Jessica hiked 5 miles in 2 hours. At this same rate, what is the total number of miles Jessica could hike in 14 hours?

Answer:

[tex]\text{$f(x)$ is increasing for $(-\infty, -\frac{1}{3})$ and $(4, \infty)$} \\ \text{$f(x)$ is decreasing for $(-\frac{1}{3}, 4)$}[/tex]

Step-by-step explanation:

We have the function:

[tex]f(x)=x^3-\frac{11}{2}x^2-4x[/tex]

And we want to determine the intervals for which the function is increasing or decreasing.

We will need to first find the critical points of the function. Note that our original function is continuous across the entire x-axis.

To find the critical points, we need to find the first derivative and then solve for the x. So:

[tex]f^\prime(x)=\frac{d}{dx}[x^3-\frac{11}{2}x^2-4x][/tex]

Differentiate:

[tex]f^\prime(x)=(3x^2)-\frac{11}{2}(2x)-(4) \\ f^\prime(x)=3x^2-11x-4[/tex]

Set the derivative equal to 0 and solve for x:

[tex]0=3x^2-11x-4[/tex]

Factor:

[tex]0=3x^2-12x+x-4 \\ 0=3x(x-4)+(x-4) \\ 0=(3x+1)(x-4)[/tex]

Zero Product Property:

[tex]3x+1=0\text{ or } x-4=0 \\ x=-\frac{1}{3}\text{ or } x=4[/tex]

Therefore, our critical points are -1/3 and 4.

We can thus sketch the following number line:

<————-(-1/3)——————————————(4)—————>

Now, let’s test values for the three intervals: less than -1/3, between -1/3 and 4, and greater than 4.

For less then -1/3, we can use -1. So, substitute -1 for x for our first derivative and see which we get:

[tex]f^\prime(-1)=3(-1)^2-11(-1)-4=3+11-4=10>0[/tex]

The result is positive.

Therefore, for all numbers less than -1/3,f(x) is increasing (since its derivative is positive).

For between -1/3 and 4, we can use 0. Substitute 0 for our derivative:

[tex]f^\prime(0)=3(0)^2-11(0)-4=-4<0[/tex]

The result is negative.

Therefore, for all numbers between -1/3 and 4, f(x) is decreasing (since its derivative is negative).

And finally, for greater than 4, we can use 5:

[tex]f^\prime(5)=3(5)^2-11(5)-4=16>0[/tex]

The result is positive.

Therefore, for all numbers greater than 4, f(x) is increasing (since its derivative is positive.

Therefore:

[tex]\text{$f(x)$ is increasing for $x<-\frac{1}{3}$ and $x>4$}\\ \text{ $f(x)$ is decreasing for $-\frac{1}{3}<x<4$}[/tex]

In interval notation:

[tex]\text{$f(x)$ is increasing for $(-\infty, -\frac{1}{3})$ and $(4, \infty)$} \\ \text{$f(x)$ is decreasing for $(-\frac{1}{3}, 4)$}[/tex]

Answer:

40

Step-by-step explanation:

Answer:

-6

Step-by-step explanation:

-10-(-4)=-1+4=-6

Hope this helps plz mark brainliest ;D

Answer:

probability of picking a yellow =0.4706

a blue or green = 0.2941

an orange = 0 ( there is no orange bag)

Answer:The expression is 6y - 4x

Step-by-step explanation:

Answer:

-4x+6y

Step-by-step explanation:

4x+6y-8x4

(4x-8x)+6y

−4x+6y

Answer:

Um threre is no blanks or there is no question.

Step-by-step explanation:

Answer: 14 feet

Step-by-step explanation:

Answer:

14 feet

Step-by-step explanation:

Answer:

238

Step-by-step explanation:

juans has 10 more than kevin's, so you just subtract 10 from 248, getting 238

Answer:

[tex]\frac{dy}{dx} =-\sqrt[3]{\frac{y}{x} }[/tex]

Step-by-step explanation:

Recall that using the chain rule we can state:

[tex]\frac{dy}{dt} =\frac{dy}{dx}*\frac{dx}{dt}[/tex]

and therefore solve for dy/dx as long as dx/dt is different from zero.

Then we find dy/dt  and dx/dt,

Given that

[tex]x=sin^3(t)\\dx/dt = 3 sin^2(t)* cos(t)[/tex]

And similarly:

[tex]y=cos^3(t)\\dy/dt=-3\,cos^2(t)*sin(t)[/tex]

Therefore, dy/dx can be determined by the quotient of the expressions we just found:

[tex]\frac{dy}{dx} =\frac{dy/dt}{dx/dt} =\frac{-3\,cos^2(t)*sin(t)}{3\,sin^2(t)*cos(t)} =-\frac{cos(t)}{sin(t)}[/tex]

now notice that we can find   [tex]cos(t) = \sqrt[3]{y}[/tex]  from the expression for y,

and   [tex]sin(t) = \sqrt[3]{x}[/tex]  from its expression for x.

Therefore dy/dx can be written in terms of x and y as:

[tex]\frac{dy}{dx} =-\frac{cos(t)}{sin(t)}=-\sqrt[3]{\frac{y}{x} }[/tex]

Answer:

26123 is the answer have a good day

Answer:

pls mark me brainliest the answer

Step-by-step explanation:

a gallon= 22$

1 gallon = 7.3$

Answer: 40

60÷15=4

10×4=40

I hope this is good enough:

Answer:

168

Step-by-step explanation: You would do 140/100 = 1.4 then multiply 120 by 1.4 which is 168.

5>0-3

Step By Step- 5 is greater than 0-3 because 0-3 would equal a negative number, and all positive numbers are greater than negative numbers

Answer:

5>0-3

Step-by-step explanation:

Answer:

y-8 = 2 (x-6)

Answer:

-2= y=-13, (x,y)= (-2,-13)

0= y= -3, (x,y)= (0,-3)

1= y= 2, (x,y)= (1,2).

Step-by-step explanation:

Please mark as brainliest. :)

Answer:

1/5

Step-by-step explanation:

[tex]\frac{2-1}{3--2} = \frac{1}{5}[/tex]

Answer: 1/5

Step-by-step explanation: Following our hint,

let's start with the slope formula.

m = y₂ - y₁ / x₂ - x₁

We take the second y minus the first y over the second x minus the first x.

So we have m = 2 - 1 / 3 - (-2) or 1 / 5.

So our slope is 1/5.

Answer:

1 2 3

Step-by-step explanation:

4 * 1 <16       4 is less than 16

4 * 2 <16      8 is less than 16

4 *3 <16     12 is less than 16

4 * 4   is not less than 16. 16 is not less than 16

Answer: x= -56/9

Step-by-step explanation:

34+12x=3x-22

Subtract 12x from both sides

34=-9x-22

Add 22 to both sides

56=-9x

Divide -9 by both sides to get x alone

56/-9=x

So

x=-56/9

Answer:

Yes, my partner is correct because as the fat increases the calories increase. And when the points are rising from the left to the right, this indicates a positive correlation.

Step-by-step explanation:

Answer:

$5.25

Step-by-step explanation:

Answer:

(Amount for 1 inch of red ribbon) x (240) = total cost

Step-by-step explanation:

Answer:

to create an equation that is parallel to a line, you keep the slope or rate of change the same, all you do is change the y intercept. so you have to keep

y = 2x, but then you can add any number to the end.

Answer:

3 - 3 = 0 units There is no distance, the points are in the same place.

Step-by-step explanation: