Point A
Support
3.0m
2.5m
Figure 5
Weight of girl = 600 N
Weight of diving board = 800 N

Calculate the total clockwise moment of the weight of the diving board and the weight of the girl at about Point A. Give the unit.
Use the correct equation from the Physics Equation Sheet.

The coordinates of the exponential equation are A ( 2 , 640 ) , B ( 3 , 512 ) and C ( 4 , 409.6 )

When you raise a quotient to a power you raise both the numerator and the denominator to the power. When you raise a number to a zero power you'll always get 1. Negative exponents are the reciprocals of the positive exponents.

The different Laws of exponents are:

mᵃ×mᵇ = mᵃ⁺ᵇ

mᵃ / mᵇ = mᵃ⁻ᵇ

( mᵃ )ᵇ = mᵃᵇ

mᵃ / nᵃ = ( m / n )ᵃ

m⁰ = 1

m⁻ᵃ = ( 1 / mᵃ )

Given data ,

Let the exponential equation be represented as A

Now , the value of A is

Let the first point be A ( 0 , 1000 )

Let the second point be B ( 1 , 800 )

Now , the exponential equation be represented as A

y = abˣ   be equation (1)

Substitute the value of x = 0 and y = 1000

1000 = ab⁰

So , the value of a = 1000

Substitute the value of x = 1 and y = 800

800 = ab¹

b = 800/1000

b = 0.8

So , the equation is y = 1000 ( 0.8 )ˣ  

Now , at the point A , the value of x = 2

So , y = 1000 ( 0.8 )²

y = 1000 x 0.64

y = 640

So , the point is A ( 2 , 640 )

Now , at the point B , the value of x = 3

So , y = 1000 ( 0.8 )³

y = 1000 x 0.512

y = 512

So , the point is B ( 3 , 512 )

Now , at the point C , the value of x = 4

So , y = 1000 ( 0.8 )⁴

y = 1000 x 0.4096

y = 409.6

So , the point is C ( 4 , 409.6 )

Hence , the coordinates are A ( 2 , 640 ) , B ( 3 , 512 ) and C ( 4 , 409.6 )

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The properties of limit are the following:

A limit is a value which obtained when a function approaches the output value for an input value. For a variable x approaches a particular value say "a", i.e., x → a and limit is denoted as [tex] \lim_{x \to a} f(x) \\ [/tex].

The basic properties of limit are :

1) Sum rule : limit of sum of two functions is equal to sum of individual function limit.

[tex]\lim_{x \to a} (f(x) + g(x)) = \lim_{x \to a} f(x) + \lim_{x \to a}g(x) \\ [/tex]

2) Product rule : The limit of product of two functions is equal to product of individual function limits.

[tex]\lim_{x \to a} (f(x) \times g(x)) = \lim_{x \to a} f(x) \times lim_{x \to a} g(x) \\ [/tex]

3) Difference rule : The limit of difference of two functions is equal to difference of individual function limits.

[tex]\lim_{x \to a} (f(x)-g(x))=\lim_{x \to a} f(x) - \lim_{x \to a}g(x) \\ [/tex]

4) Law of constant : The limit of a constant is equal to constant itself.

[tex]\lim_{x \to a}c \: = c \\ [/tex]

5) Constant multiply rule : The limit of product of constant with function is equal to constant times limit of function.

[tex]\lim_{x \to a} (k \times f(x)) = k\times lim_{x \to a}f(x)\\ [/tex]

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Answer:

C

Step-by-step explanation:

15% is $3.00 not $0.30

The measure of the arc NST will be the largest one. Then the correct option is C.

Let r be the radius of the sector and θ be the angle subtended by the sector at the center. Then the arc length of the sector of the circle will be

Arc = (θ/2π) 2πr

If the central angle of the arc is maximum, then the measure of the arc will be maximum.

The measure of the angle ∠NST is maximum. Then the measure of the arc NST will be the largest one.

Thus, the correct option is C.

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The 45-degree set square contains an angle of 90 degrees, and also 30/60 degree set square contains a right angle. The 45 degrees set square is utilised to draw vertical lines. With the help of set squares, we can sketch parallel lines and perpendicular lines, construct some standard angles, and so on.

Geometric tools are instruments utilised to draw different kinds of geometric shapes. In Maths, geometry is the most critical topic, in which we learn about the shapes of things. Different types of tools with different names are utilised to draw these geometric shapes while solving geometry problems.

Some of the most generally utilised geometric tools are:

Ruler

Compass

Protractor

Divider

Set-squares

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The solution of the system of equations y = 2x - 3.5 and x - 2y = -14 is (7, 10.5).

In the given question, we have to solve the solution to the system of equations

y = 2x - 3.5..................(1)

x - 2y = -14...............(2)

Now putting the value of y from the equation 1 in the equation 2.

x - 2(2x - 3.5) = -14

Now simplifying the expression using the distributive property

x - 4x + 7 = -14

-3x + 7 = -14

Subtract 7 on both side, we get

-3x = -21

Divide by -3 on both side, we get

x = 7

Now putting the value of x in the equation 1,

y = 2(7) - 3.5

y = 14 - 3.5

y = 10.5

Hence, the solution to the system of equations y = 2x - 3.5 and x - 2y = -14 is (7, 10.5).

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The complete question is:

What is the solution to the system of equations y = 2x - 3.5 and x - 2y = -14?

Answer:

see explanation

Step-by-step explanation:

using the identity

• tan A = [tex]\frac{sinA}{cosA}[/tex]

consider left side

cos A × [tex]\frac{1}{tanA}[/tex]

= cos A × [tex]\frac{1}{\frac{sinA}{cosA} }[/tex]

= cos A × [tex]\frac{cosA}{sinA}[/tex]

= [tex]\frac{cos^2A}{sinA}[/tex]

= right side

The required point D was moved to (–3, –2). Quadrilateral ABCD would then be a square.

A quadrilateral is a four-sided shape as given in the picture in question.

Here,
When we shift point D to (-3, -2),
then
it becomes AB = BC = DC = AD, implying that the quadrilateral ABCD becomes the square.

Thus, the required point D was moved to (–3, –2). Quadrilateral ABCD would then be a square.

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The leading coefficient is positive, the left side of the graph continues down the coordinate plane and the right side continues upward.

What is function ?

function can be defined in such a way that it relates an input to the output.

Given function y = x-3

The degree of the function means the highest power of the variable

Here, the degree is 1, it is odd.

The leading coefficient is 1, which is positive.

By taking sample values of x, we get values of y with the graph as shown

From the graph, we can say that the degree of the function is odd, so the ends of the graph continue in opposite directions

Because the leading coefficient is positive, the left side of the graph continues down the coordinate plane and the right side continues upward.

The following describes the function x-3  that the degree of the function is odd, so the ends of the graph continue in opposite directions.

Hence,  the leading coefficient is positive, the left side of the graph continues down the coordinate plane and the right side continues upward.

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A right angle is defined as an angle that measures exactly 90 degrees.

To prove this:

This definition of a right angle has been established by mathematical convention, and it is widely accepted and used in mathematics and geometry. The reason for this is that a right angle is the most convenient and natural angle to use as a standard unit of measure for angles.

One reason is that a right angle is easy to construct and measure. A right angle can be created by using a square or a set square, which are simple and inexpensive tools. Also, right angles are found in many natural and man-made objects, such as corners of walls and buildings, which makes them easy to recognize.

Another reason is that a right angle is a fundamental building block in Euclidean geometry, and it is used to define other geometric concepts such as parallel lines and perpendicular lines. The properties of a right angle make it a useful tool for solving geometric problems and for understanding the relationships between angles and shapes.

In summary, the 90 degrees definition of a right angle is a mathematical convention that is widely accepted due to its convenience, natural appearance in many objects, and its importance in Euclidean geometry.

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Answer:

64

Step-by-step explanation:

56+58497657=875845455*-88787887879=5545426464

Answer: -87

Step-by-step explanation:  -(−5)² + 9(−5) − 17 =

-25 - 45 - 17  = -87

Answer:

f(x)= 3

Step-by-step explanation:

If f(x) is equal to -[tex]x^{2}[/tex]+9x-17 and f(-5)

You will substitute -5 where you see all the x's

-(-5)[tex]^{2}[/tex]+9(-5)-17

That will equal to

-25+45-17

Combine all the like terms

This will lead you to answer 3

So, f(x) =3

The numerical value of both the mole and Avagadro’s number is 6.022 x 10²³.

The Avogadro constant, A, is the number of particles (such as atoms, molecules, or ions) in one mole of something. Its value is modernly defined as exactly 6.022 140 76 × 10²³. (As it is a pure number, it has no units.)

So, in 1 mol of helium, which has a mass of (very close to) 4 g, there are A

atoms; in 1 mol of sucrose, with a mass of 342 g, there are A molecules.

We can have moles of other kinds of things, including subatomic particles. The amount of charge known as the faraday is the charge of one mole of electrons (A of them; about 96 500 C).

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Let u and v be a vectors. Then u can be broken up into two components, r and s such that r is parallel to v and s is perpendicular to v.

The component of u perpendicular to v is referred to as s, while r is referred to as the projection of u onto v. Then, u v = u1v1 + u2v2 + + unvn is the dot product of u with v.

Keep in mind that u v is defined when u and v have the same number of components and that the dot product of two vectors is a scalar. Though the dot product is a union of two vectors, the outcome is not a vector, which is an intriguing observation.

In particular, u (v w) makes no sense if u, v, and w are vectors because v w is a scalar. Before confirming that the dot product has the desired geometric characteristics, we'll mention.

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When given vector u = (1, 2) and v = (1, -4), Then the value of 4u + 3v = ⟨7, -4⟩, graph in attachment.

The component of u perpendicular to v is referred to as s, while r is referred to as the projection of u onto v. Then, u v = u1v1 + u2v2 + + unvn is the dot product of u with v.

Keep in mind that u v is defined when u and v have the same number of components and that the dot product of two vectors is a scalar. Though the dot product is a union of two vectors, the outcome is not a vector, which is an intriguing observation.

Given u = (1, 2) and v = (1, -4),

4u + 3v = 4(1, 2) + 3(1, -4)

= (4, 8) + (3, -12)

= ⟨4 + 3, 8 + (-12)⟩

= ⟨7, -4⟩

Thus, 4u + 3v = ⟨7, -4⟩

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The mass of sugar in 1 bottle is 1.65kg.

The equation that represents the information in the question is:

Total kg of sugar bought = total kg of the bottes + sugar left over

Total kg of sugar bought = (number of bottles x mass of sugar in one bottles + sugar leftover

8.6 = (5 x s) + 0.35

8.6 = 5s + 0.35

In order to determine the value of s, take the following steps:

Combine and add similar terms together:

8.6 - 0.35 = 5s

8.25 = 5s

Divide both sides of the equation by 5

s = 8.25 / 5

s = 1.65 kg

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The given expressions are the results of applying the function f to a value that is being multiplied by -3 or 3.

f(-3x) means that the function is applied to -3x, in this case the output is -3f(x)

f(3x) means that the function is applied to 3x, in this case the output is 3f(x)

It should be noted that the function f(x) could be any type of function and the output depends on the function's definition.

Answer: 3x^2

Step-by-step explanation:

e2023

Answer:

read my explanation because this will take a while to put in an answer and explain.

Step-by-step explanation:

slope: 3x

y-intercept: 48.

equation: y=48-3x

we get this from reading the question.

y=48-3x is your equation! it initially starts at 48, and everytime the hour changes it decreases by 3.

for the table:

0 - 48           5 - 33

1 - 45            6 - 30

2 - 42            7 - 27

3 - 39            8 - 24

4 - 36

the graph you could have filled by yourself, but here:

and when you are done, don't forget to connect the points! i didn't do it because i had to plot them and the line would override it.

Two matrices are row equivalent if they can be transformed into each other using elementary row operations.

Elementary row operations are operations such as the addition or subtraction of two rows, the multiplication or division of a row by a non-zero constant, or the interchange of two rows. Row equivalent matrices are equal in terms of row space, meaning any linear combination of the rows of one matrix will yield the same linear combination of the rows of the other matrix. An example of two row equivalent matrices is given below:

Matrix A =

[tex]\begin{bmatrix} 1 & 2 & 3 \\4 & 5 & 6 \end{bmatrix}[/tex]

Matrix B =

[tex]\begin{bmatrix} 1 & 2 & 3 \\2 & 3 & 4 \end{bmatrix}[/tex]

These matrices are row equivalent because adding the first row of Matrix A to the second row of Matrix B yields Matrix A. To show this mathematically, let row 1 of Matrix A be represented as r1, and row 2 of Matrix B be represented as r2. We can then say that r2 + r1 =

[tex]\begin{bmatrix} 1 & 2 & 3 \\6 & 8 & 10 \end{bmatrix}[/tex]

which is equal to Matrix A.

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C = 300000

a = -0.07

The correct interpretation of x is OD. The variable x represents the number of years after 2000.

Answer:

Step-by-step explanation:

The exponential decay formula for this situation is

[tex]y=300,000(.93)^x[/tex]

where 300,000 is the initial value, .93 is decay rate (100% - 7% = 93% which is .93 as a decimal), and x represents the number of years after the year 2000. B is your answer.

Answer:

-64x^6

Step-by-step explanation:

The total area of the shape is equal to 102 cm².

Mathematically, the area of a rectangle can be calculated by using this formula:

A = LW

Where:

Next, we would determine the area of this irregular shape in parts as follows;

Area of rectangle 1 = 15 × 6

Area of rectangle 1 = 90 cm²

Area of rectangle 2 = 4 × 3

Area of rectangle 2 = 12 cm²

Total area of irregular shape = 90 + 12

Total area of irregular shape = 102 cm²

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The APR if the finance terms are $21.99 per week for 52 weeks is 83.48%. Hence option 4 is correct.

The annual percentage rate, or APR, is the interest rate that is charged on a loan balance that is still outstanding. The expected cost of the annual fees connected with a certain sort of borrowing is what the APR conceptually reflects.

APR is a commonly used formula by lenders that enables borrowers to compare various loan choices. The stated interest rate on a loan is typically insufficient on its own to help borrowers choose the best loan option.

A loan with a low stated interest rate could also have significant costs attached that should not be disregarded. The best alternative might be a loan with a smaller fee structure and a higher advertised interest rate. APR is calculated as (Periodic Interest Rate x 365 Days) x 100 i.e.

[tex]$\mathrm{APR=\left(\left(\frac{\frac{Fees+Interest}{Principal}}{n} \right) \times 365 \right) \times 100}[/tex]

​where:

Interest = Total interest paid over life of the loan

Principal = Loan amount

n = Number of days in loan term

Fees = 0

​Interest = 2​Interest = $519.48

Principal = $624.00

n = 52 × 7 = 364 days

Plug the data in the formula:-

[tex]$\mathrm{APR=\left(\left(\frac{\frac{0+519.48}{624}}{364} \right) \times 365 \right) \times 100}[/tex]

APR = 83.48%

Thus, The APR if the finance terms are $21.99 per week for 52 weeks is 83.48%. Hence option 4 is correct.

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The values of a and b  for the given equation  are 25,-25

What is Quadratic equation ?

Quadratic equation can be defined as the equation which is in the form of ax^2+bx+c = 0 .

Given ,

equation x^3 - 625 x  = 0

x^3 - 625x = 0

taking x common

x(x^2 - 625 ) = 0

x^2 - 625 = 0

(x+25 ) (x-25) = 0

It is in the form of a2-b2

hence it is equals to a+b * a-b

x = 25,-25 .

Hence, The values of a and b are 25,-25 respectively for the given equation.

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Answer:4

Step-by-step explanation:12/3=4

The 4 laws of logarithms are product property, division property, power property and change of base property.

Product property - According to this principle, multiplying two logarithmic numbers is equivalent to adding their individual logarithms.

Division property - The difference between each logarithm is equivalent to the division of two logarithmic values.

Power rule/Exponential property - According to the exponential rule, the exponent times the logarithm of m's logarithm is equivalent to m's logarithm with a reasonable exponent.

Change of base property - A logarithm in one base is changed to a logarithm in another base using the change of base rule.

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Answer:

L = 53.37 cm

Step-by-step explanation:

We have the relationship

M ∝ L³

We can rewrite this as an equation:
M = k · L³

where k, a constant, is known as the constant of proportionality

Given M = 100 kg when L = 20, we get

100 = k · 20³

100 = k · 8000

k = 100/8000 = 0.0125

If M = 1900 kg and k = 0.0125 we can plug in these values to get

1900 = 0.0125 L³

==>  L³ = 1900/0.0125

==> L³ = 152000

Therefore L = ∛152000

L = 53.36803 or

L = 53.37 cm  rounded to 2 DP

Answer:

380.00

Step-by-step explanation:

M=KL

100=20K

K=5

M=5L

1900=5L

L=380

The number of students are enrolled in PE be 447.

A percentage expressed in decimal form is a proportion, but a proportion is not always a % expressed in decimal form.

A fraction expressed in a specific way is called a decimal. For example, you can write the fraction as 0.5 instead of 1/2, with the zero in the ones place and the five in the tenths place. The word decimal is derived from the Latin word decimus, which means tenth, and the number 10 (or decem).

From the given information, we get 30% of 1490

Convert 30% into a decimal and multiply by 1490

Convert 30 % into a decimal form: 0.3

Multiply 0.3 by 1490

= 0.3 × 1490

Simplifying the values, we get

0.3 - 1490

= 447

Therefore, the number of students are enrolled in PE be 447.

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A given linear model shows negative correlation.

The correlation coefficient describes how one variable moves in relation to another. A positive correlation indicates that the two move in the same direction, with a value of 1 denoting a perfect positive correlation. A value of -1 shows a perfect negative, or inverse, correlation, while zero means no linear correlation exists.

Given that, a researcher fit a linear model to her data and calculated the correlation coefficient to be -0.29.

Here, a linear model shows negative, or inverse, correlation.

Therefore, a given linear model shows negative correlation.

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Answer:

1. A. -1.43 corresponds to an area of approximately 0.0637 under the normal curve.

B. 0.58 corresponds to an area of approximately 0.7295 under the normal curve.

C. -1.55 corresponds to an area of approximately 0.0633 under the normal curve.

D. For z>1.34, the area under the normal curve is approximately 0.0916.

--------

2. A. The 35th percentile corresponds to a z-score of approximately -0.48

B. The first quartile (Q1) corresponds to a z-score of approximately -0.67

C. For 12% of the data to fall above it, the z-score would be approximately 1.28

----------

3.  A. To find the area under the curve for x< 31 inches, we need to convert 31 inches to a z-score using the formula: z = (x - mean) / standard deviation. For this case, z = (31 - 36) / 10 = -0.6, the area under the curve for this is 0.2744

B. To find the area under the curve for x> 49 inches, we need to convert 49 inches to a z-score, the z-score is (49 - 36) / 10 = 1.3, the area under the curve for this is 0.0968

C. The area under the curve for x = 40 inches is 0.3520

D. To find the height at which 70% of 5 year olds are below it, we need to use the inverse standard normal calculator, which gives us a z-score of 0.84162, we can then use this z-score to find the corresponding x value by using the formula x = mean + (z-score * standard deviation) which in this case would be 36 + (0.84162*10) = 42.4 inches

The area of the square = 4π^2 * (38.5/π) cm^2 (circumference of circle used as side of square).

What is circumference of circle ?

Circumference is the distance around the edge of a circle. It can be calculated using the formula: C = 2πr, where C is the circumference and r is the radius of the circle.

We can use the formula C = 2πr to find the circumference of the original circle, where C is the circumference and r is the radius of the circle.

Given that the wire encloses an area of 38.5 cm square, we can use the formula A = πr^2 to find the radius of the circle.

A = 38.5 cm^2

πr^2 = 38.5 cm^2

r^2 = 38.5/π cm^2

r = (38.5/π)^0.5 cm

Now that we know the radius of the circle, we can find the circumference using the formula:

C = 2πr

Now, we can find the area of the square by squaring the length of one side of the square which is the circumference of the original circle

Area of square = C^2

Therefore, The area of the square = 4π^2 * (38.5/π) cm^2 (circumference of circle used as side of square).

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Given that the wire encloses an area of 38.5 cm square, we can use the formula A = πr^2 to find the radius of the circle.

A = 38.5 cm^2

πr^2 = 38.5 cm^2

r^2 = 38.5/π cm^2

r = (38.5/π)^0.5 cm

C = 2πr

Area of square = C^2

The area of the square = 4π^2 * (38.5/π) cm^2 (circumference of circle used as side of square).