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2 years ago

Evaluate the expression 5(-3) using a number line.

Mathematics

2 answers:

MArishka [77]2 years ago

7 0

Answer: -15

Step-by-step explanation:

evablogger [386]2 years ago

5 0

Answer:

Compare the treatment of the buffalo by these two groups of people.

Step-by-step explanation:

Native Americans relied heavily on bison for their survival and well-being, using every part of the bison for food, clothing, shelter, tools, jewelry and in ceremoniesNative Americans relied heavily on bison for their survival and well-being, using every part of the bison for food, clothing, shelter, tools, jewelry and in ceremoniesNative Americans relied heavily on bison for their survival and well-being, using every part of the bison for food, clothing, shelter, tools, jewelry and in ceremoniesNative Americans relied heavily on bison for their survival and well-being, using every part of the bison for food, clothing, shelter, tools, jewelry and in ceremoniesNative Americans relied heavily on bison for their survival and well-being, using every part of the bison for food, clothing, shelter, tools, jewelry and in ceremonies

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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 $x^2$ .

4 0

3 years ago

Simplify the following expression. 4a^-2b<br><br> A.) b/4a^2<br> B.)4b/a^2<br> C.)1/4a^b2

Sergio [31]

ANSWER

The correct answer is B

$\frac{4b}{ {a}^{2} }$

EXPLANATION

The given exponential expression is

$4 {a}^{ - 2} b$

We can rewrite this as,

$4b \times {a}^{ - 2}$

We need to simplify to obtain a positive index, so we apply the following property,

${a}^{ - m} = \frac{1}{ {a}^{m} }$

This implies that,

$4b \times {a}^{ - 2} = 4b \times \frac{1}{ {a}^{2} }$

This will finally simplify to,

$4b \times {a}^{ - 2} =\frac{4b}{ {a}^{2} }$

Therefore the correct answer is B

6 0

3 years ago

Read 2 more answers

Does anyone know what 1+1 is?

hammer [34]

1+1 = 2 that is the answer

6 0

2 years ago

Read 2 more answers

Solve the variable<br> -10+ s/1.5= -5

patriot [66]

Answer: