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3 years ago

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The library is 14.2 km away from daniels apartment. The bus takes daniel 11.15 km of the way to the library. He has to walk the

remaining distance

2 answers:

Anettt [7]3 years ago

7 0

Answer:

3050

Step-by-step explanation:

SVETLANKA909090 [29]3 years ago

5 0

He has to walk the remaining 3.05 kilometers.

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A car travels 10km southeast and then 15 km in a direction 60 degrees north of east. What is the magnitude of the car's resultan

Maurinko [17]

Answer: 15.85km

Step-by-step explanation:

The car starts at the point (0,0)

Let's define east as the positive x-axis and north as the positive y-axis.

first, the car travels 10km southeast, so the angle is -45° from the east.

Then the new position of the car is:

(10km*cos(-45°), 10km*sin(-45°)) = (7.07km, -7.07km)

Now, from this point the car travels 15km with an angle of 60° (counting from the east)

So the new position is:

(7.07km + 15km*cos(60°), -7.07km + 15km*sin(60°)) = (14.57km , 5.91km)

The magnitude of a vector (x, y) is √(x^2 + y^2)

So the magnitude of the vector (14.57km , 5.91km) is:

√((14.57km)^2 + (5.91km)^2) = 15.85km

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3 years ago

Use the figure to find the measures of the numbered angles,

Galina-37 [17]

Given:

A figure in which a transversal line t intersect the two parallel lines a and b.

To find:

The measure of the numbered angles.

Solution:

If a transversal line intersect the two parallel lines, then

1. Corresponding angles are equal.

2. Alternate interior angles are equal.

3. Alternate exterior angles are equal.

Now,

$m\angle 1+99^\circ=180^\circ$ (Linear pair)

$m\angle 1=180^\circ-99^\circ$

$m\angle 1=81^\circ$

$m\angle 2=99^\circ$ (Vertically opposite angles)

$m\angle 3=\angle 1=81^\circ$ (Vertically opposite angles)

$m\angle 4=99^\circ$ (Corresponding angles)

$m\angle 5=\angle 3=81^\circ$ (Alternate interior angles)

$m\angle 6=99^\circ$ (Alternate exterior angles)

$m\angle 7=\angle 3=81^\circ$ (Corresponding angles)

Therefore, $\angle 1=81^\circ, \angle 2=99^\circ,\angle 3=81^\circ, \angle 4=99^\circ,\angle 5=81^\circ, \angle 6=99^\circ,\angle 7=81^\circ$ .

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