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3 years ago

1=12.6cm; w=14.8cm; p=

Mathematics

1 answer:

Ratling [72]3 years ago

7 0

We are given the length and width of a rectangle and we need to find perimeter- the distance around the shape

$l$ = 12.6 cm

w = 14.8 cm

The formula for the perimeter of a rectangle is

Perimeter = 2 $l$ + 2w

This makes sense because around the shape there are 2 equal lengths and 2 equal widths- one of the definitions of a rectangle

To find perimeter plug in the know vales of $l$ and w

Perimeter = 2(12.6 cm) + 2(14.8 cm)

Now use PEMDAS to solve

= 25.2 cm + 29.6 cm

= 54.8 cm

The perimeter of the rectangle is 54.8 cm

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A jogger runs 140 m due west, then changes direction for the second leg of her run. At the end of the run, she is 374 m away fro

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Answer:

The length of her second displacement = 247.12 m.

The direction of her second displacement = 31.24° from west.

Step-by-step explanation:

As per the question,

From the figure as drawn below,

Let the starting point be O. After running 140 m due west, she reached at point A.

∴ OA = 140 m

And At the end of the run, she is 374 m away from the starting point at an angle of 20° north of west.

∴ OP = 374 m

We have to find the distance AP = x.

By using the cosine rule in triangle OAP

$cos \theta = \frac{OA^{2}+OP^{2}-AP^{2}}{2\times OA\times OP}$

After putting the given value, we get

$cos 20= \frac{140^{2}+374^{2}-x^{2}}{2\times 140\times 374}$

$x^{2}=140^{2}+374^{2} - 2\times 140\times 374\times cos 20$

∴ x = 247.12 m

Hence,the length of her second displacement = 247.12 m.

Again,

By using the cosine rule in triangle OAP, we get

$cos \alpha = \frac{OA^{2}+AP^{2}-OP^{2}}{2\times OA\times AP}$

After putting the given value, we get

$cos \alpha = \frac{140^{2}+247.12^{2}-374^{2}}{2\times 140\times 247.12}$

∴ α = 148.759°

Hence, the direction of her second displacement = 180° - α = 180° - 148.759 = 31.24° from west.

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Step-by-step explanation:

To solve the quadratic, write the quadratic in standard form and factor the equation.

x² - 4x = 60

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