1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
poizon [28]
3 years ago
15

How do I solve this??? It’s the radicals that confuses me.

Mathematics
1 answer:
son4ous [18]3 years ago
4 0
This problem cannot be solved but I solved the radical for you

You might be interested in
Calculate area and perimeter​
mina [271]

Answer:

area ≈ 12.505

perimeter ≈  16.1684

Step-by-step explanation:

We are given

- the radius of the circle (and therefore area of the circle)

- the area of the triangle

We want to find

- angle AOB/AOT. We want to find this because 360/the angle gives us how many OABs fit into the circle. For example, if AOT was 30 degrees, 360/30 = 12 (there are 360 degrees in a circle, so that's where 360 comes from). The area of the circle is equal to πr² = π6² = 36π, and because AOT is 30 degrees, there are 12 equal parts of sector OAB in the circle, so 36π/12=3π would be the area of the sector. A similar conclusion can be reached from the circumference instead of the area to find the distance between A and B along the circle, and OA + AB + BO = the perimeter of the minor sector.

First, we can say that OAT is a right triangle because a tangent line is perpendicular to the line from the center to the point on the circle, so AT is perpendicular to OA. This forms two right angles, one of which is OAT

One thing that we can start to solve is AT. We know that the area of a triangle is equal to base * height /2, and the height of this triangle is AO, with the base being AT. Therefore, we can say

15 = AO * AT / 2

15 = 6 * AT / 2

15 = 3 * AT

divide both sides by 3 to isolate AT

AT = 5

Because OAT is a right triangle, we can say that the hypotenuse ² =  the sum of the squares of the two other lengths. The hypotenuse is opposite of the largest angle (in this case, the right angle, as in a right triangle, the right angle is always the largest), so it is OT in this case. The other two sides are OA and AT, so we can say that

OA² + AT² = OT²

5²+6² = OT²

25+36=61=OT²

square root both sides

OT = √61

Next, the Law of Sines states that

sinA/a = sinB/b = sinC/c with angles A, B, and C with sides a, b, and c. Corresponding sides are opposite their corresponding angles, so in this case, AT corresponds to angle AOT, OT corresponds to angle OAT, and AO corresponds to angle ATO.

We want to find angle AOT, as stated earlier, so we have

sin(OAT)/OT = sin(ATO)/OA = sin(AOT)/AT

We know the side lengths as well as OAT/sin(OAT) and want to figure out AOT/sin(AOT), so one equation that helps us get there is

sin(OAT)/OT = sin(AOT)/AT, encompassing our 3 known values and isolating the one unknown. We thus have

sin(90)/√61 = sin(AOT) /5

plug in sin(90) = 1

1/√61 = sin(AOT)/5

multiply both sides by 5 to isolate sin(AOT)

5/√61 = sin(AOT)

we can thus say that

arcsin(5/√61) = AOT ≈39.80557

As stated previously, given ∠AOT, we can find the area and perimeter of the sector. There are 360/39.80557 ≈ 9.04396 equal parts of sector OAB in the circle. The area of the circle is πr² = 36π, so 36π / 9.04396 ≈ 12.505 as the area. The circumference is equal to π * diameter = π * 2 * radius = 12 * π, and there are 9.04396 equal parts of arc AB in the circumference, so the length of arc is 12π / 9.04396 ≈ 4.1684. Add that to OA and OB (both are equal to the radius of 6, as any point from the center to a point on the circle is equal to the radius) to get 6+6 + 4.1684 = 16.1684 as the perimeter of the sector

5 0
3 years ago
Well has -55.00 in his account if he saves $2.50 his mom gives him lunch every day, how many days will it be until he has a bala
gayaneshka [121]

Answer:

22 days

Step-by-step explanation:

55 divided by 2.5=22 days

7 0
2 years ago
Read 2 more answers
Adrian works in New York City and makes $40 per hour. She works in an office and must pay $20 a day for lunch. If she wants to m
andrew-mc [135]

Answer: She would have to work 7 hours to earn $260.

Step-by-step explanation: 40×7=280 280-20=260 Hope this helps.

6 0
2 years ago
(b) Amrita is 8 years
egoroff_w [7]

Answer:

cheap.....

7/10 + 3/10

solve d rest

5 0
2 years ago
Isolate the variable 4m=92
const2013 [10]
<span>Simplifying 4x = 92 Solving 4x = 92 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Divide each side by '4'. x = 23 Simplifying x = 23</span>
5 0
3 years ago
Other questions:
  • Your brother is 1/2 your age. Your sister is 5 years older than your brother. Your sister is 15 years old. Write and solve an eq
    6·1 answer
  • Write an equation that represents each mixed number as a sums of a whole number and unit fractions 4 1/4 and 1 5/6
    13·1 answer
  • Select the inequality below that is one of the two inequalities used to solve: |3+2x|&lt;11
    10·1 answer
  • 30g of sugar is needed to make 4 cakes. How much sugar is needed for 7 cakes?
    7·2 answers
  • Line m has no y-intercept, and its x-intercept is (3,0). line n has no x-intercept, and its y-intercept is (0-,4).
    11·1 answer
  • What is the slope of the line parallel to the line in part a above how do you know what is the relationship between lines that a
    15·1 answer
  • Marissa is tying bows to use as decorations for the holidays. She has 72 ribbon, and each bow requires 2.4 inches of ribbon. How
    8·2 answers
  • The vertex of this parabola is at (3,-2). When the x-value is 4, the y value is 3. What is the coefficient of the squared term i
    11·1 answer
  • I will mark u as the brainiest if u get this correct<br> thx<br> x
    10·2 answers
  • (4/9) ÷ (7/12) = ???
    10·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!