll try to figure it out
5 0
3 years ago
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