Cylinder M and cylinder N are similar. The radius of cylinder N is equal to its height, and the ratio of the height of cylinder N to the height of cylinder M is 5: 3. The surface area of cylinder N is 256 square feet greater than the surface area of cylinder M. Find the surface area of each cylinder.

Using the total area of the rectangular pool we know that the required width of the pathway is 3.6 ft respectively.

In the Euclidean plane, a rectangle is a quadrilateral with four right angles.

A parallelogram with a right angle or an equiangular quadrilateral, where equiangular means that all of its angles are equal, are other ways to define it.

A rectangle with four equal-length sides is a square.

Squares are not always rectangles, but rectangles are always squares.

So, the pool and walkway together have a 360 square foot total space.

Assume that the walkway is w feet in width.

Since the pool has an additional w feet of width on both sides, the total area's measurements can be expressed as (8 + 2w) by (10 + 2w).

Thus, we can construct the following equation:

(8 + 2w) x (10 + 2w) = 360

By enlarging and condensing the left side, we obtain:

4w² + 36w - 80 = 0

Using the quadratic formula, we can find w:

w = (-b ± √(b² - 4ac)) / 2a

Here, an equals 4, b equals 36, and c equals -80. When these values are added to the formula, we obtain:

w = (-36 ± √(36² - 4(4)(-80))) / 8

w = (-36 ± √(1872)) / 8

w ≈ -5.6 or w ≈ 3.6

We can ignore the first option because the width cannot be negative. Consequently, the pathway should be around 3.6 feet wide.

Therefore, using the total area of the rectangular pool we know that the required width of the pathway is 3.6 ft respectively.

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The circumference and approximate area of the given​ circle is 69.08 inches & 380.14 square inches.

What is circumference?

Circumference is the distance around the edge of a circular object or a round shape. It is the length of the boundary or perimeter of the circle. The formula is given by C = 2πr, where C is the circumference, r is the radius of the circle, and π is a mathematical constant approximately equal to 3.14.

The circumference of a circle is given by the formula:

C = 2πr

where r is the radius of the circle and π (pi) is a mathematical constant approximately equal to 3.14.

Using this formula and plugging in the given value of radius:

C = 2 x 3.14 x 11

C = 69.08 inches (rounded to two decimal places)

So the circumference of the circle with 11 inches radius is approximately 69.08 inches.

The area of a circle is given by the formula:

A = πr²

Again, using the given value of radius and approximating π to 3.14:

A = 3.14 x 11²

A = 3.14 x 121

A = 380.14 square inches (rounded to two decimal places)

So the approximate area of the circle with 11 inches radius is approximately 380.14 square inches.

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The absolute value equation that has -8 and -2 as the solution set is |x + 5| = 3

What is an absolute value equation?

An absolute value equation can be written as |expression| = value

To have -8 and -2 as the solution set, we need an absolute value equation that produces these two values when the expression inside the absolute value is either positive or negative.

We can write,

|x + 5| = 3

To solve for x, we have two cases,

Case 1: x + 5 is positive

If x + 5 is positive, then the equation becomes x + 5 = 3

Solving for x,

x = -2

This matches one of the solutions we want.

Case 2: x + 5 is negative

If x + 5 is negative, then the equation becomes -(x + 5) = 3

Solving for x,

x = -8

This also matches the other solution we want.

Therefore, the absolute value equation that has -8 and -2 as the solution set is |x + 5| = 3.

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The composite functions (f/g)(x) and (f-g)(x) are (2x-1)/√(3x-5) and (2x-1) -√(3x-5)

To calculate (f/g)(x), we need to divide f(x) by g(x):

(f/g)(x) = f(x)/g(x) = (2x-1)/√(3x-5)

The domain of (f/g)(x) is the set of all x-values for which the denominator √(3x-5) is not equal to zero and non-negative

3x-5 ≥ 0, or x ≥ 5/3

Therefore, the domain of (f/g)(x) is x ≥ 5/3.

To calculate (f-g)(x), we need to subtract g(x) from f(x):

(f-g)(x) = f(x) - g(x) = (2x-1) - √(3x-5)

The domain of (f-g)(x) is the set of all x-values for which the expression inside the square root is non-negative:

3x-5 ≥ 0, or x ≥ 5/3

Therefore, the domain of (f-g)(x) is x ≥ 5/3.

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Answer:

Axis of symmetry =1

vertex =(1,2)

y intercept =0

min/max= -6,2

domain= 0,1,2

range =y≥1,2

The value of GH in the right angle triangle, given FH and Angle FHG is 22.46 inches.

Since we have the adjacent side (FH) and want to find the hypotenuse (GH), we can use the cosine function.

cos(35°) = adjacent side (FH) / hypotenuse (GH)

We know that FH = 18.4 in. So, we can write the equation as:

cos(35°) = 18.4 / GH

GH = 18.4 / cos(35°)

GH = 18.4 / 0.81915

=  22.46 inches

So, the length of GH, the hypotenuse, is approximately 22.46 inches.

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Answer:

1/8

Step-by-step explanation:

If "over" refers to (4 * 6) as a whole,

[tex]\frac{3}{4*6}\\\\=\frac{3}{24}\\\\=\frac{1}{8}[/tex]

If "over" refers to division,

[tex]3 \div 4 \times 6\\= 0.75 \times 6\\= 4.5[/tex]

I would suppose it's the first one, so, ignore the second one if you haven't learnt BODMAS yet.

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One per 2,500 can be used to represent the rate of 80cm to 2km.

To write 80cm to 2km as a rate, we need to convert the units to the same system. We can convert 80cm to kilometers by dividing by 100,000 (since there are 100,000 centimeters in a kilometer):

80 cm/100,000 = 0.0008 km

Now we can express the rate as:

0.0008 km per 2 km

Or we can simplify it by dividing both the numerator and denominator by 0.0008:

1 per 2,500

Therefore, 80cm to 2km can be expressed as a rate of 1 per 2,500.

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In triangle ABC

a) The value of x = 29⁰

b) The angle c equal to 93⁰

A triangle is a closed plane figure that is formed by connecting three line segments, also known as sides, at their endpoints. The three endpoints, or vertices, where the sides of the triangle meet are not collinear. Triangles are important in mathematics and geometry because they are the simplest polygon that can exist in two-dimensional space.

In a triangle, the sum of all interior angles is always 180 degrees. Therefore, we can use this fact to find the value of x and angle c.

We know that:

angle a = 35⁰

angle b = 52⁰

angle c = 3(x+2)⁰

Using the fact that the sum of all interior angles in a triangle is 180 degrees, we can write:

angle a + angle b + angle c = 180

Substituting the values we know, we get:

35 + 52 + 3(x+2) = 180

Simplifying the equation, we get:

87 + 3x + 6 = 180

3x + 93 = 180

3x = 87

x = 29

Therefore, x = 29⁰

To find angle c, we can substitute the value of x into the equation we were given for angle c:

angle c = 3(x+2)

angle c = 3(29+2)

angle c = 3(31)

angle c = 93

Therefore, angle c is equal to 93⁰.

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The negation is the fourth option.

6 + 3 ≠ 9 or 6 - 3 ≠ 9

The negation of an equation is an inequality such that we just change the equal sign, by the "≠" sign.

Here we start with the two equations.

6 + 3 = 9 or 6 - 3 = 9

Just change the equal signs for different signs:

6 + 3 ≠ 9 or 6 - 3 ≠ 9

That is the negation, fourth option.

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Answer:

  (d)  25 feet and 20 feet​

Step-by-step explanation:

You want the possible dimensions of a pool with an area of 500 square feet and a perimeter of 90 feet.

The area is the product of the length and width. The area of the pools offered in the answer choices are ...

  (a)  15·30 = 450 . . . square feet

  (b)  10·35 = 350 . . . square feet

  (c)  50·10 = 500 . . . square feet

  (d)  25·20 = 500 . . . square feet

The area requirement eliminates answer choices A and B.

The perimeter is twice the sum of length and width. The perimeters of the possible pools are ...

  (c) 2(50 +10) = 120 . . . feet

  (d) 2(25 +20) = 90 . . . feet

The perimeter requirement eliminates answer choice C.

The pool's possible length and width are 25 feet and 20 feet, choice D.

__

Additional comment

You could write a quadratic equation for the pool dimensions, but doing that will generally involve more work than checking the given answer choices.

If x is the width, then 45-x is the length, and the area is ...

  x(45 -x) = 500

  x² -45x +506.25 = -500 +506.25 . . . multiply by -1, complete the square

  x = 22.5 -√6.25 = 20 . . . . take the square root; width is the smaller dimension

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The statements that provide support for Chloe's claim are A<0 because A is to the left of zero, B>0 because B is to the right of zero. So correct option is A and F.

Comparison algebra is a branch of algebra that deals with inequalities and comparisons between different quantities or expressions. In comparison algebra, the goal is to determine the relationships between different expressions or quantities, such as whether one expression is greater than, less than, or equal to another expression.

Comparison algebra involves the use of comparison symbols, such as "<" (less than), ">" (greater than), and "=" (equal to), to express these relationships. For example, if we have two expressions, A and B, we can use the "<" symbol to express the relationship that A is less than B, as in A < B.

In comparison algebra, we can also manipulate inequalities and equations in similar ways as we do with regular algebraic expressions. For instance, we can add, subtract, multiply, or divide both sides of an inequality or equation by the same number or expression, while maintaining the inequality's direction.

The statements that provide support for Chloe's claim are:

A. A<0 because A is to the left of zero.

F. B>0 because B is to the right of zero.

Statement A supports Chloe's claim because Point A is to the left of zero on the number line, which means its value is negative. Statement F also supports Chloe's claim because Point B is to the right of zero on the number line, which means its value is positive.

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The total net amount the supermarket owes the wholesaler for the order is $231.31.

A discount is a reduction in the price of a product or service. It is often offered by businesses to encourage customers to buy more or to make a purchase they might not otherwise make. A discount can be expressed as a percentage or a specific dollar amount, and it is usually subtracted from the original price of the item or service.

To find the total net amount the supermarket owes the wholesaler for the order, we need to first calculate the cost of each case of soup and baked beans after the 39% trade discount is applied, and then multiply those costs by the number of cases ordered.

The trade discount rate is 39%, which means the supermarket will receive a discount of 39% off the list price of each case of soup and baked beans. To calculate the cost of each case after the discount is applied, we can use the following formula:

Discounted cost = List price - (Discount rate x List price)

For the soup, the discounted cost per case is:

$18.90 - (0.39 x $18.90) = $11.51

For the baked beans, the discounted cost per case is:

$33.50 - (0.39 x $33.50) = $20.42

Now we can calculate the total net amount owed by the supermarket to the wholesaler:

Total net amount = (Number of cases of soup x Cost per case) + (Number of cases of baked beans x Cost per case)

Total net amount = (13 x $11.51) + (4 x $20.42)

Total net amount = $149.63 + $81.68

Total net amount = $231.31

Therefore, the total net amount the supermarket owes the wholesaler for the order is $231.31.

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Answer:

5.4

Step-by-step explanation:

square of 29 = 5.385164807

5.385164807 estimated is 5.4

The appropriate measurement unit for force is  kg.m/s²

A force is simply referred to as either a push or pull of an object resulting from the object's interaction with another object.

From Newton's Second Law, force is expressed as;

F = m × a

Where is mass of object and a is the acceleration

One Newton is defined as the force required to accelerate a mass of one kilogram at a rate of one meter per second squared.

Since F = m × a

Plug in m = kg and a = m/s²

F = kg × m/s²

F = kg.m/s²

Therefore, the unit of measurement is kg.m/s².

Option B is the correct answer.

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The expression that has the greatest value when n is equal to 4 is option B, n + 30, with a value of 34.

To determine which mathematical expression has the greatest value when n is equal to 4, we can simply substitute 4 for n in each expression and compare the results.

A. 5n = 5(4) = 20

B. n + 30 = 4 + 30 = 34

C. 50 - n = 50 - 4 = 46

D. 80 ÷ n = 80 ÷ 4 = 20

The complete question is: Which expression has the greatest value when n is equal to 4? A. 5n B. n + 30 C. 50 – n D. 80 ÷ n

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The solution of the differential equation y'' + y = t with the initial conditions y(0)=1 and y'(0)=-2 is y(t)= 1-2t+te-t.

Equation is a mathematical statement that expresses the equality of two expressions. It shows the relationship between two or more variables and can be written using symbols, numbers, and operations. Equations are used to describe physical laws, to make calculations, and to solve problems. Examples of equations include the Pythagorean theorem, Newton's laws of motion, and linear equations.

We solve this differential equation using Laplace inverse, with the initial conditions y(0)=1 and y'(0)=-2. First, we take the Laplace transform of the equation:

L[y''+y]=L[t]

Using the properties of Laplace transform, we can write this as:

s2Y(s)-sy(0)-y'(0)+Y(s)= (1/s)

Substituting the initial conditions and rearranging terms, we have:

Y(s)= (1/s) + (2/s2) + (1/s2)

We can then invert the Laplace transform to get the solution of the original equation:

y(t)= 1-2t+te-t

Therefore, the solution of the differential equation y'' + y = t with the initial conditions y(0)=1 and y'(0)=-2 is y(t)= 1-2t+te-t.

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Answer: The area of the door can be calculated as:

Area of door = width x height

= 0.9 m x 2.1 m

= 1.89 square meters

The area of one window can be calculated as:

Area of window = width x height

= 1.5 m x 1.2 m

= 1.8 square meters

Since there are four windows, the total area of the four windows is:

Total area of four windows = 4 x Area of window

= 4 x 1.8 square meters

= 7.2 square meters

Therefore, the total area of the door and the four windows is:

Total area = Area of door + Total area of four windows

= 1.89 square meters + 7.2 square meters

= 9.09 square meters

Hence, the total area of the door and the four windows is 9.09 square meters.

Step-by-step explanation:

Answer:

finding the perimeter, you sumthe distance all round that is 7+7.5+17.8+6=38.3

38.3 is the perimeter

Step-by-step explanation:

to find the interest she needs to pay back every month, we need to use this formula:

I = PRT/12

in this case the principle is $300,000, the rate is 7% p.a. and the amount of time is 1 year, if we substitute in our values we:

I = (300,000)(7)(1)/12 = $17,500 in interest every month

to find her yearly income from rent, we have to multiply the monthly rent by 12

1500 × 12 = $18,000

to calculate her loss percentage in a year, we have to subtract 18,000 from 3000 which is 15,000

she said that she hopes the property's value will increase to cover the loss she made.

to cover the loss of $15000 per year, the property needs to increase in value by at least $15000. the percentage increases value can be written as

Percentage increase = (difference in increase/Original price) × 100

so

percentage increase = (15000/300000) × 100 = 5%

so the property needs to increase in value by at least 5% per year to cover the loss.

The woman needs to pay $1750 monthly as interest. Her yearly income from the rent is $18,000. After considering all other costs, she is at a loss of $6000 per year, so the property needs to increase in value by 2% per year to cover this loss.

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If a researcher is standing in a corner (point c) of a triangle plot. the angle to point a is S76E .  the distance between point A and point B is 210 ft.

To find the distance between points A and B, we can use the Law of Cosines. Let's first label the angles of the triangle:

   Angle ACB = 180 - (76 + 32) = 72 degrees

   Angle BAC = 76 degrees

   Angle ABC = 32 degrees

Using the Law of Cosines, we have:

AB^2 = AC^2 + BC^2 - 2(AC)(BC)cos(ACB)

where;

AB is the distance between points A and B

AC is the distance between points A and C (210 ft

BC is the distance between points B and C (150 ft)

ACB is the angle between AC and BC (72 degrees)

Plugging in the values, we get:

AB^2 = 210^2 + 150^2 - 2(210)(150)cos(72)

AB^2 = 44100

AB = sqrt(44100)

AB = 210 ft

Therefore, the distance between point A and point B is 210 ft.

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Answer: The formula for compound interest is:

A = P(1 + R/100)^t

where A is the amount after t years, P is the principal amount, R is the rate of interest per annum, and t is the time period in years.

Here, P = Rs. 3,500, R = 8%, and t = 2 years.

So, the amount after 2 years will be:

A = 3,500(1 + 8/100)^2

= 3,500(1.08)^2

= 3,892.32

Therefore, the compound interest for 2 years will be:

CI = A - P

= 3,892.32 - 3,500

= 392.32

Hence, the compound interest on Rs. 3,500 for 2 years at the rate of 8% per annum is Rs. 392.32.

Step-by-step explanation:

The equation of the normal plane is 4y = 4π, or equivalently, y = π.

The word osculate comes from the Latin osculatus, which is a past participle of the verb osculari, which means "to kiss." Thus, an osculating plane is one that "kisses" a submanifold.

To find the osculating plane and normal plane of the curve x = sin 2t, y = t, z = cos 2t at the point (0, π, 1), we need to follow these steps:

Step 1: Find the first and second derivatives of the curve with respect to t.

x' = 2cos2t

y' = 1

z' = -2sin2t

x'' = -4sin2t

y'' = 0

z'' = -4cos2t

Step 2: Evaluate the derivatives at t = π.

x'(π) = 2cos2π = 2

y'(π) = 1

z'(π) = -2sin2π = 0

x''(π) = -4sin2π = 0

y''(π) = 0

z''(π) = -4cos2π = -4

So the velocity vector at the point (0, π, 1) is v = ⟨2, 1, 0⟩, the acceleration vector is a = ⟨0, 0, -4⟩, and the curvature vector is κv = ⟨0, 4, 0⟩.

Step 3: Use the velocity and acceleration vectors to find the normal vector of the osculating plane.

The normal vector of the osculating plane is given by the cross product of the velocity and acceleration vectors:

n = v × a = ⟨2, 1, 0⟩ × ⟨0, 0, -4⟩ = ⟨4, 0, 0⟩

Step 4: Use the normal vector and the point (0, π, 1) to find the equation of the osculating plane.

The equation of the osculating plane is given by:

4(x - 0) + 0(y - π) + 0(z - 1) = 0

Simplifying, we get:

4x - 4 = 0

So the equation of the osculating plane is 4x = 4, or equivalently, x = 1.

Step 5: Use the curvature vector to find the normal vector of the normal plane.

The normal vector of the normal plane is given by the curvature vector:

n' = κv = ⟨0, 4, 0⟩

Step 6: Use the normal vector and the point (0, π, 1) to find the equation of the normal plane.

The equation of the normal plane is given by:

0(x - 0) + 4(y - π) + 0(z - 1) = 0

Simplifying, we get:

4y - 4π = 0

So, the equation of the normal plane is 4y = 4π, or equivalently, y = π.

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Answer:

1629.24m

Step-by-step explanation:

starting with the easy ones

1) Rectangle 1:

Surface area of rectangle=Length x width

SAR= 24x21

= 504m

2) Rectangle 2:

SAR= 19x21

=399

3) Rectangle 3

SAR= 21x8

=168

4) Rectangle 4:

SAR= 21x11

=231

*because the top and bottom are trapeziums the formular for it is

A=1/2(a+b)h

although those trapeziums don't have h(Height)

it needs to be broken down into two triangles and a rectangle. to find the height*

5) side/height of triangle A:

formula: C squared= a squared + b squared

in this case we already have C and A. meaning we have to rearrange the formula to:

x = c^2 - a^2

x = 8^2 - 2.5^2

x = sqrt 57.75

x = 7.61

6) Trapezium

SA= 1/2(a+b)h

SA= 1/2(19+24)7.61

=163.62

7) add all surface area together

which should equal 1629.24m

Answer: t=2.59

Step-by-step explanation:

This is a matter of clearing out the equation

set 1151=800e^0.14t

1151/800=e^0.14t

ln(1151/800)/0.14=t

t=2.59

The histogram should be modified as follows:

A histogram is a type of graphical representation that displays the distribution of a dataset. It is a bar graph-like chart where the data is divided into intervals, called "bins", which are represented by adjacent rectangular bars of varying heights.

Then the height of the histogram gives the number of observations into each data interval.

Hence the histogram should be modified as follows:

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The coordinates of the vertices of the image rectangle M'P'A'T' are:

M'(2,1), P'(3,1), A'(3,3), T'(2,3).

What is rectangle?

A rectangle is a geometric shape that has four sides and four right angles (90 degrees) with opposite sides being parallel and equal in length.

To find the coordinates of the vertices of the image rectangle M'P'A'T', we need to apply a transformation to each vertex of the original rectangle MPAT.

We can see that the original rectangle MPAT has sides parallel to the x and y-axes, which suggests that it is aligned with the coordinate axes. We can also see that the length of its sides are equal, which means it is a square.

To transform this square, we can use a combination of translations, rotations, and reflections. However, since we don't have any information about the type of transformation that is being applied, we can assume that the simplest transformation is a reflection across the line y=x.

To reflect a point (x,y) across the line y=x, we swap its x and y coordinates to get the reflected point (y,x). Therefore, the coordinates of the vertices of the image rectangle M'P'A'T' are:

M'(2,1)

P'(3,1)

A'(3,3)

T'(2,3)

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a) the exponential equation equivalent to log8 1/64 = 2 is 1/64 = [tex]8^{(-2)}[/tex]

b)  the logarithmic equation equivalent to 3^0 = 1 is log3 1 = 0.

What is exponential equation?

An exponential equation is one in which the exponent contains a variable.

(a) We can rewrite the logarithmic equation as an exponential equation by using the definition of logarithms. The logarithmic equation

log8 1/64 = 2

means that 8 raised to the power of 2 is equal to 1/64:

[tex]8^2 = 1/64[/tex]

Thus, we can write the exponential equation as:

[tex]1/64 = 8^{(-2)}[/tex]

Therefore, the exponential equation equivalent to log8 1/64 = 2 is 1/64 = [tex]8^{(-2)}.[/tex]

(b) We can rewrite the exponential equation as a logarithmic equation by using the definition of logarithms. The exponential equation

[tex]3^0 = 1[/tex]

means that the logarithm of 1 to the base 3 is equal to 0:

log3 1 = 0

Therefore, the logarithmic equation equivalent to 3^0 = 1 is log3 1 = 0.

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Answer: 4.8%

Step-by-step explanation: the total amount of pens in the drawer is (10+12+3)  = 25

the amount of red pens in the drawer is 3

the probability of picking out a red pen from the drawer = 3/25

the amount of blue pens in the drawer is 10

the probability of picking out a red pen from the drawer = 10/25

the probability of picking out a red pen then a blue pen afterwards = (10/25 x 3/25) = 4.8%

The correct option -D. 5;  Thus, the value of x for the given external secant segment and the tangent on the circle is found as:x = 5.

A line that precisely intersects a circle at two points is said to be a secant.

The size of the angle created when two tangents, two secants, or two tangents cross outside of a circle is equal to one-half a positive difference between the sizes of the intercepted arcs.

Using the Theorem:

The square of a length of tangent is equal the the product of such external secant segment and the overall length of the secant if one secant and one tangent both drawn to a circle from a single exterior point:

4(4 + x) = 6²

16 + 4x = 36

4x = 36 - 16

4x = 20

x = 20/4

x = 5

Thus, the value of x for the given external secant segment and the tangent on the circle is found as:x = 5.

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