what is 3 to the power of 8 times 3 to the power of 4 divided by 3 to the power of 2 times 3 to the power of 8?

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A jogger ran 3 miles due east of his house. then he ran 5 miles at a heading of 30o east of north (or 30o ne). how far is he fro

Natasha_Volkova [10]

Magnitude of the net displacement: 7.0 miles

Step-by-step explanation:

In order to find the total displacement of the man, we have to resolve each displacement along the x- and y- direction.

Taking x as positive x direction and y as positive north direction:

- The first motion is 3 miles due east, so

$A_x = 3 mi\\A_y = 0$

- The second motion is 5 miles at $30^{\circ}$ east of north, so:

$B_x = 5 sin 30^{\circ}=2.5 mi\\B_y = 5 cos 30^{\circ}=4.3 mi$

So the components of the net displacement are

$R_x = A_x + B_x = 3 + 2.5 = 5.5 mi\\R_y = A_y+B_y = 0 + 4.3 = 4.3 mi$

And so the magnitude of the net displacement is

$d=\sqrt{R_x^2+R_y^2}=\sqrt{5.5^2+4.3^2}=7.0 mi$

So, he is 7.0 miles far from the house.

Learn more about distance and displacement:

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4 0

3 years ago

Triangle MNP has vertices N(2, 2) and P(0, –2). The triangle is symmetric about the y-axis. What is the approximate measure of t

Evgesh-ka [11]

Point M of the triangle is (-2,2) to make triangle MNP as shown in the attached image

Triangle MNP has a base of 4 units and a height of 4 units. We can work out the angle x and angle y using trigonometry ratio

We use tan ratio to find both angles

$Tan (x) = \frac{opposite}{adjacent}$
$Tan(x)= \frac{4}{2}$
$Tan(x)=2$
$Tan^{-1}(2)=63.43494882$
$Angle x=63.43$

$Tan(y)= \frac{opposite}{adjacent}$
$Tan(y)= \frac{2}{4}$
$Tan^{-1}(0.5)=26.56505118$
$Angle y=26.6$

Angle MNP = Angle NMP = 63.43 degrees (this is based on the fact that the triangle is an isosceles triangle)

Angle MPN = 2×26.6 = 53.2 degrees (we multiply by 2 as angle y is only a half of angle MPN - as shown in the diagram)