Types of discontinuities

Identify and Classify the discontinuities in the function, please

A formula for y in terms of x and c is y = c⁵√x

In inverse variation, as the value of one of the variables increases, the value of the other decreases and as the value of one of the variable decreases, the other increases.

From the information given, we have that;

y ∝1/√x

Now, let's find the constant value, k, we have;

y√x = k

We have that their values are;

y = c⁴, x = c²

Substitute the values, we have;

c⁴√c² = k

k = c⁵

Now, substitute the values

y = k√x

y = c⁵√x

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Answer:

120

Step-by-step explanation:

25% is equal to 1/4. If you divide 30 by 1/4 you get 120. To check this, if you multiply 120 by 1/4 you get 30.

Answer: 120

Step-by-step explanation:

In order to find the missing value, divide the provided value by the percentage as follows:

30 / 0.25 = 120

This can be double-checked by plugging the number into the statement afterwards: 25% of 120 is 30, which is true

Answer:

Step-by-step explanation:

actual area : 60 x 12 = 720

1/2 = 0.5

60 + 0.5 = 60.5        12 + 0.5 = 12.5  -max area = 60.5 x 12.5 = 756.25

60 - 0.5 = 59.5         12 - 0.5 = 11.5    -min area =  59.5 x 11.5 = 684.25

absolute error :  1/2(756.25-684.25) = 36

relative error : 36/720 = 0.05

 ... your welcome  

Answer:

V ≈ 1809 ft^3

Step-by-step explanation:

Given:

r (radius) = 6ft

h (height) = 16ft

π = 3,14

Find: V (volume) - ?

[tex]v = \pi {r }^{2} \times h[/tex]

[tex]v = 3.14 \times {6}^{2} \times 16 ≈1809 \: {ft}^{3} [/tex]

The result of the logarithm function is equal to 9. (Correct choice: D)

The statement shows an incomplete logarithm, whose result must be found by understing relationships between trascendent functions. Logarithm functions and exponential functions are related in the following way:

aᵇ = n ↔ ㏒ₐ n = b

Where:

If we know that (base) a = 3 and (exponent) b = 2, then the value of the result (n) is now defined:

n = 9

3² = 9

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Answer:

16 = 6+2.5h

Step-by-step explanation:

The total cost is 16 dollars.  She spends 6 dollars for shoes and 2.50 per hour.

16 = 6+2.5h

To solve, subtract 6 from each side

16-6 = 6+2.5h-6

10 = 2.5h

Divide each side by 2.5

10/2.5 = 2.5h/2.5

4 =h

She can climb for 4 hours.

Once again, we get the same answer: Kristin had $32 before receiving the $18 for cleaning the attic. we solve this by forming equation and solving it

what is equation ?

An equation is a mathematical statement that shows that two expressions are equal. It usually consists of variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. Equations are used to solve problems in various fields, including mathematics, physics, engineering

In the given question,

Let's use "x" to represent the amount of money Kristin had before receiving the $18 for cleaning the attic. We can set up the following equation:

x + 18 = 50

This equation represents the total amount of money Kristin has now, which is $50, after receiving the $18 for cleaning the attic. To solve for "x", we can subtract 18 from both sides of the equation:

x + 18 - 18 = 50 - 18

x = 32

Therefore, Kristin had $32 before receiving the $18 for cleaning the attic.

Alternatively, we can also use a diagram to represent the situation. We can draw a rectangle to represent the total amount of money Kristin has now, which is $50. We can then divide the rectangle into two parts: one part representing the $18 she received for cleaning the attic, and the other part representing the amount of money she had before. We can label this unknown amount as "x", and set up the following equation:

x + 18 = 50

This equation is the same as the one we set up earlier. To solve for "x", we can again subtract 18 from both sides of the equation:

x + 18 - 18 = 50 - 18

x = 32

Once again, we get the same answer: Kristin had $32 before receiving the $18 for cleaning the attic.

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All real numbers greater than 5 can be expressed in interval notation as:

(5, ∞)

Interval notation is a way of representing an interval on a number line. Simply, it is a method of writing subsets of the real number line.

All real numbers greater than 5 can be expressed in interval notation as:

(5, ∞)

Where the round bracket "(" means 5 is not included in the interval, and the infinity symbol "∞" means the interval continues indefinitely to the right.

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Answer:

x = 100

Step-by-step explanation:

1 and 2 are a linear pair and sum to 180° , that is

x + [tex]\frac{4}{5}[/tex] x = 180 ( multiply through by 5 to clear the fraction )

5x + 4x = 900

9x = 900 ( divide both sides by 9 )

x = 100

Answer:

Step-by-step explanation: 5

The given angles are 7π/4, 10π/3 & 510°.

Calculations for 7π/4(4th Quadarant)

sin(7π/4) = -1/√2

cos(7π/4) = 1/√2

tan(7π/4) = -1

cosec(7π/4) = -√2

cot(7π/4) = -1

sec(7π/4) = √2

Calculations for 10π/3(3rd Quadarant)

sin( 10π/3) = -√3/2

cos(10π/3) = -1/2

tan(10π/3) = √3

cosec(10π/3) = - 2/√3

cot(10π/3) = 1/√3

sec(10π/3) = -2

Calculations for 510°(2nd Quadarant)

sin( 510°) = 1/2

cos(510°) = -√3/2

tan(510°) = -1/√3

cosec(510°) = 2

cot(510°) = -√3

sec(510°) = -2/√3

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The composition of functions is solved and the expressions are

a) ( g o f ) ( -1 ) = 1

b) ( g o f ) ( 0 ) = 4

c) ( f o g ) ( -1 ) = -2

d) ( f o g ) ( 4 ) = -1

Given data ,

Let the composition of function be represented as A

Now , the value of A is

a)

( g o f ) ( -1 ) = g ( f ( -1 ) )

On simplifying the function , we get

when x = -1 , f ( -1 ) = 2

g ( 2 ) = 1

So , ( g o f ) ( -1 ) = 1

b)

( g o f ) ( 0 ) = g ( f ( 0 ) )

On simplifying the function , we get

when x = 0 , f ( 0 ) = 0

g ( 0 ) = 4

So , ( g o f ) ( 0 ) = 4

c)

( f o g ) ( -1 ) = f ( g ( -1 ) )

On simplifying the function , we get

when x = -1 , g ( -1 ) = 2

f ( 2 ) = -2

So , ( f o g ) ( -1 ) = -2

d)

( f o g ) ( 4 ) = f ( g ( 4 ) )

On simplifying the function , we get

when x = 4 , g ( 4 ) = 1

f ( 1 ) = -1

So , ( f o g ) ( 4 ) = -1

Hence , the composition of function is solved

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snip, that's wrong nvm (not sure how to delete)

The probability that the woman's height is between 62.9 in and 63.9 in is 0.1580

From the question, we have the following parameters that can be used in our computation:

So, the z-scores are

z = (62.9 - 63.6)/2.5 = -0.28

z = (63.9 - 63.6)/2.5 = 0.12

i.e. between a z-score of -0.28 and a z-score of 0.12

This is represented as

Probability = (-0.28 < z < 0.12)

Using a graphing calculator, we have

Probability =  0.1580

Hence, the probability is 0.1580

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Answer:

Step-by-step explanation:

A=4

b Base

1

h Height

4

b

h

a

h

h

b

a

a

P

A

b

Solution

A=bh=1·4=4 hope helps  byee

The matrix formed by performing the row operation 4R₂ + R₃ — R₃ will result to R₁ = [-4 0 1 5], R₂ = [-6 5 -1 8], and R₃= [-33 24 -9 32]

Row operations are a set of operations that can be performed on the rows of a matrix in order to transform it into a row equivalent matrix, which has the same solution set as the original matrix.

performing the row operation 4R₂ + R₃ — R₃, we have;

4(-6) + (-9) = -33 {row 3 column 1}

4(5) + 4 = 24 {row 3 column 2}

4(-1) + (-5) = -9 {row 3 column 3}

4(8) + 0 = 32 {row 3 column 4}

Therefore, the matrix formed by performing the row operation 4R₂ + R₃ — R₃ will give a new one with R₁ = [-4 0 1 5], R₂ = [-6 5 -1 8], and R₃= [-33 24 -9 32]

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Answer: 48

Step-by-step explanation:

180-132=48

Answer:

48

Step-by-step explanation:

angle = 132

supplementary angle = 180

measure of supplementary angle = 180 - 132 = 48

thus the measure of the supplement is 48

hope you got your answer.

The resulting matrix from an elementary row operation to get a 1, in row 1 column 1 is:

R₁ = [1 4 -8] and R₂ = [2 4 7]

A rectangular array of numbers or mathematical objects which are arranged in rows and columns is called a matrix. Each row of a matrix is a horizontal sequence of numbers or objects that are separated by commas and enclosed within square brackets, and it represents a vector in the row space of the matrix.

The row operation R₁ - 4 — R₁ will be carried out as follows:

5 - 4 = 1 {row 1 column 1}

9 - 4 = 5 {row column 2}

-4 - 4 = -8 {row column 3}

Therefore, the resulting matrix from an elementary row operation to get a 1, in row 1 column 1 will have:

R₁ = [1 4 -8] and R₂ = [2 4 7]

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The expression that Sally can use to determine how many dominoes can fit in the tin based on the number of dominoes in each row stacked is (Number of rows stacked ÷ 0.75) x (9 x 4)

Sally can use the fact that she can fit 3 dominoes stacked on top of each other, 9 dominoes side-by-side, and 4 dominoes end-to-end in the tin to figure out how many dominoes can fit in the tin. Since she knows that 27 dominoes fit in one row stacked, she can use addition to determine the total number of dominoes that can fit in the tin.

First, she can find the number of dominoes that can fit in one layer of the tin by multiplying the number of dominoes that fit side-by-side and the number that fit end-to-end: 9 x 4 = 36.

Then, she can divide the total number of dominoes that fit in one row (27) by the number of dominoes that can fit in one layer (36): 27 ÷ 36 = 0.75.

This means that each layer of the tin can hold 0.75 rows of dominoes.

To find the total number of dominoes that can fit in the tin, Sally can multiply the number of layers by the number of dominoes in each layer: Number of layers x Number of dominoes in each layer = Total number of dominoes that can fit in the tin.

Therefore, the expression that Sally can use to determine how many dominoes can fit in the tin based on the number of dominoes in each row stacked is:

Total number of dominoes = Number of layers x Number of dominoes in each layer

Total number of dominoes = (Number of rows stacked ÷ 0.75) x (9 x 4)

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The measure of the side length x is 15.04.

The figure in the image is a right triangle.

Angle θ = 43 degrees

Adjacent to angle θ = 11

Hypotenuse = x

To determine the measure of the side length x, we use the trigonometric ratio.

Note that: cosine = adjacent / hypotenuse

Plug in the values:

cos( 43° ) = 11 / x

Solve for x

x = 11 / cos( 43° )

x = 15.04

Therefore, the value of x is 15.04 units.

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The solution to the given inequality is: 10 > x ≤ 12

Inequalities are defined as mathematical expressions that involve the symbols >(greater than), <(less than), ≥(greater than or equal to) and ≤(less than or equal to).

In order for us to 'solve' an inequality, we have to find a range, or ranges, of values that an unknown x can take and still satisfy the inequality.

We are told that the angle (9x + 7)° is greater than 97° and at most 118°

Thus:

9x + 7 > 97

9x > 90

x > 10

Similarly:

9x + 7 ≤ 115

9x ≤ 108

x ≤ 12

Thus, the solution to the inequality is: 10 > x ≤ 12

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Answer:

To write 1/4 (x - 12) in words, you would say "one-fourth of the quantity obtained by subtracting 12 from x."

To plot the above linear regression on a graph, follow the procedures outlined below.

You may use the following steps to plot the supplied data on a graph:

1) Create an x- and y-axis coordinate plane.

2) Label the x-axis with the numbers 1 through 13 (to represent the 13 data points).

3) Label the y-axis with a suitable scale that encompasses the data's greatest and lowest values (e.g., 0 to 2200 with 200 increments).

4) For each point, try to find  the associated x -value on the x-axis and the corresponding y-value on the y- axis, and then place a point at the intersection of the two values.

For example, if the first point is (1, 1000), you would identify the x-axis point labeled "1" and the y-axis point labeled "1000" and add a point at it  intersection.

5) based  on the pattern in the data, connect the points of the coordinares using  a line or a curve. Because the data appears to increase gradually with some fluctuations in this case, a line connecting the points would be appropriate.

After plotting the data on the graph, you may study the pattern and draw inferences about the data's trend over time. Please see the attached sample graph.

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The incorrect statement is b. When an aeroplane takes off, the work done by its weight is negative.

The inaccurate assertion is:

b) When a plane removes, the work done by its weight is positive.

The right assertion is:

b) When a plane removes, the work done by its weight is negative.

Clarification:

At the point when a plane removes, the work done by the heaviness of the plane is negative in light of the fact that the weight acts the other way to the dislodging of the plane. As indicated by the work-energy hypothesis, work done by the heaviness of the plane will diminish its motor energy, and that implies that the work done is negative. Hence, articulation (b) is inaccurate.

a) Work and energy have various units.

This assertion is right. Work has units of Joules (J) and energy additionally has units of Joules (J), however they are not exactly the same thing.

c) The possible energy of spring increments when it is broadened and diminishes when it is packed.

This assertion is right. The potential energy put away in a spring is straightforwardly corresponding to its expansion or pressure. While a spring is broadened, its potential energy increments, and when it is packed, its potential energy diminishes.

d) On the off chance that the work done by outside powers on a framework is negative, the energy of the framework diminishes.

This assertion is right. On the off chance that the work done by outside powers on a framework is negative, the energy of the framework diminishes.

The work-energy hypothesis expresses that the net work done on a framework is equivalent to the adjustment of its motor energy, and in the event that the net work is negative, the dynamic energy diminishes, and that implies that the energy of the framework diminishes.

e) When a body is falling unreservedly from a level, its dynamic energy stays consistent.

This assertion is erroneous. At the point when a body is falling unreservedly from a level, its potential energy is changed over into dynamic energy as it falls. Hence, its motor energy increments as it falls, and its potential energy diminishes.

f) The unit of force is watt.

This assertion is right. The unit of force is watt (W), which is characterized as the pace of taking care of business or the pace of move of energy.

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The complete question is:

Identify the wrong statement among the following. Rewrite them by making necessary corrections.

a) Work and energy have different units.

b) When an aeroplane takes off, the work done by its weight is positive.

c) The potential energy of spring increases when it is extended and decreases when it is compressed.

d) If the work done by external forces on a system is negative then the energy of the system decreases.

e) When a body is falling freely from a height, its kinetic energy remains constant.

f) The unit of power is watt.

Answer:To find sin(π/4), we can use the fact that sin(π/4) = sin(45°). We also know that sin(45°) = 1/√2 or approximately 0.707 (rounded to 3 decimal places). Therefore, sin(π/4) is approximately equal to 0.707.

Step-by-step explanation: