A clock pendulum swings back and forth once every two seconds. If its length is one meter and the greatest
angle that it makes with the vertical is 12 degrees, how many kilometers does the bottom end of the pendulum travel in
one day?

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:

Answer:  36600 = E

Step-by-step explanation:

Given:

T=.2 (E - 10600)      

T=5200  

Find:  E

Solution:  

>substitute into thequation.  You know T=5200

5200 = .2(E-10600)     > Divide both sides by .2

26000 = E- 10600       > add 10600 to both sides

36600 = E                    

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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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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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

The given identity (P+1/P-1 + P+1/P+1)-(P-1/P+2 + P+1/P-2)=-4(2p² + 1)/(p²-4) (p² - 1) is proven below

Given the following equation

(P+1/P-1 + P+1/P+1)-(P-1/P+2 + P+1/P-2)=-4(2p² + 1)/(p²-4) (p² - 1)

We start by simplifying the left-hand side of the equation:

(P+1/P-1 + P+1/P+1)-(P-1/P+2 + P+1/P-2)= [(P²+1)/(P(P-1))] + [(P²+1)/(P(P+1))] - [(P²-1)/((P+2)P)] - [(P²+1)/((P-2)P)]

Next, we have the following steps to simplify the expression

= [(P³ + P² + P + 1)/(P(P²-1))] - [(P³ - 3P)/(P(P²-4))]

= [(P³ + P² + P + 1)(P²-4) - (P³ - 3P)(P²-1)]/[(P(P²-1))(P(P²-4))]

= [(P⁵ - 3P³ + P³ - 3P² + P² - 4P + P² - 4P - 4 + P³ - 3P)/(P⁴ - 5P² + 4)]

= [P⁵ - 2P³ - 6P² - 8P - 4]/[(P²-4)(P²-1)]

= -4(2p² + 1)/(p²-4) (p² - 1)

Hence, the given identity is proven.

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The left-handed students in the music program are option A 15 students.

A table that shows the frequencies of two category variables is known as a two-way frequency table. It is a method for succinctly and clearly organising and displaying data for two variables. One variable is represented by the table's rows, while the other variable is represented by the table's columns. The frequency of each combination of categories is displayed in the table's cells. To examine the relationship between the two variables and to spot patterns and trends in the data, a two-way frequency table can be employed. To summarise and analyse data, it is frequently used in statistics, the social sciences, and other disciplines.

From the given table the number of students that are in music program and left handed is given by the intersection of the row and column of the two.

Thus, he left-handed students in the music program are 15.

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The index forms are simplified to;

1. [tex]5^6^\sqrt{2}[/tex]

2.[tex]3^5\sqrt{3}[/tex]

3.  [tex]2^2^\sqrt{25}[/tex]

It is important to note the following about the rules of index forms;

From the information given, we have that;

[tex]5^\sqrt{2}[/tex] × [tex]5^\sqrt{50}[/tex]

Add the exponents, we have;

[tex]5^\sqrt{2} ^+ 5\sqrt{2}[/tex]

Then, we have;

[tex]5^6^\sqrt{2}[/tex]

2. [tex]3\sqrt{12}[/tex] × [tex]3^\sqrt{27}[/tex]

We have;

[tex]3^2^\sqrt{3} + 3\sqrt{3}[/tex]

Add the exponents

[tex]3^5\sqrt{3}[/tex]

3. [tex]2^2^\sqrt{25}[/tex]

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Answer:

3rd choice:  when b>1

Step-by-step explanation:

For this function, a is the starting value (initial amount).  b is the decay or growth factor.  If b>1, then the function is a growth function.

FYI, if 0 < b < 1, then it is a decay function.

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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Using the table feature of a graphing utility  the intensity of an earthquake with an amplitude of 200,000 micrometers for 0.5 seconds would be 2.16 x 10¹⁴ joules/second/meter².

First, note that the   intensity of an earthquake with an amplitude of 200,000 micrometers for 0.5 seconds can be calculated using the formula..

I = (1/2)ρv²

Here I   Intensity

ρ = density of the medium - this is a constatnt

v = velocity of the S-waves

If we used a graphing tool

a coumun ffor v will be created

a column for the formula for velocity will also be created.

The formula for velocity is

V = A/ T

A = amplitude

T = time or period in seconds


Since A = 200,000 micrometers; and

T = 0.05 secons

v = 200,000 / 0.5

v = 400,000 micrometer/sec

Back o the table, we ahve to add another oclumn for V²

then enter the values for V²

V² = 400,000²
v² = 160,000,000,000 micrometer²/sec²


Nowe we add another column which is

I = 1/2(pv²)

I = 2.16 x 10¹⁴ joules/second/meter².


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The measure of the angle is 36.9^o. Option B.

A right triangle is a form or type of triangle in which the measure of one of its internal angles is 90^o. As such, either the trigonometric functions or Pythagorean theorem can be applied to determine any of its properties as the case may be.

From the details given in the question, we can deduced that;

Sin θ = 3/5

       = 0.6

So that,

θ = Sin^-1 0.6

  = 36.87

θ = 36.9^o

The measure of the angle is 36.9^o. Option B.

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a) is Right angle Triangles both of them

b) The scale factor is 1:2.

Given AFD = 90 degrees, So CFD = 90 degrees.

So it a Right Angle Triangle.

Again ABC = 90 degrees, It's also a Right Angle Triangle.

Here see both the Triangle are opposite to each other so according to the theorem sum of all three angles of a triangle is 180 degrees

so if any angle is 90 deg then the other two sum is also 90 deg.

Given the scale Factor, 1/6 inch = 1 foot,

So it is a Reducing Scale so let 'x' be in inches

So the Scale Factor = 1:2

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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:

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  

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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About 120 students have travel times within the quoted interquartile range.

The interquartile range (IQR) represents the range of the middle 50% of a set of data, which is the difference between the third quartile (Q3) and the first quartile (Q1).

Assuming that the travel times are normally distributed and that we have information on the quartiles, we can use the formula:

IQR = Q3 - Q1

To find the number of students whose travel times fall within the interquartile range, we need to know the values of Q1 and Q3.

Since the IQR is 32 minutes:

32 = Q3 - Q1

We also know that the total number of students in Year 12 is 240. Assuming that all students have reported their travel times, we can use the interquartile range to estimate the proportion of students whose travel times fall within this range.

If the interquartile range covers the middle 50% of the data, then each quartile should cover 25% of the data. Therefore, we can estimate that the number of students whose travel times fall within the interquartile range is:

Number of students = 240 x 0.50 = 120

Therefore, we estimate that 120 of the 240 Year 12 students have travel times within the interquartile range of 32 minutes.

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Answer: 2.5

Step-by-step explanation:

the base is always positive, and it says f(x)= 1/2*5^x
1/2*5 is 2.5, so I think the base is 2.5

hope it helped:)

The initial velocity of the car before the brake was pulled is 30m/s

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

A car pulls the emergency hand brake, accelerating at -4.0 m/s2 for 7.5 seconds

This means that

Acceleration = -4.0m/s^2

Time = 7.5 seconds

Using the above as a guide, we have the following:

Initial velocity = -Acceleration  * Time

substitute the known values in the above equation, so, we have the following representation

Initial velocity = 4  * 7.5

Evaluate

Initial velocity = 30

Hence, the initial velocity is 30

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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 = 25

Step-by-step explanation: Since 36 divided by 2 equals 18, which would cancel out the two on the left side leaving us with. (x - 7) = 18 we can add 7 to both sides to get. X = 25

Edit: To whoever said my math is incorrect is wrong, I even double checked with multiple sources and people. It must’ve been a different equation or number. Sorry for not being able to help, however the math was correct.

The feasible region on the attached graph of the inequalities created with MS Excel indicates that the maximum value of g = 8·x + 12·y is 100

The feasible region is the region on the graph of the inequalities that satisfies the specified constraints.

The specified equations obtained from the constraints in slope intercept form are;

y = -0.5·x + 7; The region below the graph is shaded

y = -0.75·x + 9; The region below the graph is shaded

x = 0; The region to the right of the line x = 0 is shaded

y = 0; The region above the line y = 0 is shaded

The point of intersection of the graphs can be found from the equation; -0.5·x + 7 = -0.75·x + 9

Which indicates that at the intersection, x = 8, and y = -0.5×8 + 7 = 3

The corner points are; (0, 0), (0, 7), (8, 3), (12, 0)

The value of the function g for each of the feasible region are therefore;

g(0, 0) = 8 × 0 + 12 × 0 = 0

g(0, 7) = 8 × 0 + 12 × 7 = 84

g(8, 3) = 8 × 8 + 12 × 3 = 100

g(12, 0) = 8 × 12 + 12 × 0 = 96

Please find attached the graph of the inequalities showing the feasible region created with MS Excel

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The solution is: the area of the shaded base in square centimeters is:

B= 15 cm²

Here, we have,

The base of the triangular shaped wedge of cheese is a right-triangle.To find the area of a right-triangle you apply the formula for half base by height.

A=1/2*b*h

 = base area

 = B

In this case, assume the sides of the triangle given are;

a=5 cm and b=6 cm,

thus area will be 1/2*6*5 =15 cm²

Hence, the area of the shaded base in square centimeters is :

B= 15 cm²

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complete question:

Evelyn cut a wedge of cheese into the shape of a triangular prism-like the one shown below. The shaded part represents one of the bases of the prism.

A formula for the volume of a triangular prism is v=Bh . Which equation can be used to find B , the area of the shaded base in square centimeters?

The total units of length for the ice rink away from the origin is 14.42 units.

In Mathematics and Geometry, the distance between two (2) end points that are on a coordinate plane can be calculated by using the following mathematical equation:

Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]

Where:

x and y represent the data points (coordinates) on a cartesian coordinate.

Note: Ice rink is located at point (12, 8).

By substituting the given end points into the distance formula, we have the following;

Distance = √[(12 - 0)² + (8 - 0)²]

Distance = √[(12)² + (8)²]

Distance = √[144 + 64]

Distance = √208

Distance = 14.42 units.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Answer:

60

Step-by-step explanation:

14 rounds to 10

23 rounds to 20

28 rounds to 30

10+20+30=60