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andrew11 [14]
3 years ago
6

Write a formula for rrr in terms of \thetaθtheta for the following figure.

Mathematics
2 answers:
xxMikexx [17]3 years ago
3 0

Answer:  r = 4cm/θ

Step-by-step explanation:

For a circle of radius R, the perimeter is:

P = 2*pi*R

Now, if we have an arc with an angle θ, the cord of this arc is:

C = (θ/2*pi)*2*pi*R

Where you can see that if θ = 2*pi (this is the full circle) we have the perimeter of the circle.

In this case, we can see that the cord for an angle θ is 4cm, then:

C = 4cm = (θ/2*pi)*2*pi*r = θ*r

Now we can solve this for r:

 r = 4cm/θ

Gennadij [26K]3 years ago
3 0

Answer:

4/Ф

Step-by-step explanation:

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4 0
2 years ago
At a certain time of day, the angle of elevation is 40°. To the nearest foot, find the height of a tree whose shadow is 31 feet
elena-s [515]

Answer: Height of tree = 26 ft

Make a triangle ABC with 40 degrees angle. The shadow is the base of the triangle equals 31 feet.

Base = AC = 31

Perpendicular = CB = ?

Hypotenuse = AB

Using trigonometric equation

tan 40 (deg) = CB / AC

CB = Tan 40 x AC

CB = 0.83909 x 31

CB = 26.011

Thus the height of the tree = 26 ft

7 0
2 years ago
The venticles of a right angle are a[0,4], b[3,-2] c[-3, -4] Find It's area.​
givi [52]

Answer:

The area of this triangle is about 21.2132 square units.

Step-by-step explanation:

First, find the lengths of the legs AB and BC.

Length of AB ===

Find the difference in position vertically:

-2-4=-6

The points are 6 units apart vertically.

Find the difference in position horizontally:

3-0=3

The points are 3 units apart horizontally.

These lengths form a right triangle with the distance between the points as the hypotenuse, so you can use the pythagorean theorem to solve:

a^2+b^2=c^2\\3^2+6^2=c^2\\9+36=c^2\\45=c^2\\c\approx6.7082

AB is about 6.7082 units long.

Length of BC ===

Same process as above.

Find the vertical distance:

-4--2=-2

2 units apart vertically.

Find the horizontal distance:

-3-3=-6

6 units apart horizontally.

Use the pythagorean theorem:

2^2+6^2=c^2\\4+36=c^2\\40=c^2\\c=6.3246

BC is about 6.3246 units long.

Area ===

Finally, you can use these to find the area of the triangle. The area of a right triangle is just half the area of a rectangle with the same base and height:

A=\frac{b\times h}{2}\\\\A=\frac{6.7082\times6.3246}{2}\\\\A=\frac{42.4264}{2}\\\\A=21.2132

The area of this triangle is about 21.2132 square units.

4 0
3 years ago
The exterior angles of a hexagon are 56º, 730, 2xº, 3x°, 4x° and 5xº.<br> Find the value of x.
Nookie1986 [14]

Answer:

x = 16.5

Step-by-step explanation:

im assuming you meant 73 degrees instead of 730.

56+73 = 129

2x+3x+4x+5x = 14x

360-129 = 231

231 = 14x

231/14 = 16.5

x = 16.5

7 0
3 years ago
A bat and a ball together cost $1.10. The bat cost $1 more than the ball. How much does the ball cost? (This seems simple, but i
Andrei [34K]

Answer:

2.10?????????????

8 0
3 years ago
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