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2 years ago

How to find the area of the shaded region

Mathematics

1 answer:

KiRa [710]2 years ago

6 0

Answer:

61 cm^2.

See below.

Step-by-step explanation:

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Indicate the answer choice that best completes the statement or answers the question.

eduard

The answer would be c. I can give an example if you want

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3 years ago

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Find dy/dx for y= x^3 ln (cot x)

ICE Princess25 [194]

<h3>Answer</h3>

$\dfrac{dy}{dx} = 3x^2 \ln(\cot x)-x^3 \csc(x)\sec(x)$

<h3>Explanation</h3>

By the product rule $(d/dx)(f(x)g(x)) = f(x)g'(x) + g(x)f'(x)$ , we have

$\begin{aligned}\frac{dy}{dx} &= \left(x^3 \ln (\cot x) \right)' \\&= x^3\big(\ln (\cot x)\big)' + \ln (\cot x) \cdot \left(x^3\right)' \end{aligned}$

By the chain rule:

$\begin{aligned}\big(\ln (\cot x)\big)' &= \dfrac{1}{\cot x} \cdot (\cot x)' \\ &= \dfrac{1}{\cot x} \cdot -\csc^2 x\\&= -\tan (x) \csc^2(x) \\&= - \frac{\sin x}{\cos x} \cdot \frac{1}{\sin^2 x} = - \frac{1}{\cos x} \cdot \frac{1}{\sin x} \\&= -\csc(x)\sec(x)\end{aligned}$

By the power rule:

$(x^3)' = 3x^2$

thus

$\begin{aligned}\frac{dy}{dx} &= x^3\big(\ln (\cot x)\big)' + \ln (\cot x) \cdot \left(x^3\right)' \\&= x^3\big( -\csc(x)\sec(x) \big) + \ln(\cot x) \cdot (3x^2) \\&= -x^3 \csc(x)\sec(x) + 3x^2 \ln(\cot x) \\&= 3x^2 \ln(\cot x)-x^3 \csc(x)\sec(x)\end{aligned}$

Nothing to do to simplify any further, other than factoring out $x^2$ .

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3 years ago

How can we use the graph of a logarithmic function to verify the domain of a function?PLEASE HELP

guajiro [1.7K]

The function y = log 2 x has the domain of set of positive real numbers and the range of set of real numbers. Remember that since the logarithmic function is the inverse of the exponential function, the domain of logarithmic function is the range of exponential function, and vice versa.

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3 years ago

Drag expressions into order to show a way to find 3 × 56.

lina2011 [118]

As we could "drag" these together, we could then do it the easy way.

56
+56
+56
-------
168
------------------------

Or we could also do the following:

56 $*$ 3:

6 $*$ 3= 18.

Carry the one.

5 $*$ 3 = 15+1 (which was carried). = 16

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the graph starts at an x intercept.

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