What angle (in radians) corresponds to 0.75 rotations around the unit circle?

Learning Task 1: Write and answer the following in your answer sheet

Marina CMI [18]

Answer:

Evaluating Polynomials:

a. f(1) = -10

b. f(-3) = -239

c. f(2)² = 3125

Factoring Polynomials:

a. (x + 1)(x² - 5x + 6) = (x + 1)(x - 3)(x - 2)

b. (x² - x - 6)(x² + 6x + 9) = (x - 3)(x + 2)(x + 3)(x + 3)

c. x³ + 3x² - 4x - 12 = (x + 3)(x - 2)(x + 2)(x - 2)(x + 2)

4 0

2 years ago

1) Let f(x)=6x+6/x. Find the open intervals on which f is increasing (decreasing). Then determine the x-coordinates of all relat

brilliants [131]

Answer:

1) increasing on (-∞,-1] ∪ [1,∞), decreasing on [-1,0) ∪ (0,1]

$x = -1$ is local maximum, $x = 1$ is local minimum

2) increasing on [1,∞), decreasing on (-∞,0) ∪ (0,1]

$x = 1$ is absolute minimum

3) increasing on (-∞,0] ∪ [8,∞), decreasing on [0,4) ∪ (4,8]

$x = 0$ is local maximum, $x = 8$ is local minimum

4) increasing on [2,∞), decreasing on (-∞,2]

$x = 2$ is absolute minimum

5) increasing on the interval (0,4/9], decreasing on the interval [4/9,∞)

$x = 0$ is local minimum, $x = 4/9$ is absolute maximum

Step-by-step explanation:

To find minima and maxima the of the function, we must take the derivative and equalize it to zero to find the roots.

1) $f(x) = 6x + 6/x$

$f\prime(x) = 6 - 6/x^2 = 0$ and $x \neq 0$

So, the roots are $x = -1$ and $x = 1$

The function is increasing on the interval (-∞,-1] ∪ [1,∞)

The function is decreasing on the interval [-1,0) ∪ (0,1]

$x = -1$ is local maximum, $x = 1$ is local minimum.

2) $f(x)=6-4/x+2/x^2$

$f\prime(x)=4/x^2-4/x^3=0$ and $x \neq 0$

So the root is $x = 1$

The function is increasing on the interval [1,∞)

The function is decreasing on the interval (-∞,0) ∪ (0,1]

$x = 1$ is absolute minimum.

3) $f(x) = 8x^2/(x-4)$

$f\prime(x) = (8x^2-64x)/(x-4)^2=0$ and $x \neq 4$

So the roots are $x = 0$ and $x = 8$

The function is increasing on the interval (-∞,0] ∪ [8,∞)

The function is decreasing on the interval [0,4) ∪ (4,8]

$x = 0$ is local maximum, $x = 8$ is local minimum.

4) $f(x)=6(x-2)^{2/3} +4=0$

$f\prime(x) = 4/(x-2)^{1/3}$ has no solution and $x = 2$ is crtitical point.

The function is increasing on the interval [2,∞)

The function is decreasing on the interval (-∞,2]

$x = 2$ is absolute minimum.

5) $f(x)=8\sqrt x - 6x$ for $x>0$

$f\prime(x) = (4/\sqrt x)-6 = 0$

So the root is $x = 4/9$

The function is increasing on the interval (0,4/9]

The function is decreasing on the interval [4/9,∞)

$x = 0$ is local minimum, $x = 4/9$ is absolute maximum.

5 0

2 years ago

HELPPPPPPPP PLSSSS I HAVE 30 BEFORE THIS IS DUE

postnew [5]

Answer:

The line equation in slope-intercept form is:

$y\:=-\frac{2}{5}x+4$

Hence, option D is true.

Step-by-step explanation:

Given the points

(0, 4)

(5, 2)

Finding the slope between the points

$\left(x_1,\:y_1\right)=\left(0,\:4\right),\:\left(x_2,\:y_2\right)=\left(5,\:2\right)$

$\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}$

$m=\frac{2-4}{5-0}$

$m=-\frac{2}{5}$

As the y-intercept is obtained by setting the value x = 0.

As we know that when x = 0, the vale of y-intercept y = 4

so the y-intercept is b = 4.

As the slope-intercept form is

substituting the slope m = -2/5 and the y-intercept b=4

$y = mx+b$

$y\:=-\frac{2}{5}x+4$

Therefore, the line equation in slope-intercept form is:

$y\:=-\frac{2}{5}x+4$

Hence, option D is true.

6 0

2 years ago

12. A flat, square roof needs a square patch in the corner to seal a leak. The side length of

NISA [10]

Answer:

Step-by-step explanation:

Area of the good part= area of whole roof - area of bad part

Since the roof is a square roof, the area will be calculated using the formulae for area of a square

Area of a square =length²

Area of good part =(x+12)²-x²

A= {(x+12)(x+12)} - x²

A = (x²+12x+12x+144) -x²

Open the bracket and rearrange the equation

A= x²-x²+24x+144

A=(24x+144) ft

5 0

2 years ago

Find the term to term rules for the following sequences 28, 25 ,22, 19, 16

Hoochie [10]

Answer: -3n+31

Step-by-step explanation:

1. 28-55=3

25-22=3

22-19=3

19-16=3

This means that n = -3 as we are subtracting

2. We then do the opposite, we take the first number and we add 3 instead of taking it away we get 31.

That is how you get your answer

-3n+31

4 0

2 years ago

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