Fine the missing side lengths. Leave your answers as radicals in the simplest form.

Fine The Missing Side Lengths. Leave Your Answers As Radicals In The Simplest Form.

Answers

Answer 1

Answer:

x = 33;

y = 3

Step-by-step explanation:

Use trigonometry:

[tex] \sin(30°) = \frac{y}{6} [/tex]

Cross-multiply to find y:

[tex]y = 6 \times \sin(30°) = 6 \times 0.5 = 3[/tex]

Use the Pythagorean theorem to find x:

[tex] {x}^{2} = {6}^{2} - {y}^{2} [/tex]

[tex] {x}^{2} = {6}^{2} - {3}^{2} = 36 - 9 = 27[/tex]

[tex]x > 0[/tex]

[tex]x = \sqrt{27} = \sqrt{9 \times 3} = 3 \sqrt{3} [/tex]


Related Questions

a customer opens a checking account and a savings account at a bank. They will deposit a maximum of $600, some in the checking account and some in the savings account (They might not deposit all of it and instead keep some of it as cash.) If the costumer deposits $200 in their checking account what can you say about the amount they deposit in their savings account?

Answers

The customer can deposit up to $400 in their savings account as long as the total amount deposited between the two accounts does not exceed $600, since they deposited $200 in their checking account.

The problem tells us that the customer will deposit a maximum of $600 between their checking and savings accounts. This means that the total amount deposited in both accounts cannot be more than $600.

We also know that the customer deposited $200 in their checking account. Since they can deposit at most $600 in total, this means that they can deposit up to an additional $400 in their savings account. This is because $600 (maximum total deposit) - $200 (amount deposited in checking account) = $400 (maximum amount that can be deposited in savings account).

So, we can say that the amount the customer can deposit in their savings account is less than or equal to $400. In other words, they can deposit any amount from $0 to $400 in their savings account, as long as the total amount deposited between the two accounts does not exceed $600.

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QUESTIONS
WHALE CAN FLY FASTER THAN A
CROW?
TRUE
FALSE

Answers

Answer: False

Step-by-step explanation:  A whale can't fly

Answer:

False

Step-by-step explanation:

Because a whale cannot fly

A boat is heading towards a lighthouse, whose beacon-light is 136 feet above the
water. From point A, the boat's crew measures the angle of elevation to the beacon,
6°, before they draw closer. They measure the angle of elevation a second time from
point B at some later time to be 19°. Find the distance from point A to point B.
Round vour answer to the nearest foot if necessary.

Answers

Answer:

Rounding to the nearest foot, the distance from point A to point B is 719 feet.

find the value of 8w+6 given that -7w+1=8

Answers

Answer: -2

Step-by-step explanation:

-7w + 1 = 8

Subtract 1 from both sides

-7w + = 7

Divide -7 from both sides

w = -1

then

8(-1) = -8

-8 + 6 = -2

Determine any data values that are missing from the table, assuming that the data represent a linear function. x y 1 6 2 10 3 a. 6 c. 16 b. 15 d. 14 Please select the best answer from the choices provided

Answers

The missing data value in the table of values is y = 14

Determining the missing data values

We can use the two given data points (1,6) and (2,10) to find the equation of the linear function that represents the data.

First, we can use the slope formula to find the slope of the line:

slope = (change in y) / (change in x) = (10-6) / (2-1) = 4/1 = 4

Next, we can use the point-slope formula to find the equation of the line using one of the given points. Let's use (1,6):

y - 6 = 4(x - 1)

We can simplify this equation to slope-intercept form (y = mx + b) by solving for y:

y = 4x + 2

Now we can use this equation to find the missing data value when x = 3:

y = 4(3) + 2 = 14

Therefore, the missing data value is y = 14, and the correct answer is (d) 14.

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The length of a radius of a circle, measured in centimeters, is represented by the expression x + 1.5. The diameter of the circle is 9 2/5
cm.
What is the value of x?
Enter your answer as a decimal or mixed number in simplest form in the box.
X =

Answers

Answer:

The value of x of a circle with radius x + 1.5 and diameter of 9 2 / 5 cm is 7.9 cm

Radius of a circle

Radius of a circle is half of the diameter of a circle. The radius extend from the centre of the circle to the circumference.

Mathematically,

radius = 1 / 2 (diameter)

Therefore,

radius = (x + 1.5) cm

diameter = 9 2 / 5 cm = 47 / 5 cm

let's find x with the relationship above.

Therefore,

x + 1.5 = 47 / 5

subtract 1.5 from both sides

x + 1.5 - 1.5 = 9.4 - 1.5

x = 7.9 cm

Step-by-step explanation:

an angle measure 14.6 degrees more than the measure of its supplementary angle. what is the measure of each angle?

Answers

The measure of the angles are 82. 7 degrees and 97. 3 degrees

What are supplementary angles?

Supplementary angles are simply described as those angles whose sum is equal or equivalent to 180 degrees.

Note that pair of angles on a straight line are supplementary to each other.

From the information given, we have that;

Let the angle of one be x

Then,

Angle 1 = x

Angle 2 = 14. 6 + x

Equate the angles

x + 14. 6 + x = 180

collect the like terms, we get;

2x = 180 - 14. 6

subtract the values

2x = 165. 4

x = 82. 7 degrees

Then, the second angle = 82. 7 + 14. 6 = 97. 3 degrees

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Complete this proof using SSS.
Given: ∆ABD and ∆DCB; AB ≅ DC and AD ≅ BC Prove: ∆ABD ≅ ∆DCB

STATEMENTS
1. ∆ABD and ∆DCB; AB ≅ DC; AD ≅ BC
2. BD ≅ BD
3. ___
REASONS
1. ___
2. ___ Prop. of ≅
3. SSS​

Answers

Answer (Please mark as brainliest):

STATEMENTS

∆ABD and ∆DCB; AB ≅ DC; AD ≅ BC

BD ≅ BD

∆ABD ≅ ∆DCB

REASONS

Given

Reflexive Property of Congruence

By SSS, since AB ≅ DC, AD ≅ BC, and BD ≅ BD.

Therefore, ∆ABD ≅ ∆DCB by SSS.

Write the equation of the line in slope-intercept form.

Answers

Answer:

y = (- 3/4)x + 8

---------------------

Slope-intercept form is:

y = mx + b, where, m - is the slope, b - is the y-intercept

Use two points on the line:

(0, 8) and (4, 5)

The first point represents the y-intercept, b = 8.

Find the slope, using the slope equation:

m = (y₂ - y₁)/(x₂ - x₁)m = (5 - 8)/(4 - 0) = -3/4

Substitute the found values to get the equation of the line:

y = (- 3/4)x + 8

To make blackberry jam, you must cook blackberries until they become juice. If 4 cups of blackberries give you 1 1/3 cups of juice, find the constant of proportionality of juice to blackberries.

I don't need sleep, I need answers.

Answers

The constant of proportionality of juice to blackberries is 3. This means that for every cup of blackberries, you will get 1/3 cup of juice.

Describe Constant of proportionality ?

The constant of proportionality is a mathematical term used to describe the relationship between two quantities that are directly proportional to each other. When two quantities are directly proportional, they vary in proportion to each other such that if one quantity doubles, the other also doubles. The constant of proportionality is the number that relates the two quantities together.

To find the constant of proportionality, we need to divide the amount of juice by the amount of blackberries.

Let x be the amount of blackberries required to make 1 cup of juice. Then we have:

4 cups of blackberries = 1 1/3 cups of juice

Divide both sides by 1 1/3 cups of juice:

4 cups of blackberries / (4/3) cups of juice = 3 cups of blackberries / cup of juice

So the constant of proportionality of juice to blackberries is 3. This means that for every cup of blackberries, you will get 1/3 cup of juice.

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In a large population, 91% of the households have cable tv. A simple random sample of 196 households is to be contacted and the sample proportion computed. What is the probability that the sampling distribution of sample porportions is less than 87%?
a) 0.2786
b) 0.7214
c) 0.0126
d) 0.0252
e) 0.9748

Answers

Answer:

Step-by-step explanation:

B. Now, look at the list of verbs in part A. Select the correct subject pronoun for each verb.

11) ___ escribimos

A. ustedes

B. nosotros

(Need help please and thank you!)

Answers

Answer:

Step-by-step explanation:

F

x=weeks

5=inital

y=total money saved

Use the spinner below.
P(>7) =

Answers

The probability of landing on a number greater than 7 is 4÷12 or 1÷3, which is approximately 0.333 or 33.3%.

What is Probability ?

Probability is a branch of mathematics that deals with the study of random events or outcomes. It is a measure of the likelihood or chance of an event occurring, expressed as a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event.

If the spinner has 12 sections labeled with the numbers 1 through 12, then the probability of landing on a number greater than 7 would be:

There are 12 equally likely outcomes when the spinner is spun.

Out of these 12 outcomes, 4 are greater than 7: 8, 9, 10, and 11.

Therefore, the probability of landing on a number greater than 7 is 4÷12 or 1÷3, which is approximately 0.333 or 33.3%.

So P(>7) = 1÷3 or 0.333 or 33.3%.

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15) Find mMP
12x + 3
P
M
45°
S
R
3x + 12

Answers

Answer:

Determine the lengths of sides and measures of angles in a right triangle by ... 9 = 12x. Cross Products Property. 9 = 3x. Subtract 9x from each side. 3 = x.

in triangle ABC AC =10 in. ,BC =2.5 in., and m angle C =63°. what is the area of triangle ABC?​

Answers

The area of triangle ABC is approximately 11.14 square inches.

What is the area of triangle ABC?​

To find the area of triangle ABC, we can use the formula:

Area = 1/2 * AC * BC * sin(C)

where the base is BC and the height is the perpendicular distance from A to BC.

To find the sine 63, we can use the sine of angle C:

sin C = sin(63)

Therefore, the area of triangle ABC is:

Area = 1/2 * 10 * 2.5 * sin(63)

When evaluated, we have

Area ≈ 11.14 square inches

So, the area of triangle ABC is approximately 11.14 square inches.

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Which of the following equations are true for the number 9? Select all that apply. A. 4÷□=94 B. 19=□÷9 C. 7÷□=79 D. □÷19=81

Answers

In summary, equations A, C, and D are true for the number 9, while equation B is not.

How do we determine if a value satisfies an equation?

In order to resolve this issue, we must substitute a number or expression that makes the equation true for the value 9 in the area denoted by the symbol "." Let's look at each equation individually:

A. 4 ÷ □ = 9/4

We can cross-multiply and simplify to find the answer to :

4(9/4) = □\s9 = □

Hence, for = 9, this equation is accurate.

B. 1/9 = □ ÷ 9

We may multiply both sides by 9 to find the answer to:

1 = □

This equation is valid for = 1, thus.

C. 7 ÷ □ = 7/9

We can cross-multiply and simplify to find the answer to :

7(9) = □\s63 = □

Hence, this equation is true for the value of = 63/7, which reduces to 9.

D. □ ÷ 1/9 = 81

We can multiply both sides by 1/9 to find the answer to:

□ = 81(1/9)\s□ = 9

So, this equation is true for □ = 9.

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Accidents can happen to anyone at any
time, and individuals must make
financial choices to help protect then in
case of unforeseen events. What
elements were in the Perez family's
financial plan before the accident that
helped them prepare for their
unexpected event (Camila's accident)?
What could the family have done to
better prepare financially for an
unexpected event?

Answers

Answer:

Step-by-step explanation:

there is no passage

The perimeter of a rectangular garden is 372 m
If the width of the garden is 88 m, what is its length?

Answers

Answer:

Let L be the length of the rectangular garden. We know that the perimeter of a rectangle is given by: P = 2L + 2W where P is the perimeter, L is the length, and W is the width. In this case, we are given that the perimeter is 372 m and the width is 88 m. Substituting these values into the equation, we get: 372 = 2L + 2(88) Simplifying and solving for L, we get: 372 = 2L + 176 2L = 196 L = 98 Therefore, the length of the rectangular garden is 98 m.

Answer: L = 98 m

Step-by-step explanation:

The perimeter of a rectangle can be found with this formula:

      P = 2W + 2L

➜ P is Perimeter

➜ W is Width

➜ L is Length

We will input known values and solve for the length. To solve, we will use multiplication and inverse operations.

      372 m = 2(88 m) + 2L

      372 m = 176 m + 2L

      196 m = 2L

      L = 98 m

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Set up a proportion and solve for x

Answers

Thus value of x in the given the proportion is 7.

How to find the value of x?

Here, both triangles are congruent due to sss congruency,

Thus,

6 : 12

6k = 12

k = 12/6

k = 2

Also, The expressions are

(x+2) : 3x - 3

(x+2)k = 3x - 3

(x+2)2 = 3x - 3

2x + 4 = 3x - 3

3x - 2x = 4 + 3

x = 7

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I really need help please help

Answers

Answer:

Question 7 is correct.

205,000 (For Question 8)

Step-by-step explanation:

First, we need to find the value of x.

We need to subtract 1995 from 2010 to find out how many years would have passed.

This gives us 15, which is our x value.

Next, we need to solve for y.

We multiply 2000 by 15 to get 30,000.

Then, add 175,000 to 30,000 to get 205,000. That leaves us with the equation y = 205,000.

The Y value is equivalent to the population in 2010.

One child can complete her homework twice as fast as her partner. When working together, both children can complete the homework in 45 minutes. If they work by themselves, how long will it take each child to complete the homework?

HINTS: 1) Let t = the time needed for the faster child to complete the homework.
2) Portion of the homework completed=rate ×time (P=rt)
3) When a child works alone the portion of the work completed is all the homework. That is (P=1)


1) The rate at which the faster child is working is ___________ Write an algebraic expression.

2) The rate at which the slower child is working is ___________Write an algebraic expression.

3) The part of the homework was done by the faster child in 45 minutes is ___________Write an algebraic expression.

4) The part of the homework was done by the slower child in 45 minutes is ___________ Write an algebraic expression.


5) The time taken by the faster child to do the homework by herself is _______________Give your answer in minutes.


6) The time taken by the slower child to do the homework by their self is _______________Give your answer in minutes.


Answers

1. The rate at which the faster child is working is 1/t.

2.The rate at which the slower child is working is 1/(2t)

3.The homework done by the faster child in 45 minutes is (1/t) * (3/4), since both children can complete the homework in 45 minutes.

4.The part of the homework done by the slower child in 45 minutes is (1/(2t)) * (3/4),

5.Thus, t=30 minutes, which is the time taken by the faster child to do the homework by herself.

6. Thus, 2t=90 minutes and t=45 minutes, which is the time taken by the slower child to do the homework by herself.

What is time?

Time is a concept used to describe the progression of events from the past, through the present, and into the future. It is a measure of duration or an interval between two events, and it is often represented in units such as seconds, minutes, hours, days, weeks, months, and years.

1. Let t = the time needed for the faster child to complete the homework.

The faster child completes the homework twice as fast as the partner. Therefore, the rate at which the faster child is working is 1/t.

2.The rate at which the slower child is working is 1/(2t) since the slower child takes twice as long as the faster child to complete the homework.

3.The part of the homework done by the faster child in 45 minutes is (1/t) * (3/4), since both children can complete the homework in 45 minutes. In 45 minutes, the faster child completes 3/4 of the homework because she is working at a rate of 1/t, while the slower child is working at a rate of 1/(2t).

4.The part of the homework done by the slower child in 45 minutes is (1/(2t)) * (3/4), since both children can complete the homework in 45 minutes. In 45 minutes, the slower child completes 3/4 of the homework because she is working at a rate of 1/(2t), while the faster child is working at a rate of 1/t.

5.Let's use the equation P=rt, where P=1 (since the entire homework is done by one child alone) and r=1/t (since the faster child completes the homework in t time). Thus, t=30 minutes, which is the time taken by the faster child to do the homework by herself.

6.Similarly, we can use the equation P=rt, where P=1 (since the entire homework is done by one child alone) and r=1/(2t) (since the slower child takes twice as long as the faster child to complete the homework). Thus, 2t=90 minutes and t=45 minutes, which is the time taken by the slower child to do the homework by herself.

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Find the area of this shape pls help

Answers

Answer:

Area = 63.2 cm²

Step-by-step explanation:

To find the area of the given shape, we can split it into two shapes: a trapezium and a rectangle (as shown in the attached diagram).

Doing so gives us a rectangle with a length of 10 cm and a breadth of 2.8 cm at the bottom of the shape. Therefore its area:

Area = length × breadth

        = 10 cm × 2.8 cm

        = 28 cm²

We also get a trapezium, whose area can be found using the following formula:

[tex]\boxed{\mathrm{Area = \frac{1}{2} \times (a + b) \times h}}[/tex]

where:

• a, b ⇒ length of the parallel sides of trapezium

• h ⇒ distance between the parallel sides a and b

From the diagram attached below, we can see that the two parallel sides have lengths of 10 cm and 6 cm. Moreover, the distance between the parallel sides is 7.2 - 2.8 = 4.4 cm.

Therefore, using the above formula and information, we can calculate the area of the trapezium:

Area = [tex]\frac{1}{2}[/tex] × (6 + 10) cm × 4.4 cm

        = [tex]\frac{1}{2}[/tex] × 16 cm × 4.4 cm

        = 35.2 cm²

Now that we have the areas of the rectangle and trapezium, we can find the area of the whole shape simply by adding those two areas:

Area of shape = 28 cm² + 35.2 cm²

                        = 63.2 cm²

Therefore, the area of the given shape is 63.2 cm².

Airplanes are sometimes used to fight fires. A certain airplane can deliver 4x10^4 liters of water in one trip. How much water can this airplane deliver in 38 trips?

Write your answer in scientific notation.

Answers

Answer:

1.52×10⁶ liters of water

Step-by-step explanation:

38(4×10⁴)

If you bet $5 in a Pick 4 lottery game, you either lose $5 or gain $9,995. (The winning prize is $10,000, but your $5 bet is not returned, so the net gain is $9,995.) The game is played by selecting
a four-digit number between 0000 and 9999. What is the probability of winning? If you bet $5 on 1234, what is the expected value of your gain or loss? What is the probability of winning?

Answers

Answer:

the expected value of your gain or loss is a net loss of $0.5006.

The probability of winning is 1/10,000 = 0.0001.

Step-by-step explanation:

There are 10,000 possible four-digit numbers between 0000 and 9999. Only one of those numbers is the winning number. Therefore, the probability of winning the Pick 4 game is:

Probability of winning = 1/10,000 = 0.0001

If you bet $5 on 1234, there are two possible outcomes:

-You lose $5 with probability 0.9999

-You gain $9,995 with probability 0.0001

The expected value of your gain or loss is the sum of the products of each outcome and its probability:

Expected value = (-$5 x 0.9999) + ($9,995 x 0.0001)

Expected value = -$0.5006

Answer:

Step-by-step explanation:

Given that sin(x)
A. 4
B.
11
NEF=
7
11
C. 11
7
D. 11
4
=
7
11'
find cos (90-x).

Answers

The value of cos (90 - x ) = sin (x) = 7/11.

option B.

What is the value of cos (90 - x)?

In trigonometry identity, we know that sin(x) = opposite / hypotenuse. Therefore, we can draw a right triangle with an angle x and opposite side 7 and hypotenuse 11.

Using the Pythagorean theorem, we can find the adjacent side of the triangle:

adjacent² = hypotenuse² - opposite²

adjacent² = 11² - 7²

adjacent² = 120

adjacent = √(120)

adjacent = 2 √(30)

Now, we can use the definition of cosine to find cos(90 - x):

cos(90 - x) = sin(x)

Therefore, cos(90 - x) = 7/11.

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$1000 is deposited in an account with a 8.5% interest rate, compounded continuously. What is the balance after 5 years?​

Answers

By answering the presented question, we may conclude that the balance  interest after 5 years is approximately $1,484.71.

what is interest ?

In mathematics, interest is the amount of money gained or payable on an original investment or loan. You can use either simple or compound interest. Simple interest is calculated as a percentage of the initial amount, whereas compound interest is calculated on the principal amount plus any previously earned interest. If you invest $100 at a 5% annual simple interest rate, you will get $5 in interest per year for three years, for a total of $15.

for calculating the balance

[tex]A = Pe^(rt)\\[/tex]

this formula,

[tex]A = 1000e^(0.085*5)\\A = 1000e^(0.425)\\[/tex]

A ≈ $1,484.71

the balance after 5 years is approximately $1,484.71.

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Answer:1529.59

Step-by-step explanation:

1000e^(.085)5

A student is solving the equation 3(x−12)=9x . Which describes a first step the student could use to solve the equation correctly? Responses The student can distribute 3 on the left side of the equation, resulting in 3x−36=9x . The student can distribute 3 on the left side of the equation, resulting in 3 x − − 36 = 9 x . The student can distribute 3 on the left side of the equation, resulting in 3x−12=9x . The student can distribute 3 on the left side of the equation, resulting in 3 x − − 12 = 9 x . The student can divide both sides of the equation by 3 , resulting in x−12=6x . The student can divide both sides of the equation by 3 , resulting in x − − 12 = 6 x . The student can divide both sides of the equation by 3 , resulting in x−4=3x .

Answers

Step-by-step explanation:

The correct first step the student could use to solve the equation 3(x-12)=9x is to distribute 3 on the left side of the equation, resulting in 3x - 36 = 9x.

This is because the distributive property states that a(b + c) = ab + ac. In this case, we have 3(x - 12), so we can distribute the 3 by multiplying it by both terms inside the parentheses: 3(x - 12) = 3x - 36.

Then, we can simplify the equation by subtracting 3x from both sides: -36 = 6x. Finally, we can solve for x by dividing both sides by 6: x = -6.

Therefore, the correct option is: "The student can distribute 3 on the left side of the equation, resulting in 3x−36=9x."

Final answer:

The first step in solving the equation 3(x−12)=9x is to distribute the 3 on the left-hand side of the equation. You multiply each term inside the parentheses by 3, resulting in a simplified equation: 3x - 36 = 9x.

Explanation:

If you're aiming to solve the equation 3(x−12)=9x, the initial step would be to distribute the 3 into the parentheses on the left side of the equation. This is achieved by multiplying each term inside the parenthesis by 3. Here's the process in detail:

Step 1: Start with the initial equation, which is 3(x−12)=9x.

Step 2: Remove the parentheses by distributing 3, resulting in 3x - 36 = 9x.

This is a viable initial step because now you have simplified equations on both sides, which helps you to get closer towards isolating the variable x.

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What are the ordered pair solutions
for this system of equations?
y = -x² + 2
y = x
First, set the equations equal to each other and
move everything to one side.
A:-x²+x+2=0
C:-x² + 2 = x
B:x²+x-2 = 0
D:x²+x+2=0

Answers

To find the ordered pair solutions, we need to solve the system of equations by setting them equal to each other:

-x² + x + 2 = x

Simplifying:

-x² + 2x + 2 = 0

We can solve for x using the quadratic formula:

x = (-2 ± sqrt(2^2 - 4(-1)(2))) / (2(-1))

x = (-2 ± sqrt(12)) / (-2)

x = 1 ± sqrt(3)

So the x-values of the ordered pair solutions are:

x = 1 + sqrt(3)

x = 1 - sqrt(3)

To find the corresponding y-values, we can substitute these x-values into either equation. Let's use y = x:

When x = 1 + sqrt(3):

y = 1 + sqrt(3)

When x = 1 - sqrt(3):

y = 1 - sqrt(3)

5. A map is drawn to a scale of 1: 20 000. (a) The perimeter of a lake is 2.5 km. Find, in cm, the perimeter of the lake on the map. (b) The area of the lake on the map is 12.5 cm². Find, in km², the actual area of the lake.​

Answers

Step-by-step explanation:

2.5 km = 250000 cm

250000 cm /20000 = 12.5 cm on the map

12.5 cm ^2  x 20 0000 x 20 000   = 5 000 000 000 cm^2 = 500 000 m^2  

In a circle, an angle measuring
radians intercepts an arc of length
. Find the radius of the circle in simplest form.

Answers

The formula to find the length of an arc of a circle is given by L = rθ, where L is the length of the arc, r is the radius of the circle, and θ is the angle measured in radians and the radius of the circle is 2.

To find the length of the arc, we use the formula L = rθ. Substituting the given values, we get:

L = rθ

L = r( [tex]\frac{\pi}{2}[/tex]) or ( [tex]\frac{\pi}{2}[/tex])r

We are also given that the length of the arc is 1π, so we can write:

( [tex]\frac{\pi}{2}[/tex])r = 1π

Simplifying this equation, we get:

r = (1π) ÷ ( [tex]\frac{\pi}{2}[/tex])

r = 2

We can say that the length of an arc that is intercepted by an angle of  [tex]\frac{\pi}{2}[/tex] radians is equal to half the circumference of the circle. Since the length of the arc is given as 1π, we can find the radius of the circle by dividing 1π by [tex]\frac{\pi}{2}[/tex], which gives us 2.

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The complete question is:

In a circle, an angle measuring  [tex]\frac{\pi}{2}[/tex] radians intercepts an arc of length 1π. Find the radius of the circle in simplest form.

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