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leva [86]
3 years ago
10

The area of a square is 144 square centimeters. Find the length of the diagonal. Write your answer in simplest radical form.

Mathematics
1 answer:
maks197457 [2]3 years ago
3 0

Answer:

12\sqrt{2}\ cm

Step-by-step explanation:

step 1

Find the length side of the square

we know that

The area of a square is equal to

A=b^{2}

where

b is the length side

we have

A=144\ cm^2

substitute in the formula of area

144=b^{2}

solve for b

square root both sides

b=12\ cm

step 2

Find the length of the diagonal

Applying the Pythagorean Theorem

d^2=b^2+b^2

see the attached figure to better understand the problem

substitute the given values

d^2=12^2+12^2

d^2=288

square root both sides

d=\sqrt{288}\ cm

simplify

d=12\sqrt{2}\ cm

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After traveling exactly half of its journey from station A to station B, a train was held up for 10 minutes. In order to arrive
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Let's define variables:
 s = original speed
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 The time for the second half of the route is:
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 The equation for the time of the trip is:
 60 / s + 60 / (s + 12) + 1/6 = 120 / s
 Where,
 1/6: held up for 10 minutes (in hours).
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8 0
3 years ago
Find two vectors in R2 with Euclidian Norm 1<br> whoseEuclidian inner product with (3,1) is zero.
alina1380 [7]

Answer:

v_1=(\frac{1}{10},-\frac{3}{10})

v_2=(-\frac{1}{10},\frac{3}{10})

Step-by-step explanation:

First we define two generic vectors in our \mathbb{R}^2 space:

  1. v_1 = (x_1,y_1)
  2. v_2 = (x_2,y_2)

By definition we know that Euclidean norm on an 2-dimensional Euclidean space \mathbb{R}^2 is:

\left \| v \right \|= \sqrt{x^2+y^2}

Also we know that the inner product in \mathbb{R}^2 space is defined as:

v_1 \bullet v_2 = (x_1,y_1) \bullet(x_2,y_2)= x_1x_2+y_1y_2

So as first condition we have that both two vectors have Euclidian Norm 1, that is:

\left \| v_1 \right \|= \sqrt{x^2+y^2}=1

and

\left \| v_2 \right \|= \sqrt{x^2+y^2}=1

As second condition we have that:

v_1 \bullet (3,1) = (x_1,y_1) \bullet(3,1)= 3x_1+y_1=0

v_2 \bullet (3,1) = (x_2,y_2) \bullet(3,1)= 3x_2+y_2=0

Which is the same:

y_1=-3x_1\\y_2=-3x_2

Replacing the second condition on the first condition we have:

\sqrt{x_1^2+y_1^2}=1 \\\left | x_1^2+y_1^2 \right |=1 \\\left | x_1^2+(-3x_1)^2 \right |=1 \\\left | x_1^2+9x_1^2 \right |=1 \\\left | 10x_1^2 \right |=1 \\x_1^2= \frac{1}{10}

Since x_1^2= \frac{1}{10} we have two posible solutions, x_1=\frac{1}{10} or x_1=-\frac{1}{10}. If we choose x_1=\frac{1}{10}, we can choose next the other solution for x_2.

Remembering,

y_1=-3x_1\\y_2=-3x_2

The two vectors we are looking for are:

v_1=(\frac{1}{10},-\frac{3}{10})\\v_2=(-\frac{1}{10},\frac{3}{10})

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