Answer:
96
Step-by-step explanation:
IT IS CONVENTIONAL to let the letter s symbolize the length of an arc, which is called arc length. We say in geometry that an arc "subtends" an angle θ; literally, "stretches under."
Now the circumference of a circle is an arc length. And the ratio of the circumference to the diameter is the basis of radian measure. That ratio is the definition of π.
π = C
D .
Since D = 2r, then
π = C
2r
or,
C
r = 2π .
arc lengthThat ratio -- 2π -- of the circumference of a circle to the radius, is called the radian measure of 1 revolution, which are four right angles at the center. The circumference subtends those four right angles.
arc length
Radian measure of θ = s
r
Thus the radian measure is based on ratios -- numbers -- that are actually found in the circle. The radian measure is a real number that indicates the ratio of a curved line to a straight, of an arc to the radius. For, the ratio of s to r does determine a unique central angle θ.
Answer:
30
Step-by-step explanation:
44 - 14 = 30 more
Given:
A grandfather is 9 times older than his granddaughter.
In 8 years the grandfather will be 5 times older than his granddaughter.
To find:
The present age of grandfather and granddaughter.
Solution:
Let x be the present age of granddaughter.
Then, present age of grandfather = 9x
After 8 years,
Age of granddaughter = x+8
Age of grandfather = 9x+8
In 8 years the grandfather will be 5 times older than his granddaughter.
Isolate variable terms.
Divide both sides by 4.
Now,
Present age of granddaughter = 8
Present age of grandfather = 9(8) = 72
Therefore, the present age of granddaughter is 8 years and present age of grandfather is 72 years.
Answer:The dogs eat 3 7/8 pounds of food together each week.
Step-by-step explanation:
First dog eats eats 21/2 pounds of food each week
The second eats eats 1 3/8 pounds of food each week
In total the two dogs eat
2 1/2 + 1 3/8 = 3 (4+3)/8
=3 7/8
The dogs eat 3 7/8 pounds of food together each week.
Answer:
1. AC is perpendicular to BD
1. Given
2. ACB is a right angle
2. Definition of perpendicular lines
3. Triangle ACB is a right triangle
3. Definition of right triangles
4. Angles 1 and 3 are complementary
4. Interior angles of a triangle add up to 180 degrees (Triangle Interior Angle Sum Theorem), and m<ACB = 90 degrees (definition of right angles), so m<1 + m<3 = 90 degrees (subtraction property of equality). By the definition of complementary angles, angles 1 and 3 are complementary.