A security lighting system spreads its illumination over an angle of 40° to a distance of 48 m. Convert the angle to radians and use the result to find the sector area that is lit, correct to 3 significant decimal places.

Answer:

f = -8

Step-by-step explanation:

We know the slope formula is:

[tex]m = \frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

Because we already know the slope and three other points, we can let point f represent y2 and solve for it:

[tex]\frac{1}{8}=\frac{f-(-6)}{-8-8}\\ \frac{1}{8}=\frac{f+6}{-16}\\ -2=f+6\\ -8=f[/tex]

The total amount of its donated funds is  43[tex]\frac{23}{29}[/tex].

Given,

In the question:

A charity received a donation of 12.7 million.

If this represents 29% of the charity's donated funds.

To find the total amount of its donated funds.

Now, According to the question:

Based on the given conditions:

Received donation is = 12.7 million

Charity Funds = 29%

Formulate;

12.7 ÷ 29%

12.7/29%

= 12.7/0.29

Multiply both the numerator and denominator with the same integer

= 1270/29

= 43[tex]\frac{23}{29}[/tex]

Hence,  The total amount of its donated funds is  43[tex]\frac{23}{29}[/tex].

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Answer:

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

-3x

2y

-6

12

-4y

Expressing the complex number 2i(i +3) in a + bi form gives -2 + 6i

Complex numbers are numbers that are expressed as a + ib,

where a and b are real numbers and i is an fictitious number called "iota."

i has the value (-1). As an illustration, the complex number 2+3i is made up of the real number 2 (Real number) and the imaginary number 3i.

The multiplication of 2i(i + 3)

= 2i^2  + 6i

= -2 + 6i

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The integral Value is [tex]\pi[/tex] or 22/7 or 3.14

Integral Value: It is a value which is obtained after integrating.

Triple Integral: Integral function of a three variable over a region in R³ ( real number 3D space) are called triple integral.

            For x = 2,

              x = 2y² + 2z²

equating those two functions, we get,

                         1 = y² + z²

that gives -1≤ y≤ 1 and -(√x/2 -y²) ≤ z≤ (√x/2 - z²) and  2y²≤ x ≤ 2

so after the integration, the form is quite complicated to solve so use the following form instead letting x = 2 and x = 2y² + 2x², so that the integral became

      ∫∫∫ 2y² + 2z² dx dA which becomes

     ff (2 - 2y² - 2z²) da now use polar coordinate where y= 1 cos Ф          and z = 1 sinФ

now, integral becomes

       2 ∫¹₀ (1- r²) r dr dФ

= 4[tex]\pi[/tex] ( r²/2 - r⁴ /4)¹ ₀

= 4[tex]\pi[/tex] ( 1/2 - 1/4)

= 4[tex]\pi[/tex] × 2 - 1/4

= [tex]\pi[/tex]

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Answer:

$693.80

Step-by-step explanation:

Answer:

15%

Step-by-step explanation:

180/1200 × 100% = 15%

Answer:

h

Step-by-step explanation:

p depends on h

h won't change according to p

p will change according to h

Answer:

Step-by-step explanation:

should be h

The likely error was that B. Your classmate multiplied the exponents

Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both. Addition, subtraction, multiplication, and division are all possible mathematical operations.

In this case, your teacher asks the class to evaluate the expression (2^3)^1. This will be:

= 2³

= 8

The fact that the person got 16 means the person multiplied it and then joined 1.

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The equation in point-slope form is y=4x-25.

A line passing through the point (x 1, y1) has a slope of "m," and its point slope form is given by the equation y - y1=m (x - x1).

A horizontal line's equation is of the form y=b when it passes through the points (a, b).

Step 1: Write down the  line's slope, "m," and the coordinates (x 1, y 1) of the point that is given and is on the line.

Step 2: Replace the given values in the calculation for the point slope: y - y1 = m. (x - x1).

Point-slope form is y=mx+b.

To get the equation of the line in standard form, simplify in step three.

Given, m(slope)= 4.

The point is (8,7)= (x1,y1)

y-7=4(x-8)

y-7=4x-32

y=4x-32+7

y=4x-25

Hence, the equation in point-slope form is y=4x-25.

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The number of laddus who were there at the beginning Rohan has is 48.

Here we have to find the number of laddu Rohan at the beginning.

Let x be the number of laddu Rohan have.

He gave on the first day = x × 1/3= x/3

The leftover laddu = x - x/3

= 2x/3

Laddu is given on the second day = 2x/3 × 1/4

= x/6

Here we know that the laddu given by Rohan is 8,

So

x/6 = 8

x = 48

Therefore we get the number of laddu Rohan has 48.

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Answer:

if there are at least 9 chairs at each table then yes

Step-by-step explanation:

this question might be something

so lets divide 145 by 18 to see how many seats at each table is required for everyone to fit

145/18

8.05555

and since we cant have 0.555 of a chair or person we round up to the nearest whole chair which is 9

hopes this helps please mark brainliest

Answer: x=1, y=2

Step-by-step explanIation:

I hope this is right  :)

Answer A, B, D

Step-by-step explanation:

The volume of the right cone is 7 units.

The radius of a cone can be found as follows:

The volume of the right cone is 245π unit³. The height of the right cone is 15 units.

Therefore,

volume of a right cone = 1 / 3 πr²h

where

Hence,

volume of the right cone = 245π

h = 15 units

Hence,

245π = 1 / 3 × π × r²  × 15

divide both sides by π

245 = 15 / 3 r²

245 = 5r²

r² = 245 / 5

r = √49

r = 7 units

Therefore,

radius of the cone = 7 units

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The solution set for inequality 3|x + 1| < 9 is option(C).

What is inequality?

A relationship between two expressions or values that is not equal to each other is known as an "inequality" in mathematics. The "not equal symbol (≠)" is typically used to indicate that two values are not equal that is there is inequality.

The equals sign in the equation-like statement 5x - 4 > 2x + 3 has been replaced by an arrowhead. This is a prime instance of inequality. This indicates that the left half, 5x - 4, is larger than the right part, 2x + 3, in the equation.

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The distance between the two points in simplest radical form is 5.

The length of the line segment connecting two points in a plane is the distance between them. The formula for calculating the distance between two places is typically d=((x₂ - x₁)² + (y₂ - y₁)²). This formula is used to calculate the distance between two locations on a coordinate plane or the x-y plane.

In geometry, distances are usually positive unless the points coincide.  Consider two points A(a, b) and B to obtain the formula for the distance between two points in the plane (c, d).

The linear distance between two points is equal to the square root of the sum of the squared x-axis and y-axis distances. To continue with the example, the distance between (3,2) and (7,8) is sqrt (52), or 7.21 units.

Given,

The two points are (7,1), (4,5)

Distance between two points

AB=√(x₂-x₁)²+(y₂-y₁)²

AB=√(4-7)²+(5-1)²

=√3²+4²

=√9+16

=√25

=5

Distance between two points=5

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The distance from coordinates Point p (5, 7) to coordinates (–2, 1) and (4, 1) in line n are  9.21 units and 6.08 units respectively.

The distance between two points is defined as the length of the line segment between two places representing their distance.

Line n contains points (–2, 1) and (4, 1). Point p has coordinates (5, 7).

The distance from coordinates p (5, 7) to coordinates (–2, 1) in line n will be

⇒ √[(-2-5)² + (1-7)²]

⇒ √[(-7)² + (-6)²]

⇒ √[49 + 36]

⇒ √85

⇒ 9.21 units

The distance from coordinates p (5, 7) to coordinates (4, 1) in line n will be

⇒ √[(4-5)² + (1-7)²]

⇒ √[(-1)² + (-6)²]

⇒ √[1 + 36]

⇒ √37

⇒ 6.08 units

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Hence in 1990 town a will have a population of 90518 and town B will have a population of 9051.85.

What is the arithmetic operation?

The four fundamental operations of arithmetic are addition, subtraction, multiplication, and division of two or more quantities. Included in them is the study of numbers, especially the order of operations, which is important for all other areas of mathematics, including algebra, data management, and geometry. The rules of arithmetic operations are required in order to answer the problem.

To calculate the size of town A in 1990, multiply the current population by 2000 + (200x40) and add 40 years to account for population growth.

To work out how big town B will be in 1990

We have to use the equation 2000 X 1.1^40 because to work out plus 10 percent you need to do 1.1 and do it to the power of 40 for how many years

So 2000* 45.259 = 90518. for 2000people of A Town

And 200* 45.259 = 9051.8 for 200people of B Town

Hence in 1990 town, a will have a population of 90518 and town B will have a population of 9051.85

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Answer:

the answer is because u need trust me6

Using inequality the number of 105  of 120-kilogram crates that can be loaded into the shipping container.

What is inequality?

A difference between two values indicates whether one is smaller, larger, or simply not equal to the other. In mathematics, the term "inequality" refers to a relationship between two expressions or values that is not equal to one another.

The greatest weight that container can hold = 27500

Shipment weight already  in the container =14900

Amount of weight that may be loaded = 27500 - 14900 = 12600

Weight of each crates = 120 kg

Let x be the maximum number of 120 kg crates that can be loaded to the container then,

Weight of 'x' number of 120 kg crates = 120x

Therefore, the required inequality is as follows

=>120x< 12600

(since the maximum amount of weight of crates that can be put in the container should be less than or equal to the total weight of the maximum number of crates that can be loaded into the container).

Then the inequality is ,

=> x [tex]\leq \frac{12600}{120}[/tex]

=> x ≤ 105.

Thus, a maximum of 105 crates can be loaded into the container.

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Answer:

[tex] \huge{ \bold{y - 3 = 7(x +9)}}[/tex]

Step-by-step explanation:

The equation of a line in point-slope form is represented by the formula

[tex]y - y_1 = m(x - x_1)[/tex]

where

(x1, y1) is the point and m is the slope

From the question the point is (-9,3) and m = 7

So we substitute the given variables into the formula and solve

We have

[tex]y - 3 = 7(x - - 9) \\ y - 3 = 7(x + 9)[/tex]

Hope this helps you

The sentence is true because the expressions are equivalent.

An equation can be represented by a linear function. The standard form for the linear equation is: y= mx+b , for example, y=7x+3. Where:

m= the slope.

b= the constant term that represents the y-intercept

For the given example: m=7 and b=3.

The linear equations are considered equivalent when they are equal.

The given equations are 5y+4−3y = 2y+4. Solving theses equations, you have:

5y+4−3y = 2y+4

2y+4 = 2y+4

Like the both equation present the slope and the constant term equal, the expressions are equivalent.

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(1) The explicit formula and the 21st term for the first sequence are:

aₙ = 10 - 5n and a₂₁ = -95

(2) The explicit formula and the 21st term for the second  sequence are:

aₙ = 1.5n + 1.5 and a₂₁ = 33

A sequence in which the difference between any two consecutive terms is the same is known as an arithmetic sequence.

(1)

The given sequence is 5, 0, -5, -10,...

Note the difference between two consecutive terms of the sequence is the same, which is -5.

Therefore, the sequence is an arithmetic sequence with a common difference of d = -5.

The [tex]n^{th}[/tex] term of an arithmetic sequence is given by:

aₙ = a₁ + (n-1)d

Substitute a₁ = 5 and d= -5 into the equation,

aₙ = 5+ (n-1)(-5)

   = 5 - 5n + 5

aₙ = 10 - 5n

To find the 21st term, substitute n = 21 into the above equation,

a₂₁ = 10 - 5n

a₂₁ = 10 - 5(21)

a₂₁ = 10 - 105

a₂₁ = -95

Hence, the explicit formula and the 21st term for the first sequence are:

aₙ = 10 - 5n and a₂₁ = -95

(2)

The given sequence is 3, 4.5, 6, 7.5, 9,...

Note that the difference between two consecutive terms is 1.5, therefore, the sequence is an arithmetic sequence with a common difference of

d = 1.5.

The [tex]n^{th}[/tex] term of an arithmetic sequence is given by:

aₙ = a₁ + (n-1)d

Substitute a₁ = 3 and d= 1.5 into the equation,

aₙ = 3 + (n-1)1.5

aₙ = 3+1.5n-1.5

aₙ = 1.5n+1.5

To find the 21st term, substitute n = 21 into the above equation,

a₂₁ = 1.5(21) + 1.5

a₂₁ = 31.5 + 1.5

a₂₁ = 33

Hence, the explicit formula and the 21st term for the second  sequence are:

aₙ = 1.5n + 1.5 and a₂₁ = 33

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The total cost to the nearest cent = 2675 cents.

Given that:

The cost of backpack = $25

Tax = 7%

To calculate the total cost, we can also approach the problem in two ways:

1). Multiply the amount by 7% ($25 x 0.07 = $1.75, rounded up to the nearest cent at 175 cents or $1.75). This will tell us how much tax we will have to pay. Add this to the cost to get the total amount one has to pay (25 + 1.75 = $26.75 or 2675 cents).

2). Multiply the amount by 107%. This includes both steps from 1 in one step. ($25 x 1.07 = $26.75; $26.75 rounded to dollars).

We know that,

1 dollar ($) = 100 cents

Multiply both sides by 26.75

$ 26.75 = 2675 cents.

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The quadrilateral above is a parallelogram.

A parallelogram is a quadrilateral with opposite sides equal to each other. Opposite sides of a parallelogram is parallel to each other.

The sum of angles in a parallelogram is 360 degrees.

Opposite angles of a parallelogram is congruent to each other.

Adjacent angles of a parallelogram sum up to 180 degrees. This means adjacent angles are supplementary.

Let's check if the Known adjacent angles of the quadrilateral is supplementary.

Therefore,

105 + 75 = 180 degrees.

Hence, the quadrilateral is a parallelogram.

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The distance between the point (-3,3) and (a, b) is;

⇒ d = √(a + 3)² + (b - 3)²

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

Two points are,

(-3,3) and (a, b)

Now,

The distance between the point (-3,3) and (a, b) is;

d = √(a - (-3))² + (b - 3)²

d = √(a + 3)² + (b - 3)²

Thus, The distance between the point (-3,3) and (a, b) is;

⇒ d = √(a + 3)² + (b - 3)²

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For given equation x_(n+1) = ((x_n)^3 - 5)/10,

a) (i) x2 = -0.6

(ii) x3 = -0.5216

b)  the solution to 6 decimal places, x5 = -0.513594

Given equation, x_(n+1) = ((x_n)^3 - 5)/10

also, x1 = -1

a)

(i) we need to find the value of x2

Substitute n = 1 in given equation,

x_(1+1) = ((x1)^3 - 5)/10

x_2 = [(-1)^3 - 5]/10

x_2 = (-1 - 5)/10

x2 = -6/10

x2 = -0.6

(ii) we need to find the value of x3

Substitute n = 2 in given equation,

x_(2+1) = ((x2)^3 - 5)/10

x3 = [(-0.6)^3 - 5]/10

x3 = (-0.216 - 5)/10

x3 = -5.216/10

x3 = -0.5216

b)

We need to find the solution to 6 decimal places.

First we find the value of x4.

Substitute n = 3 in given equation,

x_(3+1) = ((x3)^3 - 5)/10

x4 = [(-0.5216)^3 - 5]/10

x4 = (-0.1419 - 5)/10

x4 = -5.1419/10

x4 = -0.51419

Substitute n = 4 in given equation,

x_(4+1) = ((x4)^3 - 5)/10

x5 = [(-0.51419)^3 - 5]/10

x5 = (-5.13595)/10

x5 = -0.513594

Therefore, for given equation x_(n+1) = ((x_n)^3 - 5)/10,

a) (i) x2 = -0.6

(ii) x3 = -0.5216

b)  the solution to 6 decimal places, x5 = -0.513594

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