A central angle has a measure of 2. 3 radians and the subtended arc length is 12 cm. What is the radius of the circle to the nearest 10th
Answers
If A central angle has a measure of 2. 3 radians and the subtended arc length is 12 cm, then the radius of the circle is approximately 5.2 cm.
The formula relating the central angle, radius, and arc length of a circle is:
arc length = radius × central angle
We can use this formula to find the radius of the circle, given the central angle and arc length.
Substituting the given values, we get:
12 cm = r × 2.3 rad
Solving for r, we divide both sides by 2.3 rad:
r = 12 cm / 2.3 rad
Using a calculator, we get:
r ≈ 5.2174 cm
Rounding to the nearest tenth, we get:
r ≈ 5.2 cm
Learn more about radius here
#SPJ4
Related Questions
Imagine you are an engineer for a soda company, and you must find the most economical shape for its aluminum cans. You are given this set of constraints. The can must hold a volume, V, of liquid and be a cylindrical shape of height h and radius r, and you need to minimize the cost of the metal required to make the can. a) First, ignore any waste material discarded during the manufacturing process and just minimize the total surface area for a given volume, V. Using this constraint, show that the optimal dimensions are achieved when h = 2r. The formula for the volume of a cylinder is V = πr 2h. The formula for the lateral area of a cylinder is L = 2πrh. b) Next, consider the manufacturing process. Materials for the cans are cut from flat sheets of metal. The cylindrical sides are made from curved rectangles, and rectangles can be cut from sheets of metal leaving virtually no waste material. However, the process of cutting disks for the tops and bottoms of the cans from flat sheets of metal leaves significant waste material. Assume that the disks are cut from squares with side lengths of 2r, so that one disk is cut out of each square in a grid. Show that, in this case, the amount of material needed is minimized when: h/r = 8/π ≈ 2.55 c) It is far more efficient to cut the disks from a tiling of hexagons than from a tiling of squares, as the former leaves far less waste material. Show that if the disks for the lids and bases of the cans are cut from a tiling of hexagons, the optimal ratio is h/r = 4√3/π ≈ 2.21. Hint: The formula for the area of a hexagon circumscribing a circle of radius r is A = 6r/2 √3 . d) Look for different-sized aluminum cans from the supermarket. Which models from problems a–c best approximate the shapes of the cans? Are the cans actually perfect cylinders? Are there other assumptions about the manufacture of the cans that we should consider? Do a little bit of research, and write a one-page response to answer some of these questions by comparing our models to the actual dimensions used.
A local clothing shop is marking down all of its summer clothes by 75%. sarah would like to purchase a swimsuit that is originally priced at $80. when she gets to the register, she signs up for a loyalty cars that saves her an additional 10%. how much did she spend on the swimsuit and what total percent did she receive off?a. Find the markdown price of the swimsuit.b. Then, find the markdown of the loyalty card.c. Subtract to find the final price.
The numbers on a certain combination lock start with 0 and go through 10. If a combination consists of 3 numbers, how many different lock combinations are possible?
Divide 10 by 4and then subtract 6.2
Answers
Final answer:
In the scenario, a right triangle is formed with the board, the ground, and the wall. We use the Pythagorean theorem to find the height the board will reach up the wall and get the result as 8 feet.
Explanation:
This is a geometry problem where we need to determine the height the board will reach up the wall. This appears to be a right triangle since the board is leaning against the wall. The length of the board is the hypotenuse (10 feet), and the distance from the wall is one of the legs of the triangle (6 feet).
To find the height the board will reach up the wall, which is the other leg of the triangle, we can use the Pythagorean theorem: a² + b² = c² where a and b are the legs and c is the hypotenuse.
Substitute the given values to the formula: a² + 6² = 10²
Solving this equation gives: a² = 10² - 6²
Then, a² = 64
So, a = √64 = 8
Thus, the height the board will reach up the wall is 8 feet.
Learn more about the Pythagorean theorem here:
#SPJ3
a.5/2
b.2
c.1/2
Answers
0.5x² - 1.25x - 3 = 0
Comparing to the quadratic function, ax² + bx + c = 0,
a = 0.5, b = -1.2, c = -3.
Sum of roots = -b/a = -(-1.25)/0.5 = 1.25/0.5 = 2.5
2.5 = 5/2 Option (a)
Answers
Answer: $52.5
Step-by-step explanation:
Given : Last month you used 125 minutes and your bill was $37.50.
i.e. Charges for each minute used =
i.e. it charges $0.3 for each minute home phone used.
If this month you used 175 minutes.
Then , your this month's home phone bill will be :-
Hence, you month home phone bill will be $52.5 .
0.3*175=52.5
so his bill is $52.50
7, 28, 56, 112
7, 11, 15, 19
28, 112, 448, 1792
Answers
Therefore, the obvious answer is the first choice!
7, 28, 112, 448
Decimal to fractions
Answers
Answer: 15/2 or 7 1/2
Step-by-step explanation: