Mario is setting up a new tent during a camping trip . The tent came with 7 feet of rope . The instructions are to use 34.5 inches of the rope to a tie the tent stakes in the ground . Mario will use all of the rope as instructed. Write and solve an equation to determine the number of 8 1/4 inch sections of a rope Mario can cut from the rope . Show your work

The number of    inch sections of a rope Mario can cut from the rope is 6.

Step-by-step explanation:

Given:

Mario is setting up a new tent during a camping trip . The tent came with 7 feet of rope . The instructions are to use 34.5 inches of the rope to a tie the tent stakes in the ground . Mario will use all of the rope as instructed

Now, to write and solve equation to determine the number of 8 1/4 inch sections of a rope Mario can cut from the rope.

Let the number of sections be

The length of rope Mario can cut from the rope =

Total length of rope = 7 feet.

So, 1 feet = 12 inches.

Thus, the length of rope in inches = 7 × 12 = 84 inches.

The length of rope to tie the tent stakes in the ground = 34.5 inches.

According to question:

Now, to get the number of sections we put an equation:

Dividing both sides by  8.25  we get:

The number of sections = 6.

Therefore, the number of    inch sections of a rope Mario can cut from the rope is 6.

reduce the friction between its moving parts

step-by-step explanation:

in fact, by reducing the friction between the moving parts of the machine, it is possible to reduce the energy wasted due to this friction; therefore, more input energy is converted into useful work, and this will improve the efficiency of the machine.

x= -3 and

step-by-step explanation:

to find the roots of a cubic, use division or factoring to find the factors then set equal to 0. as this is a difference of cubes, it factors into

where a is the cube root of .

here   this is 27 and the cube root of 27 is 3. so we write using the form:

.

set each factor to 0 and solve for x.

x-3=0

x=3

the quadratic expression does not factor and must be solved using the quadratic formula.

where a = 1, b=3, and c=9

this cubic has two complex roots.