How do I work this out?

[tex]\qquad \qquad \textit{Inverse Trigonometric Identities} \\\\ \begin{array}{cccl} Function&Domain&Range\\[-0.5em] \hrulefill&\hrulefill&\hrulefill\\ y=cos^{-1}(\theta)&-1 ~\le~ \theta ~\le~ 1& 0 ~\le~ y ~\le~ \pi \\\\ y=tan^{-1}(\theta)&-\infty ~\le~ \theta ~\le~ +\infty &-\frac{\pi}{2} ~\le~ y ~\le~ \frac{\pi}{2} \end{array} \\\\[-0.35em] ~\dotfill[/tex]

[tex]cos^{-1}\left( -\cfrac{\sqrt{2}}{2} \right)\implies \theta \hspace{5em}\stackrel{\textit{so we can say}}{cos(\theta )=-\cfrac{\sqrt{2}}{2}} \\\\\\ \theta =cos^{-1}\left( -\cfrac{\sqrt{2}}{2} \right)\implies \stackrel{ \textit{on the II Quadrant} }{\theta =\cfrac{3\pi }{4}} \\\\[-0.35em] ~\dotfill\\\\ sin\left[ cos^{-1}\left( -\cfrac{\sqrt{2}}{2} \right) \right]\implies sin\left( \cfrac{3\pi }{4} \right)\implies \boxed{\cfrac{\sqrt{2}}{2}}[/tex]

now let's find the angle for the inverse tangent

[tex]sin\left( \cfrac{\pi }{2} \right)\implies 1\hspace{5em}\stackrel{\textit{so we can say}}{tan^{-1}\left[ sin\left( \frac{\pi }{2} \right) \right]}\implies tan^{-1}(1) \stackrel{ \textit{on the I Quadrant} }{\implies\boxed{\cfrac{\pi }{4}}} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ sin\left[ cos^{-1}\left( -\frac{\sqrt{2}}{2} \right) \right]~~ + ~~tan^{-1}\left[ sin\left( \frac{\pi }{2} \right) \right]\implies \cfrac{\sqrt{2}}{2}~~ + ~~\cfrac{\pi }{4} \implies \boxed{\cfrac{2\sqrt{2}+\pi }{4}}[/tex]

for the sine function we end up in the II Quadrant because the inverse cosine function range is constrained to the I and II Quadrants only, so our angle comes from that range.

Likewise, our angle from the inverse tangent comes from the I Quadrant, because inverse tangent range is only I and IV Quadrants.

As a result, during its flight, the football will strike the ground twice: once when it is kicked off and once more 3 seconds later.

A mathematical equation, including such 6 x 4 = 12 x 2, states that two quantities and values are equivalent. a meaningful noun. Equations are employed when two or more variables need to be added up and the results need to be computed in order to comprehend or explain the entire issue. As a result, the football will hit the ground twice during its flight: once after the game has kicked off and again three seconds later.

h =

0 = -16x² + 48x

0 = 16x(3 - x)

Either 16x or (3 - x) equals 0, which makes this equation equal to zero.

Hence, the answers to x are:

x = 0, when 16x = 0

when 3 - x = 0, x equals 3.

The football will therefore strike the ground twice during its flight—once when it is kicked off and once more 3 seconds later.

To know more about equation visit:

brainly.com/question/29538993

#SPJ1

The simplest form of the given expression is -20k + 126.

To find the simplest form of the expression 8(5k+7)−10(6k−7), follow these steps:
1. Distribute the numbers outside the parentheses to the terms inside the parentheses:
  8 × 5k + 8 × 7 - 10 × 6k + 10 × 7
2. Perform the multiplication:
  40k + 56 - 60k + 70
3. Combine like terms (terms with the same variable and exponent):
  (40k - 60k) + (56 + 70)
4. Simplify the expression by performing the subtraction and addition:
  -20k + 126
The simplest form of the given expression is -20k + 126.

for such more question on simplest form

https://brainly.com/question/344788

#SPJ11

As per the concept of parallelogram, the area of the hexagons is 1237.9 cm², one isosceles trapezoid is 130 cm², one triangle is 60 cm², one circle is 78.5 cm².

Since we know the apothem is 10 cm, we can use the tangent function to find the length of the side:

tan(72) = side length / 10

Solving for the side length, we get:

side length = 10 * tan(72) ≈ 21.2 cm

Now that we know the side length, we can use the formula for the area of a regular polygon:

area of the hexagon = (5 x side length² x √(3)) / 2 ≈ 1237.9 cm²

Next, let's find the area of the isosceles trapezoid.

To find the area, we can use the formula:

area of the trapezoid = ((base1 + base2) / 2) x height

Substituting the given values, we get:

area of the trapezoid = ((12 + 14) / 2) x 10 = 130 cm²

Now, let's move on to the triangle. We are given the base (12 cm) and the height (10 cm). To find the area of a triangle, we can use the formula:

area of the triangle = (base x height) / 2

Substituting the given values, we get:

area of the triangle = (12 x 10) / 2 = 60 cm²

Next, let's find the area of the circle. We know that the diameter of the circle is equal to the height of the isosceles trapezoid (10 cm), so the radius is half of that:

radius = 10 / 2 = 5 cm

Using the formula for the area of a circle, we get:

area of the circle = π x radius² = π x 5² ≈ 78.5 cm²

To know more about parallelogram here

https://brainly.com/question/29147156

#SPJ4

Complete Question:

There are 3 regular hecagons, one isocrles trapezoid, one triangle, one circle and one parallelogram. Use the provded measurements to find the area. You will need to use trigonometry to find some measurements

base is 12 cm, length is 14 cm and height is 10 cm

The probability that the person selected will be someone whose response is never and who is a woman is 3/7.

The probability that the person selected will be someone whose response is never and who is a woman can be found by using conditional probability.What is conditional probability?Conditional probability is the likelihood of an event occurring given that another event has already occurred. The probability of event A happening given that event B has already occurred is known as conditional probability.Mathematically, the formula for conditional probability is:P(A|B) = P(A ∩ B) / P(B)Where,P(A|B) represents the probability of event A given that event B has already occurred.P(A ∩ B) represents the probability of both A and B occurring.P(B) represents the probability of event B occurring.The given scenario states that the person selected should have two attributes: the response never and the gender woman. Let A be the event that the person selected has a response never and B be the event that the person selected is a woman. Therefore, we need to find the probability of event A given event B.P(A|B) = P(A ∩ B) / P(B)Therefore, we need to find the probability of both A and B occurring and the probability of event B occurring.P(B) = 70/120P(B) = 7/12There are 50 women in the group. The number of women who have never responded is 30. Therefore,P(A ∩ B) = 30/120P(A ∩ B) = 1/4Therefore,P(A|B) = P(A ∩ B) / P(B)P(A|B) = 1/4 / 7/12P(A|B) = 3/7The probability that the person selected will be someone whose response is never and who is a woman is 3/7.

Learn more about Probability

brainly.com/question/23017717

#SPJ11

There is a 68.26% chance of a value falling between 3 and 7 in the given normal distribution.

This indicates a normal distribution, which is a type of continuous probability distribution. It is characterized by a bell-shaped curve that is symmetric about the mean, with a specific formula given by f(x) = [tex]1/(σ√2π)e^(-(x-μ)^2/2σ^2)[/tex]where μ is the mean, σ is the standard deviation, and x is the random variable.

In terms of calculation, we can use the formula to calculate the probability of a certain event occurring. For example, if we know the mean and standard deviation of a normal distribution, we can calculate the probability of a value between two given points. For example, if the mean is 5 and the standard deviation is 2, then the probability of a value between 3 and 7 is given by the integral of f(x) from 3 to 7, which is equal to 0.6826. This means that there is a 68.26% chance of a value falling between 3 and 7 in the given normal distribution.

Learn more about normal distribution here:

https://brainly.com/question/29509087

#SPJ4

The closest value to the standard deviation of the 100 times is (C) 20 seconds.

To determine the closest value to the standard deviation of the 100 times, we would need the actual histogram or the data points themselves.

In general, the standard deviation measures the spread or dispersion of a set of values. A higher standard deviation indicates a greater dispersion, while a lower standard deviation indicates a smaller dispersion.

Looking at the given options, (A) 2.5 seconds and (B) 10 seconds are relatively small values, which suggests a low dispersion among the times. On the other hand, options (D) 50 seconds and (E) 90 seconds are larger values, indicating a higher dispersion.

Option (C) 20 seconds falls in between the smaller and larger values. While it is difficult to determine the exact standard deviation without the data, option (C) of 20 seconds seems like a reasonable choice as it represents a moderate spread among the 100 times.

Therefore, the closest value to the standard deviation of the 100 times is (C) 20 seconds.

To know more about standard deviation follow

https://brainly.com/question/28738475

#SPJ12

The estimated enrollment of a high school in 2022 is approximately 2775 students.

To calculate the estimated enrollment in 2022, we need to use the formula for compound interest:

A =[tex]P(1 + r)^t[/tex]

where:

A = final amount (enrollment in 2022)

P = initial amount (enrollment in 2012)

r = annual interest rate (increase rate)

t = number of years (10)

We know that P = 1350 and r = 0.09 (9%). We can plug these values into the formula:

A = [tex]1350(1 + 0.09)^{10[/tex]

A = [tex]1350(1.09)^{10[/tex]

A = 2774.92

Therefore, the estimated enrollment in 2022 is approximately 2775 students.

Learn more about Percentages:

https://brainly.com/question/24877689
#SPJ4

The total number of hours is 30 hours as the sum of 7/8 and 3/8 comes out to be 30 hours.

1) We know that there is a total of 24 hours in a day.

therefore, 7/8 hours of Wednesday =

number of hours in a day = 24

number of hours every Wednesday = 7/8

= 7/8 x 24 hours

= 7 x 3 hours

= 21 hours

7/8 hours every Wednesday means 21 hours every Wednesday.  

2) We know that there are a total of 24 hours in a day;

therefore, 3/8 hours of Friday =

number of hours in a day = 24

number of hours every Friday = 3/8

= 3/8 x 24 hours

= 3 x 3 hours

= 9 hours

3/8 hours every Friday means 9 hours every Friday.

therefore, the total number of hours = 21 + 9 = 30

The total number of hours is 30 hours as the sum of 7/8 and 3/8 comes out to be 30 hours.

To learn more about sum, click here:

brainly.com/question/29034036

#SPJ4

Answer:

Step-by-step explanation:

The side length of the original square is 3 1/2 inches.

To find the side length of the new square, we need to apply the scale factor of 2/3 to the original side length.

To do this, we multiply the original side length by the scale factor:

(2/3) x 3 1/2

To multiply a fraction by a whole number, we can first convert the whole number to a fraction with a denominator of 1:

(2/3) x (7/2)

To multiply two fractions, we can multiply their numerators together and their denominators together:

(2/3) x (7/2) = (2 x 7) / (3 x 2) = 14/6

We can simplify this fraction by dividing both the numerator and the denominator by their greatest common factor, which is 2:

14/6 = (2 x 7) / (2 x 3) = 7/3

Therefore, the side length of the new square is 7/3 inches.

15 divided by 289 is approximately equal to 0.0519 or 519/10000. Fifteen divided by two hundred and eighty nine is a division problem that involves dividing 15 by 289. To solve this problem, we can use long division or a calculator.

Using long division, we start by dividing the first digit of the dividend (2) by the divisor (15). Since 2 is less than 15, we add a decimal point and a zero to the dividend and continue the process. We bring down the next digit (8) and divide 28 by 15, which gives us a quotient of 1 with a remainder of 13. We add a decimal point after the quotient and bring down the next digit (9) to get 139 as the new dividend. We divide 139 by 15, which gives us a quotient of 9 with a remainder of 4. We add a decimal point after the quotient and bring down the last digit (0) to get 40 as the new dividend. We divide 40 by 15, which gives us a quotient of 2 with a remainder of 10. Finally, we add a decimal point after the last quotient and write the remainder as a fraction over the divisor to get the final answer:

15 divided by 289 is approximately equal to 0.0519 or 519/10000.

In summary, fifteen divided by two hundred and eighty nine is a division problem that can be solved using long division or a calculator. The answer is a decimal or a fraction, depending on how the division is carried out.

To know more about division problem click here:

brainly.com/question/28785787

#SPJ4

Answer:  Therefore, the maximum distance you can ride for $20 is 6 kilometers.

Step-by-step explanation:   The inequality to determine the distance in kilometers, d, you can ride for $20 is:

$5 + $2.50d ≤ $20

Simplifying the above inequality, we get:

$2.50d ≤ $15

Dividing both sides by $2.50, we get:

d ≤ 6

By using LCM, we find that the three planets  x, y and z will be in the exact same locations again after $5400$ days.

To find the minimum positive number of days before the planets are all in the exact same locations again, we need to find the least common multiple (LCM) of the three given periods of rotation.

The prime factorization of each of the given periods of rotation is as follows

$360 =[tex]2^3 \cdot 3^2 \cdot 5$[/tex]

$450 =[tex]2 \cdot 3^2 \cdot 5^2$[/tex]

$540 =[tex]2^2 \cdot 3^3 \cdot 5$[/tex]

To find the LCM, we need to take the highest power of each prime factor that appears in any of the three factorizations. So the LCM is:

[tex]$LCM = 2^3 \cdot 3^3 \cdot 5^2 = 2^3 \cdot 27 \cdot 25 = 5400$[/tex]

Therefore, the three planets will be in the exact same locations again after $5400$ days.

To know more about least common multiple (LCM):

https://brainly.com/question/17256135

#SPJ4

The circle at -6 is closed because the inequality does not include the possibility of y being equal to -6.

Inequality refers to a situation in which there is a difference or disparity between two or more things, usually in terms of value, opportunity, or outcome. Inequality can take many forms, including social, economic, and political inequality.

by the question.

the solution set of the inequality 1/2y < -3

Graph the solution set of the inequality 1/2y &lt; -3 - 1

To solve the inequality 1/2y < -3, we can begin by isolating the variable y on one side of the inequality:

1/2y < -3

Multiplying both sides by 2 yields:

y < -6

So, the solution set of the inequality is all real numbers y that are less than -6.

To graph the solution set on a number line, we can draw a closed circle at -6 and shade to the left of it, indicating that all values to the left of -6 are solutions to the inequality. The graph would look like this:

<=======o----------------------

To learn more about number:

https://brainly.com/question/13465215

#SPJ

In a rectangle where the length is 3 times the width, and the perimeter is 3 times the width. The perimeter is 96 cm, the length is 36 cm and the width is 12 cm.

Given,

Length of a rectangle is 3 times the width.

Perimeter is 3 times the width.

Perimeter is 96 cm.

Let w be the width of the rectangle.

The length of the rectangle is 3 times the width, so the length l is 3w.

The perimeter of the rectangle is equal to the sum of all its sides, so:

2w + 2(3w) = 96

2w + 6w = 96

8w = 96

w = 12

Therefore, the length is 36 cm and the width is 12 cm.

To know more about Perimeter refer here:

https://brainly.com/question/6465134

#SPJ11

The area of this polygon is equal to 428 ft².

In order to calculate the area of this polygon, we would have to determine the total area of the two different parts of the given composite figure.

Therefore, the total area of this polygon is the sum of the area of the each geometric figure (rectangle):

Area of rectangle A = Length × Width

Area of rectangle A = 13 × 26

Area of rectangle A = 338 ft²

Area of rectangle B = 9 × (23 - 13)

Area of rectangle B = 9 × 10

Area of rectangle B = 90 ft²

Therefore, total area is given by:

Total area = 90 + 338

Total area = 428 ft²

Read more on polygon here: https://brainly.com/question/26479857

#SPJ1

The given diagram represents a right circular cylinder with a base equation of (x - 0)² + (y - 0)² = 7², resulting in an ellipse with an equation of (x - 0)²/4² + (y - 0)²/5² = 1.

The given diagram represents a right circular cylinder with a height of 10 meters and a radius of 7 meters, which means the base of the cylinder is a circle with a radius of 7 meters. The equation of the circle is (x - 0)² + (y - 0)² = 7², where (0, 0) is the center of the circle.

The cylinder has been sliced by a plane that is parallel to the base and 4 meters from the center of the cylinder. This means the distance between the center of the cylinder and the plane is 4 meters.

Mathematically, the equation of the ellipse can be written as (x - 0)²/4² + (y - 0)²/5² = 1, where the center of the ellipse is (0, 0), and the semi-major axis is 5 meters and the semi-minor axis is 4 meters.

So, the given diagram described as a right circular cylinder with a base equation of (x - 0)² + (y - 0)² = 7², sliced by a plane parallel to the base and 4 meters from the center of the cylinder, resulting in an ellipse with an equation of (x - 0)²/4² + (y - 0)²/5² = 1.

To learn more about cylinder please click on below link        

https://brainly.com/question/3216899

#SPJ1

Therefore, the value of a for triangle 2 is 44 degrees.

A triangle is a closed geometric shape that has three sides and three angles. It is one of the basic shapes in geometry and is used in many different areas of mathematics and science. The sum of the angles in a triangle is always 180 degrees, and there are many different types of triangles, including equilateral, isosceles, and scalene triangles, depending on the lengths of their sides and the sizes of their angles. Triangles are also commonly used in trigonometry, which is the branch of mathematics that deals with the relationships between the sides and angles of triangles.

Here,

The sum of the interior angles of a triangle is always 180 degrees. Therefore, for triangle 1, we have:

95 + 39 + x = 180

Simplifying the equation, we get:

134 + x = 180

x = 46

For triangle 2, we have:

90 + a + x = 180

Substituting the value of x from above, we get:

90 + a + 46 = 180

Simplifying the equation, we get:

a = 44

To know more about triangle,

https://brainly.com/question/28600396

#SPJ1

x = 8 is the whole number that solves the equation, making it true. A whole number is a number that does not have any fractions or decimals.

It is a positive integer or zero, such as 0, 1, 2, 3, 4, 5, and so on. Whole numbers are used to count objects or things that can be represented as a whole, such as people, cars, apples, and so on.

Whole numbers are closed under addition, subtraction, and multiplication operations, which means that if you add, subtract or multiply two whole numbers, the result will always be another whole number. However, whole numbers are not closed under division operation, which means that when dividing two whole numbers, the result may not be a whole number.

To solve for x in the equation:

x 1/2=8/2

We can isolate x by multiplying both sides by the reciprocal of 1/2, which is 2/1:

x 1/2 * 2/1 = 8/2 * 2/1

Simplifying the left side, we get:

x = 16/2

x = 8

Therefore, the whole number that makes the equation true is x = 8.

To learn more about whole number visit;

https://brainly.com/question/29766862

#SPJ4

She needs 14 cups of fertiliser.

What is the area?

A two-dimensional figure's area is the amount of space it takes up. In other terms, it is the amount that counts the number of unit squares that span a closed figure's surface.

Area = length * width

Find the area of the garden:

Area = 9 1/3 * 12

       = 28/3 * 12

       = 112  yards²

Find the amount of the fertiliser needed:

1   yards² = 1/8 cup

112  yards² = 1/8 * 112 = 14 cups

She needs 14 cups of fertiliser.

To learn more about the area from the given link

https://brainly.com/question/25292087

#SPJ1

Answer:33

Step-by-step explanation:45-12=33

Answer: 2.

Step-by-step explanation:

Mean = Population / Number of Integers.

Mean = 7.

Subtract the integers from the mean.

5 - 7 = -2

6 - 7 = -1

10 - 7 = 3.

Put differences in absolute value.

|-2| = 2

|-1| = 1

|3| = 3.

add the differences then divide by the population number.

2 + 1 + 3 = 6

6 / 3

2

The equation for calculating the number of pairwise comparisons in a pairwise ranking matrix is: (n*(n-1))/2 where n is the number of items being compared in the matrix.

A pairwise ranking matrix is a tool that is used to rank items on the basis of pair-wise comparisons of the items. In order to find out the number of pairwise comparisons in such a matrix, one needs to use the following formula:(n*(n-1))/2where n is the number of items being compared in the matrix.

The formula works on the principle that every item in the matrix needs to be compared with every other item, but each comparison needs to be done only once. This is why the formula divides the total number of comparisons by two.

Therefore, the equation is: (n*(n-1))/2


To know more about matrix refer here:

https://brainly.com/question/28180105#

#SPJ11

Answer: b. 12

Step-by-step explanation:

16 + 4 − (5 x 2) + 2

= 16 + 4 - 10 + 2

= 20 - 12

= 12

Answer:

Step-by-step explanation:

8

Answer:

26°

Step-by-step explanation:

We know

A triangle is 180°

A triangle has Angle measures 122° and 32°

What is the measure of the third angle? ​

We take

180 - (122 + 32) = 26°

So, the measure of the third angle is 26°

As per the unitary method, the cost of one skirt is sh 20 and the cost of one blouse is sh 550.

Let us assume that the cost of one skirt is x and the cost of one blouse is y. We can now form two equations based on the given information.

Equation 1: 5x + 3y = 1750

This equation represents the cost of 5 skirts and 3 blouses together, which is given as sh 1750.

Equation 2: 3x + y = 850

This equation represents the cost of 3 skirts and 1 blouse, which is given as sh 850.

To apply the unitary method here, we can first find the value of one skirt by dividing equation 1 by 5, and then find the value of one blouse by subtracting 3 times the value of one skirt from equation 2.

Dividing equation 1 by 5, we get:

x + (3/5)y = 350

Subtracting 3 times the value of one skirt from equation 2, we get:

y = 850 - 3x

y = 850 - 3(350/5)

y = 550

So, we have found the value of y, which is the cost of one blouse. Now, we can substitute this value of y in equation 1 to find the value of x, which is the cost of one skirt.

5x + 3(550) = 1750

5x + 1650 = 1750

5x = 100

x = 20

To know more about unitary method here

https://brainly.com/question/28276953

#SPJ4

when some syrup from a bottle was poured into the container, it got half full. The volume of the syrup poured from the bottle into the container in millimeters is 576,000 cubic millimeters.

Since for solving the problem we need to find the volume of the container in millimeters. We are given the length, breadth, and height which are 12 cm,8 cm, and  36 cm.Now the volume of the container is:

V = l x w x h = 12 cm x 8 cm x 36 cm = 3,456 cubic cm. Now  we convert the above result  into millimeters by  multiplying by 1,000, so we get V= 3456 x 1000= 34560000 cubic mm

Now to find the volume of the syrup that was poured into the container,  we know that the container was one-third full before the syrup was added and half full after the syrup was added.onsidering x to be the volume of the syrup poured from the bottle into a container and n to be the volume of the syrup in the container after it was added:

1/3(V) + x = 1/2(V), where v is the  volume of the container in millimeters, so we substitute the calculated value of the volume we get :

=>1/3(V) + x = 1/2(V)

=>x = 1/2(V) - 1/3(V)

=> x = 1/6(V) = 1/6(3,456,000)  = 576,000 cubic mm

To know more about volume refer to the link brainly.com/question/1578538

#SPJ4

Answer:the jimboluis

Step-by-step explanation:

that’s it

The geometric sequence is 9 + 2 + 20 = 29.

The smallest number the third term in the geometric sequence can be is 29.

This is because when you add 2 to the second term and 20 to the third term of the three-term arithmetic sequence with a first term of 9,

the third term of the geometric sequence is 9 + 2 + 20 = 29.

Learn more about geometric sequence

brainly.com/question/30491267

#SPJ11

Answer: -2g^7h^8

Step-by-step explanation: