The cost in dollars of making x items is given by the function C(x) = 10x + 800.

Find the given value of the function.<br><br> w(t) = 3t – 1; t =1/3

natima [27]

Answer:

1/3

Step-by-step explanation:

differentiate first equation to get t , then replace t with 1/3

5 0

2 years ago

The population of a town increased from 3500 in 2005 to 5600 in 2009. Find the absolute and relative (percent) increase.

Ket [755]

Answer:

Absolute increase in population will be 2100

And percentage increase will be 60 %

Step-by-step explanation:

We have given population in 2005 is 3500

And population in 2009 is 5600

So absolute increase in population = 5600-3500 = 2100

We have to find the percentage increase in population

So relative percentage increase in population will be $\frac{2100}{3500}\times 100=60$ %

So population will increase by 60 %

6 0

2 years ago

Complete parts a through c for the given function.

victus00 [196]

Answer:

a. The critcal points are at

$x=0,-5,3$

b. Then, $x = -5$ is a maximum and $x=3$ is a minimum

c. The absolute minimum is at $x = 3$ and the absolute maximum is at $x = -5.$

Step-by-step explanation:

(a)

Remember that you need to find the points where

$f'(x)=0$

Therefore you have to solve this equation.

$20x^4 + 40x^3 - 300x^2 = 0$

From that equation you can factor out $20x^2$ and you would get

$20x^2 ( x^2 +2x - 15) = 0$

And from that you would have $20x^2 = 0$ , so $x = 0$ .

And you would also have $x^2 +2x-15 = 0$ .

You can factor that equation as $x^2 +2x -15 = (x+5)(x-3) = 0$

Therefore $x=-5 , x=3$ .

So the critcal points are at

$x=0,-5,3$

b.

Remember that a function has a maximum at a critical point if the second derivative at that point is negative. Since

$f''(x) = 80x^3 + 120x^2 -600x\\f''(-5) = 80(-5)^3 + 120(-5)^2 -600(-5) = -4000 < 0\\\\f''(3) = 80(3)^3 + 120(3)^2 -600(3) = 1440 > 0 \\$

Then, $x = -5$ is a maximum and $x=3$ is a minimum

c.

The absolute minimum is at $x = 3$ and the absolute maximum is at $x = -5.$

6 0

2 years ago

Read 2 more answers

Fill in Sin, Cos, and tan ratio for angle x. <br> Sin X = 4/5 (28/35 simplified)

Fantom [35]

Answer:

Given: $\sin(x) = (4/5)$ .

Assuming that $0 < x < 90^{\circ}$ , $\cos(x) = (3/5)$ while $\tan(x) = (4/3)$ .

Step-by-step explanation:

By the Pythagorean identity $\sin^{2}(x) + \cos^{2}(x) = 1$ .

Assuming that $0 < x < 90^{\circ}$ , $0 < \cos(x) < 1$ .

Rearrange the Pythagorean identity to find an expression for $\cos(x)$ .

$\cos^{2}(x) = 1 - \sin^{2}(x)$ .

Given that $0 < \cos(x) < 1$ :

$\begin{aligned} &\cos(x) \\ &= \sqrt{1 - \sin^{2}(x)} \\ &= \sqrt{1 - \left(\frac{4}{5}\right)^{2}} \\ &= \sqrt{1 - \frac{16}{25}} \\ &= \frac{3}{5}\end{aligned}$ .

Hence, $\tan(x)$ would be:

$\begin{aligned}& \tan(x) \\ &= \frac{\sin(x)}{\cos(x)} \\ &= \frac{(4/5)}{(3/5)} \\ &= \frac{4}{3}\end{aligned}$ .

7 0

2 years ago

Graph y=6x−7<br> Identify the x-intercept.

valina [46]

9514 1404 393

Answer:

x-intercept: 7/6

Step-by-step explanation:

The x-intercept is found by solving for x when y=0.

0 = 6x -7

7 = 6x . . . . . add 7 to both sides of the equation

7/6 = x . . . . divide both sides by 6

The x-intercept is 7/6 = 1 1/6 ≈ 1.167.

__

The y-intercept is the constant in the given equation: -7. The slope of 6 tells you the line rises 6 units for 1 unit to the right. So, the point (1, -1) is another point on the graph. The line through those two points, (0, -7) and (1, -1), will intersect the x-axis at x=7/6.

6 0

2 years ago