In the circle below, IK is a diameter. Suppose mIJ=78 and mILJ=69 . Find the following.
m
m

Calculus a broad subject that covers many topics such as derivatives, integrals, limits, and functions.

Calculus is a branch of mathematics that focuses on the study of change and motion. It provides a framework for understanding and analyzing quantities that vary continuously. The two main branches of calculus are differential calculus and integral calculus.

Differential calculus deals with the concept of derivatives. A derivative measures how a function changes as its input (usually denoted as x) changes. Geometrically, the derivative represents the slope of a function at a particular point. It can also be interpreted as the instantaneous rate of change of a function at a given point. Derivatives have various applications, such as determining the maximum or minimum values of functions, analyzing the behavior of functions, and solving optimization problems.

Integral calculus, on the other hand, focuses on the concept of integrals. An integral is a mathematical operation that measures the accumulation of quantities or the area under a curve. It essentially reverses the process of differentiation. Integrals can be used to compute the total change or accumulation of a quantity over a given interval, find the area of irregular shapes, and solve problems involving rates of change.

Calculus plays a fundamental role in many scientific and engineering disciplines. It is used extensively in physics, engineering, economics, computer science, and many other fields to model and solve real-world problems involving continuous change. The study of calculus also forms the basis for higher-level mathematics such as differential equations, vector calculus, and multivariable calculus.

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Step-by-step explanation:

To determine the constant of proportionality (k) in a proportional relationship, we need to compare corresponding values of x and y and calculate the ratio between them.

Let's examine the given values:

2. UX: x 6 15 9 y 42 200

To find the constant of proportionality (k), we can take any pair of corresponding values and calculate their ratio. Let's choose the first pair: (6, 42).

k = y / x

k = 42 / 6

k = 7

So, the constant of proportionality (k) is 7.

Now, let's find the missing values for the second set of values:

d. X: 14 y: 21 6 15 3 7 8

Since we know the constant of proportionality is 7, we can calculate the missing values of y by multiplying each corresponding x value by 7.

Missing values for y:

- For x = 21, y = 21 * 7 = 147

- For x = 6, y = 6 * 7 = 42

- For x = 15, y = 15 * 7 = 105

- For x = 3, y = 3 * 7 = 21

- For x = 7, y = 7 * 7 = 49

- For x = 8, y = 8 * 7 = 56

Therefore, the missing values of y are: 147, 42, 105, 21, 49, and 56.

The equations are solved to get

2/5 * (1 1/4 * x - 3 1/3) - 1 1/3 x here x = 1 3/5

2 1/8 x + 3/4 x + 1/6 - 7/12 x + 5 2/3 here x = 2 6/11

0.5(x + 1.6) + 1.4(3x + 2.4) = 9.8 here x = 1.2

1.

2/5 * (1 1/4 * x - 3 1/3) - 1 1/3 * x

opening the parenthesis and converting to improper fraction

1/2 x - 4/3 - 4/3 x

-5/6 x - 4/3

-5/6 x = 4/3

x = 8/5

x = 1 3/5

2.

2 1/8 x + 3/4 x + 1/6 - 7/12 x + 5 2/3

adding like terms

55/24 x + 35/6 = 0

55/24 x = - 35/6

x = 28/11

x = 2 6/11

3.

0.5(x + 1.6) + 1.4(3x + 2.4) = 9.8

removing the parentheses:

0.5x + 0.8 + 4.2x + 3.36 = 9.8

4.7x + 4.16 = 9.8

4.7x = 5.64

x = 1.2

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The number of terms n of the geometric progression is n = 12

Given data ,

Let the geometric progression be represented as A

Now , the value of A is

10 + 30 + 90 + .... = 2657200

And , let the number of terms be n

common ratio r = 30 / 10 = 3

where sum of first n terms of a GP is Sₙ = a(rⁿ-1) / ( r - 1 )

On simplifying , we get

2657200 = 10 ( 3ⁿ - 1 ) / ( 2 )

Divide by 5 on both sides , we get

3ⁿ - 1 = 5,31,440

Adding 1 on both sides , we get

3ⁿ = 5,31,441

Taking log on both sides , we get

n = 12

Hence , the number of terms of GP is n = 12

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The market equilibrium point is a supply of 1000 at $325

We have the demand of

So, the demand equation is a linear equation that passes through

(800, 350) and (1200, 300)

This equation is

d(x) = -x/8 + 450

We have the supply of

So, the supply equation is a linear equation that passes through

(700, 280) and (1400, 385)

This equation is

s(x) = 3x/20 + 175

At the market equilibrium point, we have

d(x) = s(x)

So, we have

3x/20 + 175 = -x/8 + 450

This gives

x = 1000

Also, we have

s(1000) = 3 * 1000/20 + 175

s(1000) = 325

This means that the market equilibrium point is a supply of 1000 at $325

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Complete question

A retail chain will buy 800 televisions if the price is $350 each and 1200 if the price is $300. A wholesaler will supply 700 of these televisions at $280 each and 1400 at $385 each.

Assuming that the supply and demand functions are linear, find the market equilibrium point

Answer:

$223,787

Step-by-step explanation:

r = 0.02

C = 191,000

t = 8

S = 191,000 (1 + 0.02)⁸

Follow order of operations (PEMDAS).

S = 191,000 (1.02)⁸

S = 191,000 (1.171659381)

S = 223,786.9

(We want to round to the nearest dollar, which is the ones place, so ignore all digits after the tenths place.)

Rounding, S = 223,787

Were the above figure is given, the complete sentence with regard to the triangles are

ΔAGC ~  ΔCDF

ΔCDE ~ ΔCAB

And, the length of BC is, 51

The length of DE is, 132.7

We have to given that;

⇒ CF = 32

Hence, We get;

tan 24 = CF / DF

0.44 = 32 / DF

DF = 72.7

Thus, ΔAGC ≈ ΔCDF

Here, We have;

⇒ ΔCDE ≈ ΔCAB

In triangle BCG;

BC² = 24² + 45²

BC² = 576 + 2025

BC² = 2601

BC = 51

In triangle CEF;

⇒ EC² = CF² + EF²

⇒ 68² = 32² + EF²

⇒ 4624 = 1024 + EF²

⇒ EF² = 4624 - 1024

⇒ EF² = 3600

⇒ EF = 60

Thus, We get;

DE = DF + EF

DE = 72.7 + 60

DE = 132.7

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Answer:

The relationship between the number of faces, vertices, and edges of a three-dimensional object is described by Euler's formula, which states that for any polyhedron (a solid object bounded by flat faces), the number of faces (F), vertices (V), and edges (E) satisfy the equation F + V - E = 2. This formula is true for any convex polyhedron, such as a cube or a regular tetrahedron.

The formula is based on the fact that every face of a polyhedron is bounded by a closed loop of edges, and each vertex is where three or more edges meet. The total number of edges is the sum of the number of edges around each face, which is equal to twice the number of faces since each edge is shared by two faces, and the number of edges meeting at each vertex, which is equal to the degree of the vertex (the number of edges meeting at the vertex).

Therefore, by knowing the number of faces, vertices, and edges of a three-dimensional object, we can determine if it is a convex polyhedron and use Euler's formula to check if the numbers are consistent with a solid shape.

The value of r which is the decay rate is calculated as: -0.0203

The equation for "continual" growth (or decay) is given by the expression:

[tex]A = Pe^{rt}[/tex]

where:

A is the ending amount,

P is the beginning amount (principal, in the case of money)

r  is the growth or decay rate (expressed as a decimal),

t is the time (in whatever unit was used on the growth/decay rate).

We are given that:

A = 70000

P = 93000

t = 14

Thus:

70000 = 93000 * [tex]e^{14r}[/tex]

70/93 = * [tex]e^{14r}[/tex]

14 r = In (70/93)

14r = -0.2841

r = -0.0203

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Answer:

Your answer is C and D. :)

Step-by-step explanation:

The method of bar chart is appropriate for representation.

According to the given data,

The most effective way to present the data is in a bar chart.

An effective visual representation of categorical data that shows the frequency or count of each category is a bar chart.

The length of each bar would reflect the frequency or count of each score, and the categories would be the test results in this instance.

It would be a simple and unambiguous approach to compare the various test results.

These are the three key characteristics of bar graphs:

The bar graph makes it simple to compare various sets of data among various groups.

The relationship is depicted using two axes, with the discrete values on one axis and the categories on the other.

The graph displays the key alterations in the data over time.

Hence,

Bar chart method should be used.

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Answer:

its A

Step-by-step explanation:

Time is usually represented by the x axis

The number of unique 8-card hands to be dealt are752,538,150.

The number of different 8-card hands that can be dealt from a standard 52-card deck is given by the combination formula:

[tex]C(n, k) = n! / [(n-k)! * k!][/tex]

C(52, 8) = 52! / [(52-8)! * 8!] = 52! / [44! * 8!]

Evaluating this will give the total number of different 8-card poker hands that can be dealt from a standard deck.

Using these calculations, you would find the number of unique 8-card hands to be 752,538,150.

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The solution of the function is as follows:

f(3) = 16

h(0) = -4

h(g(x)) = 3x + 5

g(y) = y + 3

f(x) - h(x) =  x² - x + 5

A function relates input and output. In other words, a function is an expression that defines a relationship between one variable (the independent variable) and another variable(dependent variable).

Therefore, let's solve the function as follows:

f(x) = x² + 2x + 1

g(x) = x + 3

h(x) = 3x - 4

Therefore,

f(3) =  (3)² + 2(3) + 1 = 9 + 6 + 1 = 16

h(0) = 3(0) - 4 = -4

h(g(x)) = 3(x + 3) - 4 = 3x + 9 - 4 = 3x + 5

g(y) = y + 3

f(x) - h(x) =  x² + 2x + 1  - (3x - 4) =  x² + 2x + 1  - 3x + 4 = x² - x + 5

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In the graph, differential is 4 or (p+k)-p = k as well as difference is -2 when y = 7 or y = 5, respectively.

A graph comprises a visual representation and diagram that displays facts or values in an organised manner in mathematics. The points of a graph are widely used to depict the connections between various objects. A. The difference between y = 7 or y = 5 is 4 and -2, respectively B. 4 is the difference, so (p+k)-p = k C. It differs by -2 D. Part C depends on 'k' rather than 'p,' not 'p'.

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The Parallelogram area is 96 square meters.

We have,

The area of a parallelogram is given by the formula A = bh, where b is the length of the base and h is the height.

In this case,

The base of the parallelogram is the length of one of its parallel sides, which is 12 m.

The height of the parallelogram is given as 8 m.

Therefore, the area of the parallelogram is:

A = bh

A = 12 m x 8 m

A = 96 square meters

Thus,

The Parallelogram area is 96 square meters.

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Step-by-step explanation:

do it yourself what do you do while teacher is teaching

do it yourself what do you do while teacher is teaching

To solve for x in the equation −1.5x−2.7=20.1+4.5x, we need to isolate x on one side of the equation. We can do this by adding 1.5x to both sides of the equation and adding 2.7 to both sides of the equation, which gives us:

-1.5x - 2.7 + 1.5x = 20.1 + 4.5x + 1.5x

Simplifying the left side of the equation and combining like terms on the right side of the equation gives us:

-2.7 = 6x + 20.1

Subtracting 20.1 from both sides of the equation gives us:

-22.8 = 6x

Dividing both sides of the equation by 6 gives us:

x = -3.8

Therefore, the value of x that satisfies the equation is -3.8.

Answer: -3 to -infinity

Step-by-step explanation:

Answer:

8 am

Step-by-step explanation:

First train has a 50 m/hr x 3 hr = 150 mile head start

Second train is going 60 - 50 = 10 m/hr faster and will close this 150 mile distance

 in 15 hours to catch the first train

2pm + 3 hours + 15 hours = 8 am

Answer:

C. Through a given point not on a given line, there is exactly one line parallel to the given line.

Step-by-step explanation:

hope i helped

Answer:

Look down

Step-by-step explanation:

Thanks for reaching out for assistance! Based on the context you provided, it seems like the correct answer is C. Playfair's axiom states that there is exactly one line parallel to a given line that can be drawn through a point not on it. I hope this helps! Let me know if there's anything else I can do for you.

The inequality in slope - intercept form is,

⇒ y ≤ x + 5

We have to given that;

The graph of the inequality is shown in image.

Let two points on the line is,

⇒ (- 5, 0) and (0, 5)

Hence, The equation of line is,

⇒ y - 0 = (5 - 0) / (0 + 5) (x + 5)

⇒ y = x + 5

Thus, The inequality in slope - intercept form is,

⇒ y ≤ x + 5

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Answer:

$2.48 and $2.15, respectively

Step-by-step explanation:

2.30 * 1.08 = 2.48

1.99 * 1.08 = 2.15

The scale factor used to create the image is given as follows:

k = 1/4.

A dilation can be defined as a transformation that multiplies the distance between every point in an object and a fixed point, called the center of dilation, by a constant factor called the scale factor.

The equivalent segment lengths for the original figure and the image are given as follows:

Hence the scale factor used to create the image is given as follows:

k = 2/8

k = 1/4.

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Answer: $0.0195

Step-by-step explanation: To find the price per ounce of apple juice, we need to divide the total cost by the number of ounces.

Price per ounce = Total cost / Number of ounces

Here, the total cost is $2.50 and the number of ounces is 128.

Price per ounce = $2.50 / 128 ounces

Price per ounce = $0.0195

Therefore, the price per ounce of apple juice is $0.0195, which is approximately 2 cents per ounce.

Answer: $0.0195 per ounce

Step-by-step explanation:

We will create a proportion to help us solve this question.

➜ To do this, we will set two fractions equal to each other with the dollar amount in the numerator and the ounce amount in the denominator.

[tex]\displaystyle \frac{\$2.50}{128\;ounces} =\frac{\$x}{1\;ounce}[/tex]

Cross-multiply:

      128x = $2.50

Divide both sides of the equation by x:

      x = $0.0195 per ounce

Answer:

2.

Step-by-step explanation:

The data is skewed towards 1-25. From this we can conclude that patients only call the doctor once or twice when they are sick.