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3 years ago

Write one number that is a factor of 13

1 answer:

4 0

So, if we need to find 1 factor, let's just multiply 13 × 2.

13 x 2 = 26.

So, 26 is your answer.

Glad I could help, and good luck!

AnonymousGiantsFan

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A graphing calculator is recommended. A function is given. g(x) = x4 − 5x3 − 14x2 (a) Find all the local maximum and minimum val

Taya2010 [7]

Answer:

The local maximum and minimum values are:

Local maximum

$g(0) = 0$

Local minima

$g(5.118) = -350.90$

$g(-1.368) = -9.90$

Step-by-step explanation:

Let be $g(x) = x^{4}-5\cdot x^{3}-14\cdot x^{2}$ . The determination of maxima and minima is done by using the First and Second Derivatives of the Function (First and Second Derivative Tests). First, the function can be rewritten algebraically as follows:

$g(x) = x^{2}\cdot (x^{2}-5\cdot x -14)$

Then, first and second derivatives of the function are, respectively:

First derivative

$g'(x) = 2\cdot x \cdot (x^{2}-5\cdot x -14) + x^{2}\cdot (2\cdot x -5)$

$g'(x) = 2\cdot x^{3}-10\cdot x^{2}-28\cdot x +2\cdot x^{3}-5\cdot x^{2}$

$g'(x) = 4\cdot x^{3}-15\cdot x^{2}-28\cdot x$

$g'(x) = x\cdot (4\cdot x^{2}-15\cdot x -28)$

Second derivative

$g''(x) = 12\cdot x^{2}-30\cdot x -28$

Now, let equalize the first derivative to solve and solve the resulting equation:

$x\cdot (4\cdot x^{2}-15\cdot x -28) = 0$

The second-order polynomial is now transform into a product of binomials with the help of factorization methods or by General Quadratic Formula. That is:

$x\cdot (x-5.118)\cdot (x+1.368) = 0$

The critical points are 0, 5.118 and -1.368.

Each critical point is evaluated at the second derivative expression:

x = 0

$g''(0) = 12\cdot (0)^{2}-30\cdot (0) -28$

$g''(0) = -28$

This value leads to a local maximum.

x = 5.118

$g''(5.118) = 12\cdot (5.118)^{2}-30\cdot (5.118) -28$

$g''(5.118) = 132.787$

This value leads to a local minimum.

x = -1.368

$g''(-1.368) = 12\cdot (-1.368)^{2}-30\cdot (-1.368) -28$

$g''(-1.368) = 35.497$

This value leads to a local minimum.

Therefore, the local maximum and minimum values are:

Local maximum

$g(0) = (0)^{4}-5\cdot (0)^{3}-14\cdot (0)^{2}$

$g(0) = 0$

Local minima

$g(5.118) = (5.118)^{4}-5\cdot (5.118)^{3}-14\cdot (5.118)^{2}$

$g(5.118) = -350.90$

$g(-1.368) = (-1.368)^{4}-5\cdot (-1.368)^{3}-14\cdot (-1.368)^{2}$

$g(-1.368) = -9.90$

7 0

3 years ago

Use logarithmic differentiation to find the derivative of the function. y = x2cos x Part 1 of 4 Using properties of logarithms,

Arisa [49]

ANSWER

${y}^{'} = 2x \cos(x) - {x}^{2} \sin(x)$

EXPLANATION

The given function is

$y = {x}^{2} \cos(x)$

We take natural log of both sides;

$ln(y) = ln({x}^{2} \cos(x) )$

Recall and use the product rule of logarithms.

$ln(AB) = ln(A ) + ln(B)$

This implies that:

$ln(y) = ln({x}^{2} ) + ln( \cos(x) )$

$ln(y) = 2 ln({x} ) + ln( \cos(x) )$

We now differentiate implicitly to obtain;

$\frac{ {y}^{'} }{y} = \frac{2}{x} - \frac{ \sin(x) }{ \cos(x) }$

Multiply through by y,

${y}^{'} = y( \frac{2}{x} - \frac{ \sin(x) }{ \cos(x) ) })$

Substitute y=x²cosx to obtain;

${y}^{'} = {x}^{2} \cos(x) ( \frac{2}{x} - \frac{ \sin(x) }{ \cos(x) ) } )$

Expand:

${y}^{'} = 2x \cos(x) - {x}^{2} \sin(x)$

7 0

3 years ago

Write as a single power of 8.<br> 8 to the power of 8<br><br> ÷<br> 8 to the power of 2

OLEGan [10]

Answer: 8^6

Step-by-step explanation:

$\frac{8^8}{8^2}$ = $8^{6}$ subtract the bottom exponent from the top exponent.

7 0

3 years ago

Flura [38]

V=1024 pi m^3 and v=250 pi m^3
the similarity ratio of the smaller to larger similar cones is
k= V/v=1024 pi m^3/250 pi m^3= 4.096
the great cone is 4.096 times of the small cone (in volume)

6 0

3 years ago

Read 2 more answers

Find the slope and the line between each pair of points

dalvyx [7]

Girl what are you talking about

4 0

2 years ago