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aivan3 [116]
2 years ago
6

HELP PLEASE!!5⁸/5³=a. 5^-5b. 1¹¹c. 5⁵d. 5 ¹¹​

Mathematics
2 answers:
sergiy2304 [10]2 years ago
8 0

Answer:

C

Step-by-step explanation:

\frac{ {5}^{8} }{ {5}^{3} }  \\

Now you may reduce the fraction

=  {5}^{5}

Alekssandra [29.7K]2 years ago
5 0
I think c if it’s not right lmk
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Answer:

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3 years ago
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If f(x)=x^3-x+2, then (f^-1)'(2)
yawa3891 [41]

Note that f(x) as given is <em>not</em> invertible. By definition of inverse function,

f\left(f^{-1}(x)\right) = x

\implies f^{-1}(x)^3 - f^{-1}(x) + 2 = x

which is a cubic polynomial in f^{-1}(x) with three distinct roots, so we could have three possible inverses, each valid over a subset of the domain of f(x).

Choose one of these inverses by restricting the domain of f(x) accordingly. Since a polynomial is monotonic between its extrema, we can determine where f(x) has its critical/turning points, then split the real line at these points.

f'(x) = 3x² - 1 = 0   ⇒   x = ±1/√3

So, we have three subsets over which f(x) can be considered invertible.

• (-∞, -1/√3)

• (-1/√3, 1/√3)

• (1/√3, ∞)

By the inverse function theorem,

\left(f^{-1}\right)'(b) = \dfrac1{f'(a)}

where f(a) = b.

Solve f(x) = 2 for x :

x³ - x + 2 = 2

x³ - x = 0

x (x² - 1) = 0

x (x - 1) (x + 1) = 0

x = 0   or   x = 1   or   x = -1

Then \left(f^{-1}\right)'(2) can be one of

• 1/f'(-1) = 1/2, if we restrict to (-∞, -1/√3);

• 1/f'(0) = -1, if we restrict to (-1/√3, 1/√3); or

• 1/f'(1) = 1/2, if we restrict to (1/√3, ∞)

6 0
2 years ago
The difference of two numbers is 15. Five times the smaller is the same as 9 less than twice the larger. Find the numbers
Usimov [2.4K]

Answer:

x= -13

y= -28

Step-by-step explanation:

To find the two numbers, write a system of equations with x as one number and y as another:

x-y=15

5x=2y-9

Use substitution to substitute one equation into another. Then solve for the variable.

x=15+y into 5x=2y-9

becomes

5(15+y) = 2y-9

75+5y = 2y- 9

75+3y= -9

3y = -84

y= -28

To find x, substitute y= -28 into one equation.

x - (-28) = 15

x+28 =15

x = 15-28

x=-13




6 0
3 years ago
What is the next term in the sequence below? 1/2, 2/6, 3/18, 4/54
lesya692 [45]
A.) 5/162

the numerator is increasing by 1 and the denominator is being multiplied by 3 each time
7 0
3 years ago
In ΔABC, if m ∠A = m∠C, m∠B = ß (where ß is an acute angle), and BC = x, which expression gives the length of b, the side opposi
chubhunter [2.5K]

Answer:

The length of b is \sqrt{2x^2(1-cos\beta)}.

Step by step explanation:

Given information: In ΔABC, ∠A =∠C, ∠B = ß (where ß is an acute angle), and BC = x.

Since two angles are same therefore triangle ABC is an isosceles triangle and side AB and BC are congruent.

AB=BC=x

According to Law of cosine

b^2=a^2+c^2-2ac\cos B

b^2=x^2+x^2-2(x)(x)\cos \beta

b^2=2x^2-2x^2\cos \beta

b^2=2x^2(1-\cos \beta)

\sqrt{2x^2(1-cos\beta)}

Therefore the length of b is \sqrt{2x^2(1-cos\beta)}.

6 0
2 years ago
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