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cestrela7 [59]
3 years ago
6

A rectangular garden has an area of 35 square miles. If its length is 78 miles, what is its width?

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

Answer:

9/20 mi

Step-by-step explanation:

  1. A= b*h
  2. Fill in the Values

35 = 78 * h

3. divide 35 by 78 = 0.44871794871

4. round that to .45

5. To make a fraction, put it over 100

45/100

7. Simplify fraction

9/20

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Answer:  \dfrac{2x^2-1}{x(x^2-1)}

Step-by-step explanation:

The given function : y=\ln(x(x^2 - 1)^{\frac{1}{2}})

\Rightarrow\ y=\ln x+\ln (x^2-1)^{\frac{1}{2}}    [\because \ln(ab)=\ln a +\ln b]

\Rightarrow y=\ln x+\dfrac{1}{2}\ln (x^2-1)}  [\because \ln(a)^n=n\ln a]

Now , Differentiate both sides  with respect to x , we will get

\dfrac{dy}{dx}=\dfrac{1}{x}+\dfrac{1}{2}(\dfrac{1}{x^2-1})\dfrac{d}{dx}(x^2-1) (By Chain rule)

[Note : \dfrac{d}{dx}(\ln x)=\dfrac{1}{x}]

\dfrac{1}{x}+\dfrac{1}{2}(\dfrac{1}{x^2-1})(2x-0)

[ \because \dfrac{d}{dx}(x^n)=nx^{n-1}]

=\dfrac{1}{x}+\dfrac{1}{2}(\dfrac{1}{x^2-1})(2x) = \dfrac{1}{x}+\dfrac{x}{x^2-1}\\\\\\=\dfrac{(x^2-1)+(x^2)}{x(x^2-1)}\\\\\\=\dfrac{2x^2-1}{x(x^2-1)}

Hence, the derivative of the given function is \dfrac{2x^2-1}{x(x^2-1)} .

8 0
4 years ago
Solve for x. 2=4x-6​
77julia77 [94]

Answer:

x = 2

Step-by-step explanation:

Rewrite the equation as 4x - 6 = 2

Move all terms not containing x to the right side of the equation:

Add 6 to both sides of the equation.

4x = 2 + 6

Add 2 and 6.

4x = 8

Divide each term by 4 and simplify.

Divide each term in 4x = 8 by 4.

\frac{4x}{4} =\frac{8}{4}

Reduce the expression by cancelling the common factors.

x=\frac{8}{4}

Divide 8 by 4.

x = 2

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