Sketch three possible rectangle of perimeter 20 feet

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

Find the center of the circle: x2 + 2x - 3 + y2 = 5.

rosijanka [135]

Answer:

$\boxed{(-1, 0)}$

Step-by-step explanation:

x² + 2x - 3 + y² = 5

Strategy:

Convert the equation to the centre-radius form:

(x - h)² + (y - k)² = r²

The centre of the circle is at (h, k) and the radius is r .

Solution:

Move the number to the right-hand side.

x² + 2x + y² = 8

Complete the square for x

(Take half the coefficient of x, square it, and add to each side of the equation)

(x² + 2x + 1) + y² = 9

Complete the square for y

The coefficient of y is zero.

(x² + 2x + 1) + y² = 9

Express the result as the sum of squares

(x + 1)² + y² = 3²

h = -1; k = 0; r = 3

The centre of the circle is at $\boxed{(-1,0)}$

The graph of the circle below has its centre at (-1,0) and radius 3.

4 0

3 years ago

Solve the system of equations and choose the correct ordered pair.

chubhunter [2.5K]

Multiply first equation by 8,
24x + 40y = 352
Multiply second equation by 3,
24x - 21y = -75

Now, subtract second from 1st,
61y = 427
y = 427/61
y = 7

Substitute it in very first equation,
3x + 5(7) = 44
3x = 44 - 35
x = 9 / 3
x =3

In short, Your Answer would be Option D) (3, 7)

Hope this helps!

7 0

3 years ago

A cylindrical can of soup has a diameter of 7 cm and a height of 10 cm. How much soup is in the can, in terms of π?

Natasha2012 [34]

Answer:

B) 122.5π cm3

Step-by-step explanation:

Volume of a cylinder = $\pi r^{2} h$

r= radius , but we are given diameter or 7cm, radius = diameter/2 =7/2 = 3.5cm

h= height, given as 10cm

$\pi = constant$

Next, plug in the numbers into the formula;

$=\pi *3.5^{2} *10\\ \\ =\pi *12.25 *10\\ \\ =122.5\pi$

Therefore, the volume of soup in the can is 122.5 $\pi cm^{3}$

7 0

3 years ago

Read 2 more answers

Jason inherited a piece of land from his great-uncle. Owners in the area claim that there is a 45% chance that the land has oil.

inn [45]

P ( A ) = 0.45 - probability that the land has oil,
P ( B ) = 0.8 - probability that the test predicts it
P ( A ∩ B ) = P ( A ) · P ( B ) = 0.45 · 0.8 = 0.36
Answer: The probability that the land has oil and the test predicts it is 36 %.

7 0

3 years ago