In a circle an arc length 10 is intercepted by a central angle of 2/3 radius

Answers

Answer 1

Answer:

We have been given that in a circle an arc length 10 is intercepted by a central angle of 2/3. We are supposed to find the radius of the circle.

We will use arc-length formula to solve our given problem.

$l=r\theta$ , where,

$l$ = Arc length,

$r$ = Radius,

$\theta$ = Central angle corresponding to arc length.

Upon substituting our given values in arc-length formula, we will get:

$10=r\cdot (2)/(3)$

$10\cdot (3)/(2)=r\cdot (2)/(3)\cdot (3)/(2)$

$5\cdot (3)/(1)=r$

$15=r$

Therefore, the radius of the given circle would be 15 units.

Could I please have BRAINLIEST?

How many minutes does the hand make 1/6 of half a rotation

Answers

The answer I believe is 5 minutes

Final answer:

The minute hand takes 5 minutes to make 1/6 of half a rotation.

Explanation:

To determine the number of minutes it takes for a hand to make 1/6 of half a rotation, we first need to understand how many degrees are in a complete rotation. A complete rotation is 360 degrees. Half of this is 180 degrees. Therefore, to find 1/6 of half a rotation, we divide 180 by 6, which gives us 30 degrees.

Now we know that the hand moves 30 degrees. In one revolution (or 360 degrees), the minute hand takes 60 minutes. Therefore, to find the number of minutes it takes to move 30 degrees, we set up a proportion:

360 degrees / 60 minutes = 30 degrees / x minutes

Cross-multiplying, we get:

360x = 30 * 60

360x = 1800

x = 1800 / 360

x = 5

So, it takes 5 minutes for the hand to make 1/6 of half a rotation.

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What is the most likely explanation for Sarah maintaining a log of each time she spends or receives money?A. making a note each time she receives money so that she does not forget where it came from
B. making a note of each expense so that she does not repeat purchases
C. preparing a report for her bank on how she spends money
D. preparing a budget to review her expenses

Answers

Answer:

D is the right answer.

Step-by-step explanation:

Given that Sarah used to maintain a log of each time she spends or receives money.

Logs are maintained normally for money receipt and payment for the following reasons.

i) To know accurate the cash balance in hand at any time

ii) To estimate the purchases still due

iii) to plan for utilizing the available money for effective uses,

iv) to prepare a budget to review her expenses

Out of the four options the last option seems to be more appropriate for this.

The answer is D. preparing a budget to review her expenses.

The circular ring of the fountain has a radius of 9 feet. what is the area of the ring?a. 4.5 square feet

b. 28.26 square feet

c. 63.61 square feet

d. 254.34 square feet

Answers

The area of the circular ring of the fountain with a radius of 9 feet is approximately 254.34 square feet.

To find the area of the ring, we need to subtract the area of the smaller circle from the area of the larger circle. The area of a circle is given by the formula A = πr^2, where r is the radius of the circle. Therefore, the area of the larger circle is π(9^2) = 81π square feet, and the area of the smaller circle is π((9/2)^2) = 20.25π square feet.

Subtracting the area of the smaller circle from the area of the larger circle, we get:

81π - 20.25π = 60.75π

Using the approximation π ≈ 3.14, we get:

60.75π ≈ 60.75(3.14) ≈ 190.845

Therefore, the area of the ring is approximately 190.845 square feet, which is closest to option (d) 254.34 square feet.

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Solve for x.

A) 10.5
B) 10
C) 6√3
D) 20

Answers

There are three right triangles in this figure. Set up Pythagorean theorem for each of them.
Let y be the altitude of the largest triangle.
Let z be the left side.
We have for large triangle:
x² + z² = (9+3)²
For left sub-triangle:
y² + 3² = z²
For right sub-triangle:
y² + 81 = x²

So the three equations are
x² + z² = 144
y² + 9 = z²
y² + 81 = x²

Solve last equation for y², plug into second equation, solve that for z² in terms of x², and lastly plug z² into the first equation to find
x² + x² - 72 = 144
2x² = 216
x² = 108
x = √108 = √(36·3) = 6√3

The answer is C) 6√3

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