Write a comparison sentence that represents this equation 5x9=45

Answer:

The variable x lies within the interval of all positive real numbers less than 5 cm.

Detailed solution:

Problem statement:

Determine the volume of the open-topped box as a function of the side length x (in centimeters) of the square cutouts.

Refer to the provided diagram for clarity.

Define:

x → length in centimeters of each square cutout side

The volume of the box with open top can be written as:

Given this, we have:

By substitution:

Determine the domain of x:

Because:

Therefore:

Domain is the interval (0,5)

That means all real numbers strictly greater than zero and less than 5 cm are valid for x.

Hence, the volume V as a function of x is:

Response:

The graph in question is linked to g(x) = -2x, though it is not provided.

Detailed explanation:

A reflection across the y-axis changes the sign of the x-coordinate for every point. To derive the new function, we substitute x with -x:

g(x) = f(-x) = 2(-x) = -2x

This leads us to g(x) = -2x.

Answer:

Step-by-step explanation:

Step 1:-

We have c1(t) = e^ t i + (sin(t))j + t³k

and c2(t) = e^−t i + (cos(t))j − 6t³k.

By adding c1(t) and c2(t):

c1(t)+c2(t) = e^ t i + (sin(t))j + t³k + e^−t i + (cos(t))j − 6t³k

Now, employing the derivative formula:

Next, differentiate with respect to 't'

By factoring out i, j, and k terms, we arrive at: