Answer:
See explanation.
Step-by-step explanation:
Let us first analyze some principle theory. By definition we know that the velocity ( ) is a function of a distance ( ) covered in some time ( ), whilst acceleration ( ) is the velocity achieved in some time. These can also been expressed as:
and
We also know that both velocity and acceleration are vectors (therefore they are characterized by both a magnitude and a direction). Finally we know that given a position vector we can find the <u>velocity and the acceleration</u>, by differentiating the vector with respect to time, once and twice, respectively.
Let us now solve our problem. Here we are givine the Position vector of a particle P (in two dimensional space of ) as:
Eqn.(1)
Let us solve.
<u>Part (a) Velocity: </u><u>we need to differentiate Eqn.(1) with respect to time as:</u>
Eqn.(2)
<u>Part (b) Acceleration: </u><u>we need to differentiate Eqn.(2) with respect to time as:</u>
<u /><u />
<u />
Thus the expressions for the velocity and the acceleration of particle P in terms of t are
and
3/(5x) + x = 3/(5x) + x/1 * (5x)/(5x)
= 3/(5x) + 5x²/5x
= (3+5x²) / 5x
Normal price for 5 pages: number of pages times the price per page
(5)*($8.75) = $43.75
Discounted rate: $8.75 - $1.45 = $7.30
Discounted price for 5 pages:
(5)*($7.30) = $36.50
A scale factor "from A to B" is a number that multiplies some dimension of A to make it equal to the corresponding dimension of B. That is, ...
(scale factor A to B) = (dimension of B)/(corresponding dimension of A)
Your triangles have one corresponding dimension. On triangle A, it is 6 ft. On triangle B, it is 5 ft. Using the above formula, we have
(a) (scale factor A to B) = (5 ft)/(6 ft) = 5/6
The reverse is also true. That is, ...
(b) (scale factor B to A) = (dimension of A)/(corresponding dimension of B)
(scale factor B to A) = (6 ft)/(5 ft) = 6/5
(c) The scale factors are reciprocals of each other.
We should find the area of the carpet squares. Since each side is 1 foot, the area will be 1. Now, Julie used 120 carpet squares, which is 1 in area. So, we will have to multiply 1 by 120.
120×1=120
The area of the floor is 120 ft².