Find the length of the third side. If necessary, round to the nearest tenth. 12 13

The spherical coordinates of the given rectangular coordinates are (10, 0, 60).

The cartesian coordinate or rectangular coordinates describes the location of a point in space using an ordered triple where each coordinate represents a distance. The spherical coordinate system describes the location of a point in space using an ordered triple where coordinate describes one distance and two angles. In the spherical coordinate system, a point is represented by the ordered triple (ρ, θ, φ).

The equations which are used to convert from rectangular coordinates to spherical coordinates are:

ρ^2=x^2+y^2+z^2

tan⁡〖θ= y/x〗

φ=arccos⁡〖z/√(x^2+y^2+z^2 )〗

The given rectangular coordinates are (5√3, 0, 5). Hence,

ρ^2=〖(5√3)〗^2+0^2+5^2 ≈ 100

ρ ≈ √100 ≈ 10

tan⁡〖θ= 0/(5√3)=0〗

θ=  tan^(-1)⁡0=0

φ=arccos⁡〖5/√(〖(5√3)〗^2+0^2+5^2 )〗= arccos 5/10=arccos⁡0.5 ≈ 60

Note:  The question is incomplete. The complete question probably is: Convert from rectangular to spherical coordinates. (Use symbolic notation and fractions where needed. Give your answer as a point's coordinates in the form (*,*,*). (5√3, 0, 5)

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To answer this question, we need to remember the concept of rate. A rate is a result of comparing two different quantities, numbers. It is also a ratio - the result of dividing two numbers. In this case, we have two different quantities (or numbers):

1. Square miles that indicate the measurement of area. In this case, 326 square miles or 326 mi².

2. Population. In this case, we have 6846 residents.

In general, we can express the relationship if we divide the population by the area of the county, as the question suggests. Then, we have:

Therefore, the rate that best represents the relationship between the population of the county and the area of the county is 21 residents per square mile (option C).

The value x in the secant line using the Intersecting theorem is 4.

Intersecting secants theorem states that " If two secant line segments are drawn to a circle from an exterior point, then the product of the measures of one of secant line segment and its external secant line segment is the same or equal to the product of the measures of the other secant line segment and its external line secant segment.

From the figure:

First sectant line segment = ( x - 1 ) + 5

External line segment of the first secant line = 5

Second sectant line segment = ( x + 2 ) + 4

External line segment of the second secant line = 4

Using the Intersecting secants theorem:

5( ( x - 1 ) + 5 ) = 4( ( x + 2 ) + 4 )

Solve for x:

5( x - 1 + 5 ) = 4( x + 2 + 4 )

5( x + 4 ) = 4( x + 6 )

5x + 20 = 4x + 24

5x - 4x = 24 - 20

x = 4

Therefore, the value of x is 4.

Option C) 4 is the correct answer.

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Answer:

The triangle won't exist.

Step-by-step explanation:

If the two shorter lengths add up to be shorter than the longest length, the triangle can't exist.

Given the length of the sides of the triangle, it is an acute angle triangle.

An acute angle triangle is a triangle in which all the interior angles are acute angles. To recall, an acute angle is an angle that is less than 90°.

Given three sides a, b, c of a triangle, where a < b < c.

If \(a^{2} + b^{2} < c^{2}\), we can say that the triangle is acute.

Since, \(3^{2} + 16^{2} = 265 < 289 = 17^{2}\), given triangle is acute.

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Therefore, the value of x in the right triangle is 24 cm.

A triangle is a two-dimensional geometric shape that has three straight sides and three angles. It is formed by connecting three non-collinear points. The sum of the interior angles of a triangle is always 180 degrees, and the measure of each angle depends on the lengths of the sides and the type of triangle. There are different types of triangles based on their side and angle measures, such as equilateral, isosceles, scalene, acute, right, and obtuse triangles. Triangles have various properties and formulas that are used in geometry and other fields.

Here,

In a right triangle, the side opposite to the right angle is the longest side and is called the hypotenuse. Therefore, in this case, 25 cm is the hypotenuse of the triangle.

Using the Pythagorean Theorem, we can find the missing length x:

a² + b² = c²

where a and b are the lengths of the legs of the right triangle and c is the length of the hypotenuse.

In this case, a = 7 cm, b = x, and c = 25 cm.

Substituting these values into the Pythagorean Theorem, we get:

7² + x² = 25²

49 + x² = 625

x² = 625 - 49

x² = 576

x = √576

x = 24

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Answer:

cos(∝) = 1/√3

cos(β) = 1/√3

cos(γ) = 1/√3

∝ = 55°

β = 55°

γ = 55°

Step-by-step explanation:

Given the data in the question;

vector is z = < c,c,c >

the direction cosines and direction angles of the vector = ?

Cosines are the angle made with the respect to the axes.

cos(∝) = z < 1,0,0 > / |z|

so

cos(∝) = < c,c,c > < 1,0,0 > / √[c² + c² + c²] = ( c + 0 + 0 ) / √[ 3c² ]

cos(∝) = c / √[ 3c² ] = c / c√3 = 1/√3

∝ = cos⁻¹( 1/√3 ) = 54.7356° ≈ 55°

cos(β) = < c,c,c > < 0,1,0 > / √[c² + c² + c²] = ( 0 + c + 0 ) / √[ 3c² ]

cos(β) = c / √[ 3c² ] = c / c√3 = 1/√3

β = cos⁻¹( 1/√3 ) = 54.7356° ≈ 55°

cos(γ) = < c,c,c > < 0,0,1 > / √[c² + c² + c²] = ( 0 + 0 + c ) / √[ 3c² ]

cos(γ) = c / √[ 3c² ] = c / c√3 = 1/√3

γ = cos⁻¹( 1/√3 ) = 54.7356° ≈ 55°

Therefore;

cos(∝) = 1/√3

cos(β) = 1/√3

cos(γ) = 1/√3

∝ = 55°

β = 55°

γ = 55°

The sum of the infinite geometric sequence is 3 3/4

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

The geometric sequence

In the geometric sequence, we have

First term, a = 3/5¹⁻¹

a = 3

Also, we have

Common ratio, r = 1/5

The sum of the infinite geometric sequence is calculated as

Sum = a/(1 -  r)

So, we have

Sum = 3/(1 -  1/5)

Evaluate

Sum = 3 3/4

Hence, the sum of the infinite geometric sequence is 3 3/4

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The complete table of values is

x    f(x) = x   g(x) = -3x

0        0              0

1          1              -3

2         2             -6

The slope of g(x) is -3 and the graph is reflected across the x-axis

From the question, the given parameters are

f(x) = x

g(x) = -3x

The x values on the tables are

x = 0, 1 and 2

So, we have

f(0) = 0, f(1) = 1 and f(2) = 2

Also, we have

g(0) = 0, g(1) = -3 and g(2) = -6

Next, we determine the slope and the transformation

We have

f(x) = x and g(x) = -3x

A linear equation is represented as

y = mx

Where m is the slope

This means that the slope of g(x) is -3

Also, because of the negative sign in g(x) = -3x, it means that the graph is reflected across the x-axis or the y-axis

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Answer: 5/3

Step-by-step explanation:

It will take Adrian 16 full months to save enough money for the electric keyboard.

- Price of the keyboard (with tax) at Macelli's: $2,400
- Adrian's monthly savings: $150
We need to find how long it will take Adrian to save for the keyboard. To do this, we'll divide the total cost of the keyboard by his monthly savings and round up to the nearest full month.
Step 1: Divide the total cost by monthly savings.
Time (in months) = (Total Cost) / (Monthly Savings) = ($2,400) / ($150)
Step 2: Calculate the result.
Time (in months) = 16
So, it will take Adrian 16 full months to save enough money for the electric keyboard.

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Another expression for the given rational function is \(x =r^\frac{1}{2}s^\frac{1}{2}\)

Given the rational function expressed as:

x = √rs

We can reconstruct the expression by writing it using exponents as shown;

\(x =\sqrt{rs}=(rs)^{\frac{1}{2} }\)

Separate to have:

\(x =r^\frac{1}{2}s^\frac{1}{2}\)

Hence another expression for the given rational function is \(x =r^\frac{1}{2}s^\frac{1}{2}\)

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Answer:

46

Step-by-step explanation:

Answer:

40

Step-by-step explanation:

8 + 15 + 17 = 40

**Hope this helped!!**

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The area of a rectangle with a width of 5.1 cm and a height of 11.2 cm is 57.12 cm².

To find the area of a rectangle, we multiply its length by its width. In this case, the width is given as 5.1 cm and the height (or length) is given as 11.2 cm.

Area = length × width

Area = 11.2 cm × 5.1 cm

Calculating the product, we get:

Area = 57.12 cm²

Therefore, the area of the rectangle is 57.12 cm².

The correct answer is: 57.12 cm².

It is important to note that when calculating the area of a rectangle, we should always include the appropriate unit of measurement (in this case, cm²) to indicate that we are dealing with a two-dimensional measurement. The area represents the amount of space covered by the rectangle's surface.

So, the area of a rectangle with a width of 5.1 cm and a height of 11.2 cm is 57.12 cm².

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Answer:

The answer is 80

Step-by-step explanation: You can trust me ok?:)

Answer:

The arrow should point at 0.5 which is half way between 0 and 1

Step-by-step explanation:

- + 1 = -3/4 + 5/4 = 2/4 = 1/2 and 1/5 in decimal form is 0.5

pls brainliest:)d

Answer: This is the answer. please give me the brainliest. Thanks

Answer:I only see one graph my guy but that is leaner

Step-by-step explanation:

Answer:

\(NO= 31.2\)

Step-by-step explanation:

See attachment for triangle

From the attachment, we have:

\(KL = 51.6\)

\(LM= 38\)

\(OP = 23\)

Required

Find NO

This will be calculated using the following equivalent ratios:

\(NO : OP = KL : LM\)

This gives:

\(NO : 23= 51.6: 38\)

Express as fraction

\(\frac{NO }{ 23}= \frac{51.6}{ 38}\)

Make NO the subject

\(NO= \frac{51.6}{ 38} * 23\)

\(NO= \frac{51.6* 23}{ 38}\)

\(NO= \frac{1186.8}{ 38}\)

\(NO= 31.2\) --- approximated

Answer:

x≈ 16.9

Step-by-step explanation:

Answer:

\(16\)

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Step-by-step explanation:

\(f(2) = 5(2) - 1= 9\)

\(g(2) = 2^2 + 3 = 7\)

\((f \ \o \ g)(2) = f(2) + g(2) = 9 + 7 = 16\)

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The length of the third side is 2√34 + 6.

We can use the triangle inequality theorem to solve this problem. According to the theorem, the sum of any two sides of a triangle must be greater than the length of the third side.

Let x be the length of the third side. Then we have:

2√34 + 6 > x

Subtracting 6 from both sides, we get:

2√34 > x - 6

Adding 6 to both sides, we get:

x < 2√34 + 6

Therefore, the length of the third side must be less than 2√34 + 6.

To find the exact length of the third side, we need to check if the triangle inequality is satisfied for an equality. In other words, we need to check if:

2√34 + 6 = x

If this is true, then the given sides can form a triangle.

Simplifying the equation, we get:

x = 2√34 + 6

The exact length is 2√34 + 6 if the triangle inequality is satisfied for an equality.

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Simple answer.

-1 x 3 = -3

3 is your x and -3 is your y.

Answer:

  70 ft

Step-by-step explanation:

You want the actual width of a gym that is represented as 7 inches on a drawing with a scale of 1 in : 10 ft.

Each inch represents 10 feet, so 7 inches will represent ...

  7 × 10 ft = 70 ft

The gym is 70 ft wide.

__

Additional comment

You can also write and solve an equation that shows the measures are proportional:

  actual width / drawing width = (10 ft) / (1 in) = (gym width) / (7 in)

Multiplying both sides of this proportion by 7 in, we have ...

  gym width = (7 in) × (10 ft)/(1 in) = 7 × 10 ft = 70 ft

The turning points of the function y = x³ - 3x² - 9x + 4 are (3, -23) and (-1, 9).

To determine the turning points of the given function y = x³ - 3x² - 9x + 4, we need to find the critical points where the derivative of the function is equal to zero.

1. Find the derivative of the function:

  y' = 3x² - 6x - 9

2. Set the derivative equal to zero and solve for x:

  3x² - 6x - 9 = 0

3. Factorize the quadratic equation:

  3(x² - 2x - 3) = 0

4. Solve the quadratic equation by factoring or using the quadratic formula:

  (x - 3)(x + 1) = 0

  This gives us two possible values for x: x = 3 and x = -1.

5. Substitute these critical points back into the original function to find the corresponding y-values:

  For x = 3:

  y = (3)³ - 3(3)² - 9(3) + 4

    = 27 - 27 - 27 + 4

    = -23

  For x = -1:

  y = (-1)³ - 3(-1)² - 9(-1) + 4

    = -1 - 3 + 9 + 4

    = 9

6. Therefore, the turning points are (3, -23) and (-1, 9).

Note: It appears that there was a typo in the original equation, where the term "-9x" should have been "-3x²". The above solution assumes the corrected equation.

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Answer:

n = -(13/4) or -3.25(In decimal form)

Step-by-step explanation:

-(5/2) = (3/4) + n

-(5/2) - (3/4)

n = -(13/4)

Number of 20-cent coins in the box are 33.

1. Let's assume the number of 20-cent coins to be x and the number of 50-cent coins to be y.

2. We can set up two equations based on the given information:

  - x + y = 54   (since the total number of coins in the box is 54)

  - 0.20x + 0.50y = 20.70   (since the total value of all the coins is $20.70)

3. We can multiply the second equation by 100 to get rid of the decimals:

  - 20x + 50y = 2070

4. Now, we can use the first equation to express y in terms of x:

  - y = 54 - x

5. Substitute the value of y in the second equation:

  - 20x + 50(54 - x) = 2070

6. Simplify and solve for x:

  - 20x + 2700 - 50x = 2070

  - -30x = -630

  - x = 21

7. Substituting the value of x back into the first equation:

  - 21 + y = 54

  - y = 33

8. Therefore, there are 21 20-cent coins and 33 50-cent coins in the box.

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9514 1404 393

Answer:

  (A)  6

Step-by-step explanation:

Divisors of 6 are ...

 1, 2, 3, 6

The sum of all but the last is 1+2+3 = 6.

Then  <<<6>>> = <<6>> = <6> = 6.

_____

Additional comment

Among integers less than 200, only 6 and 28 are solutions to <n> = n.

Answer:

the answer to the problem is 20.8%

Considering that their household expenses is of $120,000, the mortgage is 12% of their expenses.

The percentage of an amount a of an amount b is a multiplied by 100% and divided by b, that is:

\(P = \frac{a}{b} \times 100\%\)

In this problem, the mortgage is of $14,400, while the total expenses are considered to be of $120,000, hence:

\(P = \frac{14400}{120000} \times 100\% = 12\%\)

The mortgage is 12% of their expenses.

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Answer:

27 stalls

Step-by-step explanation:

111 / 4 = 27.75

So he can fill at most 27 stalls completely