find x using the trigonometric function

The speed of the boat in still water is 3 times the speed of the river current.

To find the speed of the boat in still water, we can use the concept of relative motion and the given information about the boat's speed while traveling upstream and downstream.

Let's assume the speed of the boat in still water is "v" km/h, and the speed of the river current is "c" km/h.

When the boat is traveling upstream, it moves against the current, so its effective speed is reduced.

The boat's speed relative to the ground is given by (v - c) km/h.

Similarly, when the boat is traveling downstream, it moves with the current, so its effective speed is increased.

The boat's speed relative to the ground is given by (v + c) km/h.

According to the problem, the boat can travel 40 km upstream in the same time it would take to travel 80 km downstream.

Since time is constant in both cases, we can set up the following equation:

40/(v - c) = 80/(v + c)

To solve this equation, we can cross-multiply and simplify:

40(v + c) = 80(v - c)

40v + 40c = 80v - 80c

40c + 80c = 80v - 40v

120c = 40v

Dividing both sides by 40, we get:

3c = v.

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Answer:

Step-by-step explanation:

n=30

r=12

Plug into formula

you get:

1.7 in²

Remember to use the appropriate units for measurements when calculating surface area.

To find the surface area of an object, you need to calculate the total area of all its exposed surfaces. The method for finding the surface area will vary depending on the shape of the object. Here are some common shapes and their respective formulas:

1. Cube: The surface area of a cube can be found by multiplying the length of one side by itself and then multiplying by 6 since a cube has six equal faces. The formula is: SA = 6s^2, where s is the length of a side.

2. Rectangular Prism: A rectangular prism has six faces, each of which is a rectangle. To find the surface area, calculate the area of each face and add them up. The formula is: SA = 2lw + 2lh + 2wh, where l, w, and h represent the length, width, and height of the prism.

3. Cylinder: The surface area of a cylinder includes the area of two circular bases and the area of the curved side. The formula is: SA = 2πr^2 + 2πrh, where r is the radius and h is the height.

4. Sphere: The surface area of a sphere can be found using the formula: SA = 4πr^2, where r is the radius.

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Answer: The correct ratio to represent the ratio of paperback books to hardcover books is 5:3.

The torque experienced by the rigid body is -17.10375 k N·m.

To determine the torque experienced by a rigid body when a force is applied, we need to calculate the cross product between the force vector and the radius vector from the point of application of the force to the point of rotation.

Since a force F = (4.501 - 3.25) N is applied and the radius vector is r = (1.801 + 2.50j) m, where j is the imaginary unit, we can calculate the cross product using the formula:

Torque = r x F

The cross product between two vectors is calculated as follows:

Torque = (r_x * F_y - r_y * F_x)k

Where r_x and r_y are the components of the radius vector and F_x and F_y are the components of the force vector. Furthermore, k is a unit vector in the direction of the axis of rotation.

Substituting the given values, we have:

Torque = ((1.801 * -3.25) - (2.50 * 4.501))k

Calculating the cross product:

Torque = (-5.85125 - 11.2525)k

Simplifying:

Torque = -17.10375k

Therefore, the torque experienced by the rigid body is -17.10375 k N·m.

The negative sign indicates that the torque is in the opposite direction to the axis of rotation. The magnitude of the torque is measured in newtons per meter (N·m) and represents the capacity of a force to produce a rotation in a rigid body around a specific axis.

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Answer:

If you are in Acellus trust me the answer is 394

Step-by-step explanation:

SA = 2 ( 2 x 12 ) + 2 ( 2 x 10 ) + ( 8 x 6 ) + 2 ( 3 x 8 ) + ( 3 x 6 ) + ( 12 x 16 )

SA = 48 + 40 + 48 + 48 + 18 + 192

SA = 394 square cm.

The parametric equation of the line passing through P1(2, 4, -3) and P(3, -1, 1) is:

x = 2 + t

y = 4 - 5t

z = -3 + 4t

To find the parametric equation of the line passing through points P1(2, 4, -3) and P(3, -1, 1), we can use the vector equation of a line.

Let's denote the direction vector of the line as d = (a, b, c). Since the line passes through P1 and P, the vector between these two points can be used as the direction vector.

d = P - P1 = (3, -1, 1) - (2, 4, -3) = (1, -5, 4)

Now, we can express the parametric equation of the line as follows:

x = x0 + at

y = y0 + bt

z = z0 + ct

where (x0, y0, z0) is a point on the line and (a, b, c) is the direction vector.

Let's choose P1(2, 4, -3) as the point on the line. Substituting the values, we get:

x = 2 + t

y = 4 - 5t

z = -3 + 4t

Therefore, the parametric equation of the line passing through P1(2, 4, -3) and P(3, -1, 1) is:

x = 2 + t

y = 4 - 5t

z = -3 + 4t

where t is a parameter that varies along the line.

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the correct scatter diagram that fits the given paired data is option A, as shown in the attached image.

The scatter plot that fits the given paired data is as follows:

Firstly, the data needs to be paired correctly: Systolic Blood Pressure | Diastolic Blood Pressure119                                        125131                                        130123                                        118118                                        142138                                        125131                                        128140                                        123Then the data pairs are plotted on a graph to create a scatter plot. It is a graph that shows the relationship between two sets of data. In this case, the Systolic blood pressure is on the horizontal axis (X-axis) and the Diastolic blood pressure is on the vertical axis (Y-axis).

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Step-by-step explanation:

h,k   center is  0,0 and radius is 8

(x-0)^2  + ( y-0)^2 = 8^2

x^2  + y^2  = 64

IM NOT SURE, DO YOU WANT ME TO WORK IT OUT FOR YOU?

Answer:

Step-by-step explanation:

(x^3 - 10x + K)/(X+3) = 6 GIVEN

for different values of x there are many possible values of k some i will show

when we substitute x=1

we get k=33

at x=2

weget k=42

so many values are possible for k

because there is no intervel in question which restrics us from taking different values of x or k so you take any value of x you will get different values of k

Answer:

the approximate population of the city after 14 years will be 7.96 thousand residents.

Step-by-step explanation:

to calculate the approximate population of the city after 14 years, we need to take into account the annual growth rate.

Given that the city's population grows by around 420 persons each year, we can calculate the total growth over 14 years by multiplying the annual growth rate by the number of years:

14 years × 420 persons/year = 5,880 persons

To find the approximate population after 14 years, we add the total growth to the current population:

2.08 thousand + 5.88 thousand = 7.96 thousand

The measure of the interior angle at vertex F is 72 degrees.

A hexagon is a polygon with six sides. The sum of the interior angles of a hexagon is equal to 720 degrees.

The angle of the hexagon is given in terms of x,

The sum of the angle is equal to 720 degrees

[tex]4\text{x}+4\text{x}+4\text{x}+4\text{x}+2\text{x}+2\text{x} = 720[/tex]

[tex]20\text{x} = 720[/tex]

[tex]\text{x} = 36[/tex]

[tex]\bold{2x = 72^\circ}[/tex]

Therefore, the measure of interior angle at vertex F is equal to 72 degrees.

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(a) To find the assets in 2011 using the given information: A. To find the assets in 2011, substitute 11 for x and evaluate to find A(x).

In 2011 the assets are about $669.6 billion

(b) To find the assets in 2016 using the given information: B. To find the assets in 2016, substitute 16 for x and evaluate to find A(x).

In 2016 the assets are about $931.5 billion.

(c) To find the assets in 2019 using the given information: B. To find the assets in 2019, substitute 19 for x and evaluate to find A(x).

In 2019 the assets are about $1135.4 billion.

Based on the information provided, we can logically deduce that the assets for a financial firm can be approximately represented by the following exponential function:

[tex]A(x)=324e^{0.066x}[/tex]

where:

For the year 2011, the cost (in billions of dollars) is given by;

x = (2011 - 2007) + 7

x = 4 + 7

x = 11 years.

Next, we would substitute 11 for x in the exponential function:

[tex]A(11)=324e^{0.066 \times 11}[/tex]

A(11) = $669.6 billions.

Part b.

For the year 2016, the cost (in billions of dollars) is given by;

x = (2016 - 2007) + 7

x = 9 + 7

x = 16 years.

Next, we would substitute 16 for x in the exponential function:

[tex]A(16)=324e^{0.066 \times 16}[/tex]

A(16) = $931.5 billions.

Part c.

For the year 2019, the cost (in billions of dollars) is given by;

x = (2019 - 2007) + 7

x = 12 + 7

x = 19 years.

Next, we would substitute 19 for x in the exponential function:

[tex]A(19)=324e^{0.066 \times 19}[/tex]

A(19) = $1135.4 billions.

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Answer:

The volume of the cylinder is 628.318530718

Step-by-step explanation:

The formula used to find the volume of a cylinder (v) is [tex]v = \pi r^2h[/tex], where r = radius and h = height. As the question says to keep the answer exact, we will be using pi as opposed to 3.14.

The radius is 5, and the height is 8. Plug these values into the equation and solve:

[tex]v =\pi *5^2*8[/tex]

[tex]v = 628.318530718[/tex]

So, the exact volume of the cylinder is 628.318530718. Rounded is 628.32

Answer:

200π or 628

Step-by-step explanation:

Note: your picture is not clear so I am assuming the height to be 8.

r = 5

h = 8

Volume = πr²h

= π * 5² * 8

= (25*8) π

= 200π

= 200*3.14

= 628

Answer:

D The base is 7 units and the height is 3 units.

Step-by-step explanation:

The answer is d I counted the width/base then the height/length and found answer.

33.) The volume of the given triangular prism would be= 36. That is option E.(NOTA)

To calculate the volume of a triangular prism, the formula that should be used is given as follows;

Volume= BH

where;

B= area of base = 1/2 × base×height

= 1/2×4×3

= 6

H= 6

Volume= 6×6= 36.

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Answer:

Step-by-step explanation:

Let's denote the length of the rectangle as 3x and the width as 2x, based on the given ratio.

The perimeter of a rectangle is given by the formula P = 2(length + width). In this case, we have:

P = 2(3x + 2x)

40 = 2(5x)

Now, let's solve for x:

40 = 10x

x = 40/10

x = 4

Now that we have the value of x, we can find the length of the rectangle:

Length = 3x = 3(4) = 12

Therefore, the length of the rectangle is 12.

Solution:

Formula: Total = Group 1 + Group 2 - Both + Neither

where:

- Total = total number of girls in the class (34)

- Group 1 = number of girls playing tennis (21)

- Group 2 = number of girls playing netball (18)

- Both = number of girls playing both games (what we want to find)

- Neither = number of girls playing neither game (0, since all the girls play at least one game)

Plugging in the values, we get:

34 = 21 + 18 - Both + 0

Simplifying:

34 = 39 - Both

Both = 39 - 34

Both = 5

Step-by-step explanation:

a number consists of digits in the place of certain values of the powers of 10.

2013 consists of a digit 2 in the thousands units position.

of a digit 0 in the hundreds units position.

of a digit 1 in the tens units position.

and of a digit 3 in the (single) units position.

so, to which power do we need to have this 3 ?

I think you made a mistake there. you say we need it to the power of 2013 ?

3²⁰¹³ = 2.786671338...e960 =

= 2.786671338... × 10⁹⁶⁰

Step-by-step explanation:

Parallel to the x-axis means it is just a horizontal line with the value being the y-coordinate of the point:

y = -2

Answer:

y=-2

and m=0 must be your answer

Step-by-step explanation:

as line is parallel to x axis its slope will be zero as it does not have any definite x coordinate

so

equation of line is y-y'=m(x-x')

so m=0 m is slope

y'=-2 and x'=4

so by substituting the values

y+2=0

so y=-2

and m=0 is your answer

Answer:

Step-by-step explanation:

12

The inverse of the function f(x) = 2·x - 4, is the option;

g(x) = (1/2)·x + 2

The completed statement is; Because f(x) is one to one, its inverse is a function

The inverse of a function is one that takes the output of a specified function to produce the input of the function.

The inverse of the function f(x) = 2·x - 4, can be found by making x the subject of the function equation as follows;

f(x) = 2·x - 4

f(x) + 4 = 2·x

2·x = f(x) + 4

x = (f(x) + 4)/2 = f(x)/2 + 2

x = f(x)/2 + 2

Substituting f(x) = x and x = g(x) in the above equation, we get;

g(x) = x/2 + 2

The function f(x) = 2·x - 4 is a one to one function, and the condition of a one to one function guarantees that the inverse of the function is also a function

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Answer:

A

Step-by-step explanation:

is one to one

The total petty cash expenditures would be =$130.84

To calculate the petty cash expenditures, the following is added up as follows;

The cost for stamp = $12.50

The cost for coffee supplies = $25.19

The cost for pizza delivery = $15.50

The cost for white board markers = $20.00

The cost for sympathy greeting card= $5.78

The cost of flowers for Jean's retirement farewell = $39.87

The cost of courier = $12.00

Therefore the total petty cash expenditures would be= 12.50+25.19+15.50+20+5.78+39.87+12= $130.84

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Answer:

This is an equation of a parabola.

[tex](y+6)^2=4(x+1)[/tex]

Step-by-step explanation:

A conic section is a curve obtained by the intersection of a plane and a cone. The three major conic sections are parabola, hyperbola and ellipse (the circle is a special type of ellipse).

The standard equations for hyperbolas and ellipses all include x² and y² terms. The standard equation for a parabola includes the square of only one of the two variables.

Therefore, the equation y² - 4x + 12y + 32 = 0 represents a parabola, as there is no x² term.

As the y-variable is squared, the parabola is horizontal (sideways), and has an axis of symmetry parallel to the x-axis.

The conic form of a sideways parabola is:

[tex]\boxed{(y-k)^2=4p(x-h)}[/tex]

where:

To write the given equation in conic form, we need to complete the square for the y-variable.

Rearrange the equation so that the y-terms are on the left side:

[tex]y^2 + 12y = 4x - 32[/tex]

Add the square of half the coefficient of the y-term to both sides of the equation:

[tex]y^2 + 12y+\left(\dfrac{-12}{2}\right)^2 = 4x - 32+\left(\dfrac{-12}{2}\right)^2[/tex]

    [tex]y^2 + 12y+\left(-6\right)^2 = 4x - 32+\left(-6\right)^2[/tex]

         [tex]y^2 + 12y+36 = 4x - 32+36[/tex]

         [tex]y^2 + 12y+36 = 4x +4[/tex]

Factor the perfect square trinomial on the left side of the equation:

[tex](y+6)^2=4x+4[/tex]

Factor out the coefficient of the x-term from the right side of the equation:

[tex](y+6)^2=4(x+1)[/tex]

Therefore, the equation of the given conic section in conic form is:

[tex]\boxed{(y+6)^2=4(x+1)}[/tex]

where:

The conic section of the equation y² - 9x + 12y + 32 = 0 is a parabola

The given equation is

y² - 9x + 12y + 32 = 0

The above equation is an illustration of a parabola equation

The standard form of a parabola is

(x - h)² = 4a(y - k)²

Where

(h, k) is the center

While the general form of the equation is

Ax² + Dx + Ey + F = 0

In this case, the equation y² - 9x + 12y + 32 = 0 takes the general form

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Answer:   D

Step-by-step explanation:

Similar means that if you multiplied all of the sides by the same number it would proportionally be that much larger.

D)    4x2=8

       12x2=24

       15x2=30      All sides were multiplied by 2 so D is similar

Answer:

D)

Step-by-step explanation:

Figure D is similar in all mesurements .

...

The equation 2y + 8x - 2 = 0 will satisfy the condition of having an infinite number of solutions when graphed with the given equation.

To form a system of equations that has an infinite number of solutions when graphed with the given equation, we need to find an equation that represents the same line or is a multiple of the given equation.

The given equation is: y + 4x - 1 = 0

To find an equation with an infinite number of solutions, we can multiply the given equation by a non-zero constant.

Let's multiply the given equation by 2:

2(y + 4x - 1) = 2(0)

2y + 8x - 2 = 0

The equation 2y + 8x - 2 = 0, when graphed with the given equation y + 4x - 1 = 0, will form a system that has an infinite number of solutions. The two equations represent the same line, just with different coefficients.

Therefore, the equation 2y + 8x - 2 = 0 will satisfy the condition of having an infinite number of solutions when graphed with the given equation.

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