A
4
B
40°
8

Need help

A4B408Need Help

Answers

Answer 1

Step-by-step explanation:

this represents a trigonometric triangle (right-angled) inside an imaginary circle.

imagine the triangle is turned 90° counterclockwise, so that A is the bottom left vertex, B is the bottom right vertex.

then x is the angle (40°) defining radius of the circumscribing circle.

remember, sine is the up/down leg, cosine is the left/right leg. and in a larger circle they are all multiplied by the radius.

so,

4 = cos(40) × x

x = 4 / cos(40) = 5.221629157... ≈ 5.22


Related Questions

given f(x)=x+2 setting k=4 affects the slope and y- intercept of the graph of g compared to the graph of f g(x) = 4(x + 2)

Answers

The constant term is 8, which means that the y-intercept of the graph of g is (0, 8).

What is function?

In mathematics, a function is a rule that assigns a unique output value for every input value in a set. It is a relation between a set of inputs and a set of possible outputs, with the property that each input is related to exactly one output. Functions are widely used in various fields of mathematics, science, engineering, and technology to model and analyze real-world situations, to describe how quantities depend on one another, and to solve problems.

Here,

If we set k=4, the function g(x) becomes:

g(x) = k(x+2) = 4(x+2)

The value of k affects the slope of the graph of g compared to the graph of f. In this case, since k=4, the slope of the graph of g is 4 times the slope of the graph of f.

The slope of the graph of f is 1, since the coefficient of x is 1. Therefore, the slope of the graph of g is:

4 * 1 = 4

This means that the graph of g is steeper than the graph of f.

The y-intercept of the graph of f is 2, since the constant term is 2. Setting k=4 does not affect the y-intercept of the graph of g, since the constant term remains the same:

g(x) = 4(x+2) = 4x + 8

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Determinants: Let A∈R n×n be an invertible matrix, and letdet(⋅)denote the determinant of its argument. Show thatdet(A−1)=det(A)1​

Answers

The determinant of the inverse of an invertible matrix is the reciprocal of the determinant of the original matrix.

Determinants: The determinant of an invertible matrix A is a scalar value that is used to indicate the invertibility of the matrix. If the determinant of A is non-zero, then the matrix is invertible. The determinant of the inverse of an invertible matrix is the reciprocal of the determinant of the original matrix. In other words, det(A−1)=det(A)1​.

To prove this, we can use the property of determinants that det(AB)=det(A)det(B) for any two square matrices A and B. Since A is an invertible matrix, we know that AA−1=I, where I is the identity matrix. Taking the determinant of both sides of this equation gives us:

det(AA−1)=det(I)

Using the property of determinants mentioned above, we can rewrite the left-hand side of the equation as:

det(A)det(A−1)=det(I)

Since the determinant of the identity matrix is 1, we can simplify the equation to:

det(A)det(A−1)=1

Dividing both sides of the equation by det(A) gives us:

det(A−1)=det(A)1​

Therefore, the determinant of the inverse of an invertible matrix is the reciprocal of the determinant of the original matrix.

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need help with this problem

Answers

[tex](\stackrel{x_1}{-2}~,~\stackrel{y_1}{-4})\hspace{10em} \stackrel{slope}{m} ~=~ \cfrac{1}{2} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-4)}=\stackrel{m}{ \cfrac{1}{2}}(x-\stackrel{x_1}{(-2)}) \implies y +4= \cfrac{1}{2} (x +2) \\\\\\ y+4=\cfrac{1}{2}x+1\implies {\Large \begin{array}{llll} y=\cfrac{1}{2}x-3 \end{array}}[/tex]

The mapping diagram represents a relation where x represents the independent variable and y represents the dependent variable. A mapping diagram with one circle labeled x-values containing values negative 8, negative 5, negative 1, 1, and 12 and another circle labeled y values containing values negative 4 and negative 2 and arrows from negative 8 to negative 4, negative 5 to negative 2, negative 1 to negative 2, 1 to negative 2, 12 to negative 4, and 12 to negative 2.

Answers

The mapping diagram represents a relation between the set of x-values {negative 8, negative 5, negative 1, 1, 12} and the set of y-values {negative 4, negative 2}. The arrows between the circles show how the x-values are related to the y-values.

What is mapping diagram?

A mapping diagram is a visual way to represent a relation between two sets of values, where the arrows show how the values in one set are related to the values in the other set. The input values are typically shown in one circle or column, while the output values are shown in another circle or column.

What is calculus?

Calculus is a branch of mathematics that deals with the study of rates of change and the accumulation of small changes to determine their effects on a larger scale. It is a major part of modern mathematics and is used extensively in science, engineering, and economics.

In the given question,

The mapping diagram represents a relation between the set of x-values {negative 8, negative 5, negative 1, 1, 12} and the set of y-values {negative 4, negative 2}. The arrows between the circles show how the x-values are related to the y-values.

Specifically, the arrow from negative 8 to negative 4 means that the input value of x = negative 8 is related to the output value of y = negative 4. Similarly, the arrow from negative 5 to negative 2 means that the input value of x = negative 5 is related to the output value of y = negative 2.

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Order the values from least to greatest. |-41, 10, -12, 13| A) -41, 131, 10, -12 O B) |3|, |-–4|, 10, −12 OC -12, 1-41, [3], 10 OD) -12, 131, |–4], 10 D​

Answers

The order of the number from least to greatest will be -12, |3|, |-4|, 10. Then the correct option is D.

What is ascending order?

It is the order of the numbers in which a smaller number comes first and then followed by the next number and then the last number will be the biggest one.

The numbers are given below.

|-4|, 10, -12, |3|

Determine the absolute value of the numbers, then we have

|-4| = 4

10 = 10

-12 = -12

|3| = 3

The order of the number from least to greatest will be given as,

-12, 3, 4, 10

-12, |3|, |-4|, 10

Thus, the correct option is D.

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A grocery store receives a 180-pound crate containing six 10-pound bags of potatoes and an ink own number of 5 pound bag of potatoes. How many 5 pound bags of potatoes are in the crate

Answers

There are 24 five-pound bags of potatoes in the crate.

The crate contains a total of 6 bags of potatoes weighing 10 pounds each, which is a total of 60 pounds.

So, the remaining weight of the crate is 180 pounds - 60 pounds = 120 pounds.

Let's assume that there are x five-pound bags of potatoes in the crate.

Therefore, the total weight of these x bags of potatoes would be 5x pounds.

We know that the weight of the entire crate is 180 pounds,

60 pounds (weight of 6 bags of 10-pound potatoes) + 5x pounds (weight of x 5-pound bags of potatoes) = 180 pounds (weight of the entire crate)

60 + 5x = 180

5x = 180 - 60

5x = 120

x = 24

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Jack,Sam and pandu wrote three different Maths test on Monday. Jack got 5 out of 10 for his test. Sam got 22 out of 40 for his test, and pandu got 12 out of 20. By converting the fractions into percentages , determine who achieved the best score

Answers

Among Jack, Pandu and  Sam, Pandu scored the best as his marks scored percentage is 60%.

What is percentage?

In mathematics, a percentage is a number or ratio that can be expressed as a fraction of 100. If you need to calculate the percentage of a number, divide the number by the whole number and multiply by 100. Percentages therefore mean 1 in 100. The word percent means around 100. Represented by the symbol '%'. 

Solution according to the information given:

Jack's percentage = (5/10)×100

                               = 50%

Sam's percentage = (22/40)×100

                               = (11/20)×100

                               = 55%

Pandu's percentage = (12/20)×100

                                  = 60%

Thus, Pandu scored the best marks by scoring 60%.

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A swimming camp charges $190 for 6 weeks of swimming lessons and $265 for 9 weeks of swimming lessons. How much does the swimming camp charge per week?

Answers

The camp charge per week = slope = $25 per week.

How to Apply the Slope Concept?

The slope is also referred to as the unit rate which is given as: m = change in y / change in x.

From the given scenario, let:

x = number of weeks

y = camp charges

We will therefore have these two points:

(6, 190) and (9, 265)

Use the two points to find the slope, which is the swimming camp charge per week:

Camp charge per week (m) = change in y / change in x = 265 - 190 / 9 - 6

= 75/3

= $25 per week.

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Gary and Greg share a 30-ounce box of cereal. By the end of the week, Gary has eaten 3/10 of the box, and Greg has eaten 3/5 of the box of cereal. How many ounces are left in the box?

Answers

Answer:

3

Step-by-step explanation:

cuz ik

Dina Lincoln purchases a $1,299.99 treadmill, a $52.99 treadmill mat and 2 pairs of running shorts at
$24.99 each. The state sales tax rate is 6.25% and the county tax rate is 1.5%. What is the sales tax on
her purchases?
A)$108.73
B)$106.79
C)$103.35
D) $98.21

Answers

Answer:108.73

Step-by-step explanation: To get the total sales tax you add box of the taxes together wich gives you 7.75%, then you find the total amount of money he spent, which was 1402.96. Lastly you find 7.75% of 1402.96 which is 108.73

Nina has 100 rupess note. She spent 40 rupess on clothes so she is left with 60 rupees then she spent 30 rupees on food so she is left with with 30 rupess and now she spends 18 rupess on jewellry so she is left with 12 rupees then she spends 12 rupess on snacks and now she is left with 0 rupess. Now when she adds 40, 30, 18, 12 she gets 100 rupees but when she adds 60, 30, 12 and 0 she gets 102. How?

Answers

because 60 is the bigger number rather than 40 and 30. 60 plus all that is 102 but because the 40 and others are smaller its going to be a smaller number

What is the minimum possible parameter of a rectangle whose length and breadth are whole numbers and area is 60 sq. Units?

Answers

The minimum possible parameter of the rectangle is 34 units.

What is a rectangle?

A rectangle is a quadrilateral having four sides and the sum of the angles is 180 in the rectangle the opposite two sides are equal and parallel and the two sides are at 90-degree angles.

Let's assume the length of the rectangle is L and the width is W. The area of the rectangle is given as 60 sq. units.

Area of rectangle = Length × Width = L × W = 60

We are looking for the minimum perimeter of the rectangle. Perimeter of rectangle = 2(L + W)

To find the minimum perimeter, we need to find the minimum values of L and W that satisfy the condition that the area is 60.

The factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60.

If we choose L = 1 and W = 60, then the area is 1 × 60 = 60.

If we choose L = 2 and W = 30, then the area is 2 × 30 = 60.

If we choose L = 3 and W = 20, then the area is 3 × 20 = 60.

If we choose L = 4 and W = 15, then the area is 4 × 15 = 60.

If we choose L = 5 and W = 12, then the area is 5 × 12 = 60.

If we choose L = 6 and W = 10, then the area is 6 × 10 = 60.

The minimum perimeter occurs when L and W are the closest in value, which is achieved when L = 5 and W = 12. Thus, the minimum perimeter of the rectangle is:

Perimeter = 2(L + W) = 2(5 + 12) = 34

Therefore, the minimum possible parameter of the rectangle is 34 units.

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How many 5/8's are in 1? Its supposed to be a mixed number (ex, 1 1/3)

Answers

There are 1 and 3/5 of 5/8 in 1, if Its supposed to be a mixed number.

What is a mixed number?

A mixed number is a combination of a whole number and a fraction. It is written in the form of "a b/c" where a is the whole number, b is the numerator of the fraction, and c is the denominator of the fraction.

To answer your second question, we can divide 1 by 5/8 as follows:

1 ÷ 5/8 = (1 x 8) ÷ 5 = 8/5

We can then write 8/5 as a mixed number by dividing the numerator (8) by the denominator (5) and writing the remainder as the fraction part.

8 ÷ 5 = 1 with a remainder of 3, so we write the answer as:

1 3/5

Therefore, there are 1 and 3/5 of 5/8 in 1.

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Mei and Ming both improved their yards by planting rose bushes and ivy they bought their supplies from the same store Mei spent 36 on 3 rose bushes and 1 pot of ivy Ming spent 168 on 9 rose bushes and 8 pots of ivy what's the cost of one rose bush and one pot of ivy..

Answers

The cost of one rose shrub costs $12 and one pot of ivy costs $24, respectively.

How can you theoretically solve an equation system?

It takes two equations with two variables to solve a system of equations. The variables can then be solved for using algebraic techniques like substitution or elimination.

Let x be the cost of one rose bush and y be the cost of one pot of ivy.

From Mei's purchase, we have:

3x + y = 36

From Ming's purchase, we have:

9x + 8y = 168

Use the first equation to solve for y:

y = 36 - 3x

Substituting this into the second equation, we get:

9x + 8(36 - 3x) = 168

9x + 288 - 24x = 168

-15x = -120

x = 8

Substituting x = 8 into equation of y, we get:

y = 24

Hence, the cost of one rose bush is $8, and the cost of one pot of ivy is $24.

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- 3x + 3y = 6
x + 3y = 18

solve using substitution
find x and y

Answers

Answer:x = 3 and y = 5

Step-by-step explanation:

We have two equations:

-3x + 3y = 6 ........(1)

x + 3y = 18 ........(2)

We can use the second equation to solve for y in terms of x:

-4x = -12

x = 4

Now we substitute this expression for y into the second equation:

3 + 3y = 18

3y = 15

y = 5

Therefore, the solution to the system of equations is x = 3 and y = 5.

equation 1: - 3x + 3y = 6

equation 2: x + 3y = 18

start with equation 2:

x + 3y = 18

subtract 3y from both sides:

x = 18 - 3y

plug the new equation into equation 1:

- 3x + 3y = 6

- 3 (18 - 3y) + 3y = 6

multiply:

-54 + 9y + 3y = 6

collect like terms:

-54 + 12y = 6

add 54 to both sides, then divide the whole equation by 12:

12y = 60

y = 5

plug the y value into either equation to solve for x. for example, here is equation 2:

x + 3y = 18

x + 3(5) = 18

x + 15 = 18

x = 3

check answer:

x + 3y = 18

3 + 3(5) = 18

3 + 15 = 18

18 = 18 is true

Which point is a solution to this system of inequalities?

Answers

Answer:

The solution of this system is the yellow region which is the area of overlap. In other words, the solution of the system is the region where both inequalities are true. The y coordinates of all points in the yellow region are both greater than x + 1 as well as less than x.

Solve the problem. The width of a rectangle is 2 ft less than 4 times the length. Write a model for the width W in terms of the length L. Select one: a. W=4L - 2 b. W=4L+2 c.W=2L - 4 d. W = 2L +4

Answers

The width of a rectangle is 2 ft less than 4 times the length, so the model for the width W in terms of the length L is W = 4L - 2.

To solve this problem, we need to create a model for the width W in terms of the length L. According to the problem, the width of the rectangle is 2 ft less than 4 times the length. This can be written as:
W = 4L - 2

This equation represents the relationship between the width and the length of the rectangle. It shows that the width is equal to 4 times the length, minus 2. Therefore, the correct answer is a. W=4L - 2.

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What are the other three angle measures if ∠1 has a measure of 45°?

Answers

The measures ∠2 = 135°, ∠5 = 45°, ∠6 = 135°, ∠4 = 45° and  ∠3 = 135°.

What are Angles?

An angle is formed when two straight lines or rays meet at a common endpoint.

The angle ∠1 = 45° is given.

Types of the angles are as follows;

Supplementary angle - Two angles are said to be supplementary angles if their sum is 180 degrees.

Corresponding angle - If two lines are parallel then the third line. The corresponding angles are equal angles.

Vertically opposite angle - When two lines intersect, then their opposite angles are equal.

Alternate angle - If two lines are parallel then the third line will make z -angle and z-angles are equal angles with the parallel lines.

∠1 + ∠2 = 180°    (Supplementary angle)

45° + ∠2 = 180°

∠2 = 135°

∠1 = ∠5 = 45°   (Corresponding angle)

∠2= ∠6 = 135°

∠4 = 45° (Alternate angle)

∠3 = 135°   (Alternate angle)

Hence, the measures ∠2 = 135°, ∠5 = 45°, ∠6 = 135°, ∠4 = 45° and  ∠3 = 135°.

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Find general solutions of the following trigono metric equations. a. \( 4 \sin ^{2}(x)-4 \sin (x)+1=0 \) b. \( \tan (x) \sin (x)+\sin (x)=0 \) c. \( 3 \csc ^{2}(\theta)=4 \) d. \( 2 \sin (3 x)-1=0 \)

Answers

The general solutions for this equation are [tex]\( x = \frac{\pi}{18} + \frac{2n\pi}{3} \)[/tex] and [tex]\( x = \frac{5\pi}{18} + \frac{2n\pi}{3} \)[/tex].

The general solutions of the given trigonometric equations can be found by applying the basic trigonometric identities and solving for the unknown variable.

a. [tex]\( 4 \sin ^{2}(x)-4 \sin (x)+1=0 \)[/tex]

This equation can be solved by using the quadratic formula. Let \( u = \sin (x) \), then the equation becomes [tex]\( 4u^2 - 4u + 1 = 0 \)[/tex]. Using the quadratic formula, we get:

[tex]\( u = \frac{-(-4) \pm \sqrt{(-4)^2 - 4(4)(1)}}{2(4)} \)\\\( u = \frac{4 \pm \sqrt{16 - 16}}{8} \)\\\( u = \frac{4}{8} = \frac{1}{2} \)[/tex]

Now, we can substitute back \( u = \sin (x) \) and solve for x:

[tex]\( \sin (x) = \frac{1}{2} \)\\\( x = \arcsin (\frac{1}{2}) \)\\\( x = \frac{\pi}{6} + 2n\pi \) or \( x = \frac{5\pi}{6} + 2n\pi \)[/tex], where n is an integer.

The general solutions for this equation are [tex]\( x = \frac{\pi}{6} + 2n\pi \)[/tex] and[tex]\( x = \frac{5\pi}{6} + 2n\pi \)[/tex].

b. [tex]\( \tan (x) \sin (x)+\sin (x)=0 \)[/tex]

This equation can be solved by factoring out \( \sin (x) \):

[tex]\( \sin (x)(\tan (x) + 1) = 0 \)[/tex]

This equation will be true if either[tex]\( \sin (x) = 0 \) or \( \tan (x) + 1 = 0 \)[/tex].

For \( \sin (x) = 0 \), the general solutions are[tex]\( x = n\pi \)[/tex] where n is an integer.

For \( \tan (x) + 1 = 0 \), the general solutions are [tex]\( x = \frac{3\pi}{4} + n\pi \)[/tex], where n is an integer.

The general solutions for this equation are [tex]\( x = n\pi \) and \( x = \frac{3\pi}{4} + n\pi \).[/tex]

c. [tex]\( 3 \csc ^{2}(\theta)=4 \)[/tex]

This equation can be solved by isolating [tex]\( \csc ^{2}(\theta) \)[/tex] and taking the square root of both sides:

[tex]\( \csc ^{2}(\theta) = \frac{4}{3} \)[/tex]

[tex]\( \csc (\theta) = \pm \sqrt{\frac{4}{3}} \)[/tex]

Now, we can use the identity[tex]\( \csc (\theta) = \frac{1}{\sin (\theta)} \)[/tex]to solve for \( \theta \):

[tex]\( \frac{1}{\sin (\theta)} = \pm \sqrt{\frac{4}{3}} \)\( \sin (\theta) = \pm \sqrt{\frac{3}{4}} \)[/tex]

The general solutions for this equation are[tex]\( \theta = \arcsin (\pm \sqrt{\frac{3}{4}}) + 2n\pi \)[/tex], where n is an integer.

d. [tex]\( 2 \sin (3 x)-1=0 \)[/tex]

This equation can be solved by isolating[tex]\( \sin (3x) \)[/tex] and taking the inverse sine of both sides:

[tex]\( \sin (3x) = \frac{1}{2} \)\( 3x = \arcsin (\frac{1}{2}) \)\\\( 3x = \frac{\pi}{6} + 2n\pi \) or \( 3x = \frac{5\pi}{6} + 2n\pi \)[/tex], where n is an integer.

The general solutions for this equation are [tex]\( x = \frac{\pi}{18} + \frac{2n\pi}{3} \)[/tex] and [tex]\( x = \frac{5\pi}{18} + \frac{2n\pi}{3} \)[/tex].

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Obtain the general solution to a 2nd order derivative for f(x)
with real coefficients if one of the roots of the auxiliary
equation is 3 + 7i

Answers

The general solution to a 2nd order derivative for f(x) with real coefficients can be obtained by finding the other root of the auxiliary equation and then using those roots to write the general solution.


Since one of the roots of the auxiliary equation is 3 + 7i, the other root must be the conjugate of this root, which is 3 - 7i. This is because the coefficients of the auxiliary equation are real, so the roots must come in conjugate pairs.

Now that we have both roots, we can write the general solution to the 2nd order derivative as:

f(x) = e^(3x)(C1*cos(7x) + C2*sin(7x))

where C1 and C2 are arbitrary constants.

This is the general solution to the 2nd order derivative for f(x) with real coefficients when one of the roots of the auxiliary equation is 3 + 7i.

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Please help me to solve this math problem:
-From a port P, a ship sails 46 km on a
bearing of 104 followed by 32 km on a
bearing of 310%.
a Calculate the distance and bearing of
the ship from P after this journey.
b The ship travels west until it is due
north of P, The captain says they they are
now less than 10 km from P.
Is he correct?

Answers

Since the distance between P and S is greater than 10 km, the captain is incorrect. The ship is still more than 10 km away from P.

What is function?

In mathematics, a function is a rule that maps a set of inputs (domain) to a set of outputs (codomain) in such a way that each input is associated with exactly one output. A function can be represented using various notations, including equations, graphs, and tables. A function can be thought of as a machine that takes an input and produces an output. The input is usually represented by the variable x, and the output is represented by the variable y. The relationship between the input and output is defined by the function rule. Functions are used in many areas of mathematics, science, and engineering to describe various phenomena, such as motion, growth, and decay. They are also used to model and analyze data in statistics and economics, and to design and control systems in engineering and computer science.

Here,

a) To solve this problem, we can use the Law of Cosines to find the distance and the Law of Sines to find the bearing.

First, let's label the points as follows:

P: the starting point

Q: the point reached after sailing 46 km on a bearing of 104

R: the final destination reached after sailing 32 km on a bearing of 310

To find the distance QR, we can use the Law of Cosines:

QR² = PQ² + PR² - 2(PQ)(PR)cos(QPR)

where PQ is the distance sailed on the first leg, PR is the distance sailed on the second leg, and angle QPR is the angle between the two legs.

We can calculate PQ and PR using basic trigonometry:

PQ = 46cos(14)

PR = 32cos(50)

Substituting these values into the Law of Cosines, we get:

QR² = (46cos(14))² + (32cos(50))² - 2(46cos(14))(32cos(50))cos(206)

Simplifying this expression using a calculator, we get:

QR ≈ 67.7 km

To find the bearing of QR, we can use the Law of Sines:

sin(QRP) / QR = sin(QPR) / PR

where angle QRP is the bearing we want to find.

Substituting the known values, we get:

sin(QRP) / 67.7 = sin(310 - 50) / (32sin(14))

Solving for sin(QRP) and taking the inverse sine, we get:

sin(QRP) ≈ 0.493

QRP ≈ 30.1°

Therefore, the ship is approximately 67.7 km away from P on a bearing of 30.1°.

b) If the ship travels west until it is due north of P, it will reach a point S that forms a right triangle with P and Q. Let's label the angles as follows:

angle QPS: the angle between PQ and PS

angle PQS: the angle between PS and QS

angle QSP: the right angle at S

We know that angle QPS is 90° (since the ship travels due north) and that PQ = 46 km. To find PS, we can use basic trigonometry:

PS = PQtan(QPS)

PS = 46tan(90-104)

PS ≈ 26.8 km

To check if the captain is correct, we need to find the distance between P and S. We can use the Pythagorean theorem:

PS² + SP² = PQ²

SP² = PQ² - PS²

SP² = (46)² - (26.8)²

SP ≈ 38.5 km

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The expression 4x + 13 represents the time it takes a commuter to travel in the morning to work. The expression 10x – 2 represents the time it takes a commuter to travel in the evening from work. What is the total travel time?

14x + 15
14x + 11
6x + 11
6x + 15

Answers

Answer:

The total travel time is the sum of the time it takes to travel in the morning and the time it takes to travel in the evening.

Total travel time = (morning travel time) + (evening travel time)

= (4x + 13) + (10x - 2)

= 14x + 11

Therefore, the total travel time is 14x + 11. Answer: B.

Answer:

B: 14x+11

Step-by-step explanation:

i took the test and got it right

Show all work to calculate the following exactly, include any reference triangle (a) For x > 0, if y = arccot(3x/8), find cos(y). (b) Show HOW to use your TI to approximate: sec^-1 (67). Write a sentence to tell Explain what the answer tells us. (c) Show how to find the exact value of cos^-1(cos(-5phi/6)). Show reference triangles for support:

Answers

(a)  cos(y) = adjacent/hypotenuse = 3x/√(64 + 9x^2) b) The angle whose secant is 67 is approximately 89.149 degrees. C) The exact value of cos^-1(cos(-5phi/6)) is phi/3.

For x > 0, if y = arccot(3x/8), find cos(y).Solution: First, we draw the reference triangle with y = arccot(3x/8). Since y = arccot(3x/8), we have:
tan(y) = 8/3x. This means that the opposite side is 8 and the adjacent side is 3x.

Using the Pythagorean Theorem, we can find the hypotenuse: h = √(8^2 + (3x)^2) = √(64 + 9x^2). Now, we can find cos(y) using the definition of cosine: cos(y) = adjacent/hypotenuse = 3x/√(64 + 9x^2)

To find sec^-1 (67) using a TI calculator, we can use the inverse cosine function: sec^-1 (67) = cos^-1 (1/67) On the TI calculator, we can enter: cos^-1 (1/67). And the calculator will give us an approximate value of 89.149 degrees.

The angle whose secant is 67 is approximately 89.149 degrees.
To find the exact value of cos^-1(cos(-5phi/6)).

The reference triangle for 5phi/6 is a 30-60-90 triangle, with the hypotenuse equal to 2, the opposite side equal to √3, and the adjacent side equal to 1.

Therefore, we have: cos(5phi/6) = adjacent/hypotenuse = 1/2. Now, we can find the exact value of cos^-1(cos(-5phi/6)): cos^-1(cos(-5phi/6)) = cos^-1(1/2) = phi/3. Therefore, the exact value of cos^-1(cos(-5phi/6)) is phi/3.

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Express bar (xY) in component form. Then aph bar (xY). x=[[-9],[10]] and Y=[[-4],[3]]

Answers

The component form of bar (xY) = [[36],[30]] and aph bar (xY) = [[36, 30]]

To express bar (xY) in component form, we need to multiply the matrices x and Y together. The result will be a 2x1 matrix, which is the component form of bar (xY).

First, we multiply the first row of x by the first column of Y:

[-9] * [-4] = 36

Next, we multiply the second row of x by the second column of Y:

[10] * [3] = 30

Now we can put these two results together to get the component form of bar (xY):

bar (xY) = [[36],[30]]

To aph bar (xY), we simply take the transpose of the matrix. This means that we switch the rows and columns:

aph bar (xY) = [[36, 30]]

So the final answer is:

bar (xY) = [[36],[30]]
aph bar (xY) = [[36, 30]]

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Express the product of ((2)/(3)x+(4)/(3)) and (2x+(5)/(6)) as a trinomial in simplest form.

Answers

The product of ((2)/(3)x+(4)/(3)) and (2x+(5)/(6)) as a trinomial in simplest form is (4/3)x^2 + (13/9)x + (10/9).

To express the product of ((2)/(3)x+(4)/(3)) and (2x+(5)/(6)) as a trinomial in simplest form, we need to multiply the two binomials using the distributive property.

First, we will multiply the first term of the first binomial by each term of the second binomial:
(2/3)x * 2x = (4/3)x^2
(2/3)x * (5/6) = (10/18)x = (5/9)x

Next, we will multiply the second term of the first binomial by each term of the second binomial:
(4/3) * 2x = (8/3)x
(4/3) * (5/6) = (20/18) = (10/9)

Now we will combine like terms:
(4/3)x^2 + (5/9)x + (8/3)x + (10/9) = (4/3)x^2 + (13/9)x + (10/9)

Therefore, the product of ((2)/(3)x+(4)/(3)) and (2x+(5)/(6)) as a trinomial in simplest form is (4/3)x^2 + (13/9)x + (10/9).

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Answer the next 4 questions

12) if the base area of a square prism is 15 square centimeters and the hight is eight centimeters, what is the volume of the prism?

13) if the base area of a square prism is 16 sq cm and the height is 20 centimeters, what is the volume of the prism?

14) if the base area of a cylinder is 15.6 square centimeters and the height is four centimeters, what is the volume of the cylinder?

15) if the base area of a cylinder is 1.2 square centimeters and the height is three centimeters, what is the volume of the cylinder?

Answers

Answer:

I don't know dude...............

QUESTION: LetP=[72​75​​32​31​​]. Answer the following: 1. (1 mark) Explain (briefly) whyPis a regular transition matrix. 2. (2 marks) Given the initial state vectorx0​=[103​​107​​]T, find the state vectorx2​. 3. (3 marks) Calculate the steady state vector. SHOW YOUR WORK!

Answers

1.  A transition matrix is regular if there is a positive integer k such that P^k has all positive elements.

2. The value of x2 =  [128,295, 44,557]T.

3. The value of x = [0.701, 0.299, 0]T .


1. P is a regular transition matrix because it has all positive elements, meaning that it is possible for any state to transition to any other state.

2. To find the state vector x2, we need to multiply the initial state vector x0 by the transition matrix P twice:
x2 = P^2 * x0
= P * P * x0
= P * [72 * 10 + 75 * 7, 32 * 10 + 31 * 7]T
= P * [945, 457]T
= [72 * 945 + 75 * 457, 32 * 945 + 31 * 457]T
= [128,295, 44,557]T

3. To find the steady state vector, we need to solve the equation Px = x for x. This means that we need to find the eigenvector of P corresponding to the eigenvalue

1. We can do this by finding the null space of (P - I), where I is the identity matrix:


(P - I)x = 0
=> [71 -75 0, -32 30 0, 0 0 -1]x = 0
=> x = c[75, 32, 0]T, where c is a constant.


To find the steady state vector, we need to normalize this eigenvector so that it sums to 1:
x = [75/107, 32/107, 0]T
= [0.701, 0.299, 0]T

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100 POINTS PLEASEEE SOMEBODY I NEED TO TURN THIS IN

Answers

The diagonals are 17.4 inches

The length does not meet the regulationThe measurement of KR is 8 units

How to determine the lengths of the diagonals

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

DH = 10, HK = 8.2, KB = 6, HR = 8 and KY = 6.8

Given that DHB is a right triangle, we have

DB² = HB² + DH²

So, we have

DB² = (8.2 + 6)² + 10²

DB² = 301.64

Take the square root

DB = 17.4

Does the length meet the regulation

The triangles DBY and RYB are congruent triangles

So, we have

RY = 17.4

The figure is an isosceles triangle, and the length does not meet the regulation

This is so because the length is less than the required 20 inches

The measurement of KR

The two non-parallel sides of an isosceles triangle are of equal length

So, we have

1/2x + 5 = 2x - 4

Evaluate the like terms

3/2x = 9

This gives

x = 9 * 2/3

x = 6

So, we have

KR = 1/2x + 5

This gives

KR = 1/2 * 6 + 5

KR = 8

So, the value of KR is 8 units

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La diferencia "8 menos que q​

Answers

Answer:

q - 8

Step-by-step explanation:

q - 8

Answer:

q=0

Step-by-step explanation:

Help me! Which number sentence is true?

A
B
C
D

Answers

Step-by-step explanation:

D option is the correct one.

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