Unit 10: Circles Homework 6: Tangent Lines (Can I please have this rounded to the nearest tenth Thank You)

Answers

Answer 1

A tangent line is a straight line that intersects a circle at only one point, and it is perpendicular to the radius that goes through that point.

Tangent lines are important because they help us determine the relationship between circles and other geometric shapes.
To find the tangent line to a circle, we need to first identify the point of intersection between the circle and the line.
A tangent line to a circle is a line that intersects the circle at exactly one point, called the point of tangency. The tangent line is perpendicular to the radius that intersects the point of tangency.

m = [tex]\frac{-1}{r}[/tex]

where m is the slope of the tangent line, and r is the radius of the circle.

The equation of a tangent line to a circle can be found using the point-slope form of the equation:

y - y1 = m(x - x1)

where (x1, y1) is the point of tangency and m is the slope of the tangent line.

The length of the tangent segment from the point of tangency to the point of intersection with a secant line can be found using the formula:

[tex]t^2[/tex] = s1 * s2

where t is the length of the tangent segment, and s1 and s2 are the lengths of the two segments of the secant line that intersect the circle.
In terms of calculating the tangent line, we can use the point-slope formula.

Let's say we have a circle with equation [tex]x^2[/tex] + [tex]y^2[/tex] = [tex]r^2[/tex] and we want to find the tangent line at the point (a,b).

We can start by taking the derivative of the equation with respect to x, which gives us 2x + 2yy' = 0.

Solving for y', we get y' = -x/y.

Then, we substitute the values of x and y at the point of intersection (a,b) to get the slope of the radius at that point.

Finally, we take the negative reciprocal of that slope to get the slope of the tangent line, and use the point-slope formula to find the equation of the tangent line.
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Related Questions

julio has $31.00 he earns half of that much mowing a lawn. How much money does he have in all?

Answers

Answer: $ 46.50

First divided 31 by 2

Which equals...

15.50

Then add 15.50 to 31.

46.50

The answer is $46.50

a spinner with the colors red, yellow, blue, and green is spun. what is the theoretical probability of stopping on the color blue?

Answers

1/4 or 25% chance or .25, this is because there are four colors and blue is only one of them.

The theoretical probability of stopping on the color blue when spinning a spinner with the colors red, yellow, blue, and green is 25% or 1/4.

A spinner is a tool that spins around an arrow or a pointer that points towards the numbers, colors, or pictures around its edge. The probability of a certain event is the likelihood of that event occurring. In this case, we need to find the theoretical probability of stopping on the color blue.

We have four colors on the spinner, so the probability of stopping on blue can be found using the formula of theoretical probability.

The formula for theoretical probability is:

number of favorable outcomes / total number of outcomes.

Since we have four colors on the spinner, the total number of outcomes is 4. The favorable outcomes are the number of times the spinner will land on blue, which is 1.

So the probability of stopping on the color blue can be calculated as follows:

1 (favorable outcome) / 4 (total number of outcomes) = 1/4

So, the theoretical probability of stopping on the color blue is 1/4. This is because there is an equal chance of landing on any of the four colors, and since there are four colors, each has a 25% chance of being selected.

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Subtract the following polynomials.

Answers

The subtraction of the polynomials (3.1x + 2.8z) - (4.3x - 1.2z) is -1.2x + 4x

How to subtract polynomials?

A polynomial is an expression consisting of a sum of a finite number of terms, each term being the product of a constant coefficient and one or more variables raised to a non-negative integer power.

(3.1x + 2.8z) - (4.3x - 1.2z)

open parenthesis

3.1x + 2.8z - 4.3x + 1.2z

combine like terms

3.1x - 4.3x + 2.8z + 1.2z

-1.2x + 4x

Ultimately, -1.2x + 4x is the results of the subtraction of the polynomial.

Answers

Answer:

Factor 64h^3+216k^9

Step-by-step explanation:

The given expression is a sum of two terms:

[64h^3+216k^9

Notice that each term has a common factor. For the first term, the greatest common factor (GCF) is 64h^3, and for the second term, the GCF is 216k^9. So we can factor out these GCFs to get:

64h^3+216k^9 = 64h^3(1 + 3k^6)

This expression cannot be factored any further, so the final answer is:

64h^3+216k^9 = 64h^3(1 + 3k^6)

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Last year, 89 musicians attended a jazz camp, and 15 of them were bassists. What is the experimental probability that the first musician to sign up will be a bassist?

Answers

There is a roughly 16.85% chance that a bassist will be the first musician to register for the jazz camp.

What is experimental probability?

Experimental probability is a type of probability that is based on actual observations or experiments. It is also called empirical probability

According to question:

The ratio of the frequency of an occurrence to the total number of trials or observations is known as the experimental probability. In this case, the event is the first musician to sign up being a bassist.

Since there were 15 bassists out of 89 musicians who attended the camp last year, the experimental probability of the first musician to sign up being a bassist is:

Experimental probability = Number of bassists / Total number of musicians

Experimental probability = 15 / 89

Experimental probability = 0.1685 or approximately 16.85%

As a result, there is a roughly 16.85% chance that a bassist will be the first musician to register for the jazz camp.

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a 336-m long fence is to be cut into pieces to make three enclosures, each of which is square. how should the fence be cut up in order to minimize the total area enclosed by the fence?

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The fence ought to be cut into 12 pieces, every one of length 28 m, to make three squares, each with a side length of 28 m. This will limit the total area encased by the fence.

To limit the total area encased by the fence, the three squares ought to have equivalent areas. Let x be the length of each side of the squares. Then the perimeter of each square is 4x, and the total length of the fence is 3(4x) = 12x. Since the total length of the fence is given to be 336 m, we have:

12x = 336

Addressing for x, we get:

x = 28

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PLEASE HELP MARKING BRAINLEIST JUST ANSWER ASAP AND BE CORRECT

Answers

Answer:

4t - 22

Step-by-step explanation:

To find:-

Perimeter of the given figure.

Answer:-

To find out the perimeter we can simply add all the side lengths of the given figure. Since the given figure here is a rectangle, we can add up all the four sides to find the perimeter.

The four sides given to us are t-6 , t-5 , t-6 and t-5 .

Hence the perimeter of the quadrilateral would be ,

Perimeter = t-5 + t-6 + t-5 + t-6

Perimeter = 4t - 10 - 12

Perimeter = 4t - 22

Hence the perimeter of the given figure us 4t - 22.

[tex]\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\multiput(0,0)(5,0){2}{\line(0,1){3}}\multiput(0,0)(0,3){2}{\line(1,0){5}}\put(0.03,0.02){\framebox(0.25,0.25)}\put(0.03,2.75){\framebox(0.25,0.25)}\put(4.74,2.75){\framebox(0.25,0.25)}\put(4.74,0.02){\framebox(0.25,0.25)}\multiput(2.1,-0.7)(0,4.2){2}{$\sf\large t-5$}\multiput(-1.4,1.4)(6.8,0){2}{$\sf\large t-6$}\put(-0.5,-0.4){\bf A}\put(-0.5,3.2){\bf D}\put(5.3,-0.4){\bf B}\put(5.3,3.2){\bf C}\end{picture} [/tex]

a sock drawer contains 18 black socks and 12 red socks. if you randomly choose two socks at once, what is the probability you get a matching pair?

Answers

There are 12 red socks and 18 black socks in a sock drawer. If you randomly choose two socks at once, the probability you get a matching pair is 50%.

The probability of getting a matching pair of socks can be calculated as follows:

First, we can calculate the total number of ways to choose 2 socks out of 30:

C(30, 2) = 30! / (2! * (30-2)!) = 435

Now, we need to calculate the number of ways to choose 2 socks such that they are both black or both red:

Number of ways to choose 2 black socks: C(18, 2) = 153

Number of ways to choose 2 red socks: C(12, 2) = 66

Therefore, the total number of ways to choose a matching pair of socks is 153 + 66 = 219.

Finally, we can calculate the probability of getting a matching pair of socks by dividing the number of ways to choose a matching pair by the total number of ways to choose 2 socks:

P(matching pair) = 219 / 435 ≈ 0.5034

Therefore, the probability of getting a matching pair of socks is approximately 0.5034 or 50.34%.

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In a basketball free-throw shooting contest shots made by Sam and Wil were in the ratio 7:9.Wil made 6 more shots than Sam. Find the number of shots made by each of them.

Answers

Sam = 7(3) = 21
Will = 9(3) = 27

Answer:

Sam made 21 shots, and Wil made 27 shots.

The mirror has a frame. The diameter of the mirror with
the frame is 17 inches. To the nearest hundredth, what
is the area of the mirror with the frame?

Answers

Answer:

226.865 square inches.

Step-by-step explanation:

The equation for the area of a circle is [tex]\pi r^2[/tex]. Let's use 3.14 for pi. The radius can be found by dividing 17/2 = 8.5. 8.5 squared is 72.25. Finally, multiply by pi to get 226.865.

Tammy said the product of 5/7
and 1 1/4
is 1 3/4
.

How can you tell that this answer is wrong?

Answers

Answer:

Step-by-step explanation:

To determine if Tammy's answer of 1 3/4 for the product of 5/7 and 1 1/4 is correct, we can perform the multiplication ourselves.

First, we need to convert 1 1/4 to an improper fraction:

1 1/4 = (4 x 1 + 1)/4 = 5/4

Then, we can multiply the fractions:

5/7 x 5/4 = 25/28

As we can see, 25/28 is not equal to 1 3/4. Therefore, Tammy's answer of 1 3/4 is incorrect. The correct answer is 25/28, which is an improper fraction. We can also express this as a mixed number: 0 25/28.

what's a drawback to using a histogram?

Answers

Answer:

Step-by-step explanation:

One potential drawback of using a histogram is that it can be sensitive to the choice of bin width or bin size. If the bin size is too small, the histogram may appear too noisy or have too many empty bins, which can obscure patterns in the data. If the bin size is too large, important features of the distribution may be lost or smoothed out. Additionally, histograms do not always show the actual values of the data points, but rather a summary of the data. This means that some details about the data may be lost, such as the exact values of outliers or individual data points.

Write the ratios for sin A and cos A. The diagram is not drawn to scale.
sin A= 14/50 cos A 48/50
sin A= 48/50 cos A 14/50
sin A 48/14 cos A 14/50
sin A= 48/50 cos A 14/48

Answers

The ratio of SINA and COSA = 48/50 and 14/50

What is trignometric ratios?

This is the boundary or contour length of a 2D geometric shape.

Depending on their size, multiple shapes may have the same circumference. For example, imagine a triangle made up of wires of length L.

The same wire can be used to create a square if all sides are the same length.

The length covered by the perimeter of the shape is called the perimeter. Therefore, the units of circumference are the same as the units of length.

As we can say, the surroundings are one-dimensional. As a result, you can measure in meters, kilometers, millimeters, etc.

Inches, feet, yards, and miles are other globally recognized units of circumference measurement.

According to our question,

sina = perpendicular\ hypotenuse

= 48/50

cosa= base\ perpendicular

14/50

Hence, The ratio of SINA and COSA = 48/50 and 14/50

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What is the volume of the cone expressed in terms of pi?

Answers

Answer: V≈339.29 in

Step-by-step explanation:

Which one of the following decisions most clearly reflects a lack of understanding of the concept of sunk costs? You pay to have your car towed back to the repair shop because it was not fixed properly the first time. You decide to get a master's degree because you cannot find a job in the field in which you majored. You decide to purchase a piece of machinery for your business that will eliminate three employees' positions. You study eight hours for a final exam even though there is no way now that you can pass the course.

Answers

The decision that most clearly reflects a lack of understanding of the concept of sunk costs is "You study eight hours for a final exam even though there is no way now that you can pass the course".

What are sunk costs?

Sunk costs refer to any costs that have already been incurred and cannot be recovered. Sunk costs are irrelevant in decision-making because they are already gone and cannot be recovered. Decision-makers must only consider future costs and benefits when making decisions.

What does it mean to lack an understanding of sunk costs?

A lack of understanding of sunk costs may result in individuals making decisions based on past costs rather than future costs and benefits. Decision-making that is influenced by sunk costs may result in inefficient resource allocation and lost opportunities.

Individuals must ignore sunk costs and instead focus on future costs and benefits to make effective decisions.

In the given options, "You study eight hours for a final exam even though there is no way now that you can pass the course" is the decision that most clearly reflects a lack of understanding of the concept of sunk costs.

Even though the student has already spent 8 hours studying, the sunk costs are irrelevant because the student cannot pass the course now. The student should focus on future costs and benefits and use the remaining time to study for other courses.

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How can the area of this triangle be determined by forming a rectangle?

Select from the drop-down menus to correctly complete the statements.

The length of the rectangle is what units.

The width of the rectangle is what units.

The area of the rectangle is what square units.

The area of the triangle is half the area of the rectangle, so the area of the triangle is
what square units.

Answers

Answer:

the area ot the triangle is half the area of the rectangle, so the area of the triangle is what sqauare units

Answer: It's much easier to form a rectangle and multiply the width and the length and then divide it by 2

a centrifuge in a medical laboratory rotates at an angular speed of 3450 rev/min in the positive direction. when switched off, it rotates through 45.8 revolutions before coming to rest. Find the constant angular acceleration of the centrifuge.

Answers

The constant angular acceleration of the centrifuge is approximately [tex]-331283[/tex] rad/min² in the negative direction.

To find the constant angular acceleration of the centrifuge, we can use the following kinematic equation:

ω² = ω₀² + 2αθ

Here, ω is the final angular velocity (0 rad/min, since it comes to rest), ω₀ is the initial angular velocity (3450 rev/min), α is the constant angular acceleration we want to find, and θ is the angular displacement (45.8 revolutions).

First, we need to convert the given angular values to radians. We know that 1 revolution equals 2π radians.

Initial angular velocity, ω₀ = 3450 rev/min × 2π rad/rev = 6900π rad/min

Angular displacement, θ = 45.8 rev × 2π rad/rev = 91.6π rad

Now, substitute the values into the kinematic equation:

[tex]0 = (6900π)² + 2α(91.6π)[/tex]

[tex]α = - (6900π)² / (2 × 91.6π)[/tex]

[tex]α ≈ -331283 rad/min²[/tex]

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a square has side length of 7.3 in . if the area is multiplied by 19 , what happens to the perimeter?

Answers

The new perimeter is 127.2 inches if it is multiplied by 19.

What do you mean by the are and perimeter of the square ?

The area of a square is calculated by squaring the length of one of its sides. If the area of a square is multiplied by a factor, the length of the sides will be multiplied by the square root of that factor. One way to express the concept of perimeter for a square is to state that it is the total distance around the outer boundary of the shape, which is equal to the sum of the lengths of all four sides.

Determining the the value of perimeter :

The area of the square is [tex]7.3 \times 7.3 = 53.29[/tex] square inches.

If this area is multiplied by 19, the new area will be 1012.51 square inches.

To find the new side length of the square, we take the square root of the new area:

[tex]\sqrt{1012.51} = 31.8[/tex] (rounded to one decimal place)

Therefore, the new side length of the square is 31.8 inches.

To find the new perimeter, we multiply the new side length by 4:

[tex]31.8 \times 4 = 127.2[/tex]inches

So the new perimeter is 127.2 inches.

To summarize, when the area of the square with side length 7.3 inches is multiplied by 19, the perimeter is multiplied by the square root of 19, which is approximately 4.36. The new perimeter is 127.2 inches.

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Each prism has the same volume. Which has the least surface area? Explain or show your
reasoning.

Answers

This means that the cube will have less surface area than the rectangular prism.

What is surface area?

Surface area is a measure of the total exposed area of an object, or the total area of its two-dimensional surface. It is a measurement of the total exposed area of a three-dimensional object and is used to calculate the amount of material needed to cover a given area. Surface area is commonly used in physics, chemistry, engineering, and mathematics.

The prism with the least surface area of the same volume is the cube. This is because a cube has equal length, width, and height, allowing for all of the sides to be equal in size. This means that the area of each side is the same and all six sides of the cube are congruent. This creates the least amount of surface area for a given volume, as compared to any other prism. To illustrate this, take a cube and a rectangular prism with the same volume. The cube will have 6 smaller sides, while the rectangular prism will have 5 larger sides and 1 smaller side. This means that the cube will have less surface area than the rectangular prism.

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for the beam and loading shown, (a) draw the shear and bending-moment diagrams, (b) determine the equations of the shear and bending-moment curves. 5.1

Answers

Bending moment curve equation below point A will be:

M = 15x - 3x² for 0 ≤ x ≤ b

Determination of shear and bending moment curves.

For the beam and loading shown, we can do the following:

Equation of shear curve (above point A):V = RA - w.x

For x = a,V = RA - w.a

For x = b,V = RA - w.b

Since the loading is symmetric, RA = w(a + b) / 2= (6 * 5) / 2= 15kNV = 15 - 6a for a ≤ x ≤ b

Equation of shear curve (below point A):

V = RA - w.x

For x = 0,V = RA - w.0RA = w(a + b) / 2= (6 * 5) / 2= 15kNV = 15k for 0 ≤ x ≤ a

The shear curve equation becomes;

V = 15k for 0 ≤ x ≤ a

V = 15 - 6a for a ≤ x ≤ b

Equation of bending moment curve (above point A):

M = RAx - ½w.x²For 0 ≤ x ≤ a,

M = 15x - ½(6x²) = 15x - 3x²For a ≤ x ≤ b,

M = 15x - 6a(x - a) - ½(6x²)= 15x - 6ax + 6a² - 3x²

The bending moment curve equation above point A becomes:

M = 15x - 3x² for 0 ≤ x ≤ a

M = 15x - 6ax + 6a² - 3x² for a ≤ x ≤ b

Equation of bending moment curve (below point A):

M = RAx - ½w.x²For 0 ≤ x ≤ b,

M = 15x - ½(6x²) = 15x - 3x²

The bending moment curve equation below point A becomes;

M = 15x - 3x² for 0 ≤ x ≤ b

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Tonya's income is four times as much as Nora's income. Write an Algebraic expression representing Nora's income in terms of Tonya's

Answers

An algebraic expression for representing the Nora's income in form of Tonya's income is given by y = ( x / 4 ) .

Let us consider 'x' represents the Tonya's income.

And variable 'y' represents the Nora's income.

Tonya income is equal to four times of Nora's income.

This implies,

Nora's income is equal to one fourth times of Tonya's income.

⇒ y = ( x / 4 )

Rewrite an algebraic expression to represents Tonya's income in terms of Nora's income we have,

Simplify by multiplying both the sides of the algebraic expression by 4 we get,

⇒ x = 4y

Therefore, an algebraic expression to represents the Nora's income in terms of Tonya's income is equal to y = ( x / 4 ).

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While birdwatching, Vicki saw 7 red birds, 9 white birds, and 19 black birds. Johnny saw 9 red birds, 12 blue birds, and 29 brown birds. Estimate how many more birds Johnny saw by rounding all numbers to the nearest ten before adding and subtracting.

Answers

Answer:

Step-by-step explanation:

7 rounds to 10

9 rounds to 10

19 rounds to 20

so Vicki has 40 birds

9 rounds to 10

12 rounds to 10

29 rounds to 30

so johnny has 50 birds

now subtract 50-40=10

a bag contains marbles, marbles, and marbles. if a marble is drawn from the bag, replaced, and another marble is drawn, what is the probability of drawing first a marble and then a marble?

Answers

To find the probability of drawing a marble and then another marble from the bag, we need to multiply the probabilities of the individual events. This is because the two events are independent, and the outcome of the first event does not affect the outcome of the second event.

Let P(R) denote the probability of drawing a red marble, and P(B) denote the probability of drawing a blue marble. We are given that the bag contains red, blue, and green marbles, but we do not know the exact numbers of each color.

Since we replace the marble after each draw, the probability of drawing a red marble and then a blue marble can be found as:

P(RB) = P(R) x P(B)

To find P(R), we need to divide the number of red marbles in the bag by the total number of marbles. Similarly, to find P(B), we need to divide the number of blue marbles in the bag by the total number of marbles. However, since we do not know the exact numbers of each color, we cannot compute these probabilities exactly.

Therefore, we can only say that the probability of drawing a marble and then another marble is equal to the product of the probabilities of drawing each marble separately. In other words, the probability of drawing a red marble and then a blue marble is:

P(RB) = P(R) x P(B)

where P(R) and P(B) are the probabilities of drawing a red marble and a blue marble, respectively, which we cannot determine without more information about the contents of the bag.

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The graphs of line a and b are shown in this coordinate grid
Match each line with it's equation. Drag each equation to the corresponding box for each line

Answers

The correct option for the given graph is option 1 and option 3. The equation matches the intersection point (1,1).

For option 1: intersection point (1,1)