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3 years ago

14. Michelle simplified an expression for the perimeter of the rectangle below and got X + 35.

Mathematics

1 answer:

Zigmanuir [339]3 years ago

6 0

Answer:

The correct expression for the perimeter is $P=(\frac{5}{3}x+70)\ units$

see the explanation

Step-by-step explanation:

The complete question in the attached figure

Let

L ----> the length of rectangle

W ---> the width of rectangle

we know that

The perimeter of rectangle is equal to

$P=2(L+W)$

In this problem we have

$L=(\frac{5}{6}x+23)\ units$

$W=12\ units$

substitute the values

$P=2(\frac{5}{6}x+23+12)$

$P=2(\frac{5}{6}x+35)$

$P=(\frac{10}{6}x+70)\ units$

Simplify

$P=(\frac{5}{3}x+70)\ units$

Michelle didn't multiply the sum of length and width by 2

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Then, we have to calculate the displacement in 20 minutes using the actual speed vector.

We can calculate the movement in each of the axis. For the x-axis:

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NOTE: 20 minutes represents 1/3 of an hour.

We can do the same with the y-coordinate:

$\begin{gathered} R_{3y}=R_{2y}+v_{3y}\cdot t \\ R_{3y}=167.67+491.76\cdot\frac{1}{3} \\ R_{3y}=167.67+163.92 \\ R_{3y}=331.59 \end{gathered}$

The final position is R3 = (282.53, 331.59).

To find the distance from the origin and direction, we transform the cartesian coordinates of R3 into polar coordinates:

The distance can be calculated as if it was a right triangle:

$\begin{gathered} d^2=x^2+y^2_{} \\ d^2=282.53^2+331.59^2 \\ d^2=79823.20+109951.93 \\ d^2=189775.13 \\ d=\sqrt[]{189775.13} \\ d\approx435.63 \end{gathered}$

The angle, from E to N, can be calculated as:

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If we want to express it from N to E, we substract the angle from 90°:

$\beta=90\degree-\alpha=90-49.56=40.44\degree$

Answer: the final location can be represented with the vector (282.53, 331.59).

1) The distance from the origin is 435.63 miles and

2) the direction is N-40°-E.

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