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Kay [80]
3 years ago
12

Enter the expression using exponents. 11 × 11 × 11 × 11 × 11 =

Mathematics
1 answer:
Alla [95]3 years ago
6 0

Answer:

the answer should be 11^{5} or 11^5

Explanation:

Since there are five 11 in the equation, the answer should be 11^{5} or 11^5

You shouldn't write 161051 as the answer because it is NOT a exponent.

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Factor completely: x^2-y^2-1.5(x-y)
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hammer [34]

Solve for <em>x</em> when √(<em>x</em> ² - 4) = 1 :

√(<em>x</em> ² - 4) = 1

<em>x</em> ² - 4 = 1

<em>x</em> ² = 5

<em>x</em> = ±√5

We're looking at <em>x </em>≤ 0, so we take the negative square root, <em>x</em> = -√5.

This means <em>f</em> (-√5) = 1, or in terms of the inverse of <em>f</em>, we have <em>f</em> ⁻¹(1) = -√5.

Now apply the inverse function theorem:

If <em>f(a)</em> = <em>b</em>, then  (<em>f</em> ⁻¹)'(<em>b</em>) = 1 / <em>f '(a)</em>.

We have

<em>f(x)</em> = √(<em>x</em> ² - 4)   →   <em>f '(x)</em> = <em>x</em> / √(<em>x</em> ² - 4)

So if <em>a</em> = -√5 and <em>b</em> = 1, we get

(<em>f</em> ⁻¹)'(1) = 1 / <em>f '</em> (-√5)

(<em>f</em> ⁻¹)'(1) = √((-√5)² - 4) / (-√5) = -1/√5

The sign must be negative; see the attached plot, and take note of the negatively-sloped tangent line to the inverse of <em>f</em> at <em>x</em> = 1.

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