If θ is an angle in standard position and its terminal side passes through the point (-4,1), find the exact value of csc ⁡ � cscθ in simplest radical form.

Answer:

7y + 15 - 2y = 5(y + 3)

Step-by-step explanation:

So two equations have infinitely many solutions, when they are exactly the same equation, in their most simplified form, for example: 2x = 3x-x which simplifies to 2x=2x. So in the options, three of the options have the same equation on the right side, so I'll distribute the 5. \(5(y+3) = 5y+15\). Now let's look at the options:

7y + 3-2y

5y+3 (this is not the same as 5y + 15)

7y + 15 (this is not the same as 5y + 15)

7y + 15 - 2y

5y + 15 = 5y + 15 (this is the same)

To find the powers of a relation, we need to understand the composition of relations. The composition of two relations, denoted as \(R1*R2\), is defined as follows:

Given\(R\)= {(1, 1), (1, 2), (2, 3), (3, 1), (3, 4), (4, 2)}

\(R^2\) = {(1, 1), (1, 2), (1, 3), (2, 1), (3, 1), (3, 2), (4, 1), (4, 2), (4, 3)}

Therefore,\(R^2\) = {(1, 1), (1, 2), (1, 3), (2, 1), (3, 1), (3, 2), (4, 1), (4, 2), (4, 3)}

\(R^2*R\) = {(1, 1), (1, 2), (1, 3), (2, 1), (2, 2), (2, 4), (3, 1), (3, 3), (4, 1), (4, 2), (4, 3)}

Therefore, \(R^3\)= {(1, 1), (1, 2), (1, 3), (2, 1), (2, 2), (2, 4), (3, 1), (3, 3), (4, 1), (4, 2), (4, 3)}

Hence, \(-R^2\) and\(R^3\)are:

\(-R^2\) = {(-1, -1), (-1, -2), (-1, -3), (-2, -1), (-3, -1), (-3, -2), (-4, -1), (-4, -2), (-4, -3)}

\(R^3\)= {(1, 1), (1, 2), (1, 3), (2, 1), (2, 2), (2, 4), (3, 1), (3, 3), (4, 1), (4, 2), (4, 3)}

The relation \(-R^2\) represents the negation of each element in the relation \(R^2\),assuming the set includes negative integers as well.

Learn more about relation here:

https://brainly.com/question/6241820

#SPJ11

r = {(1, 1), (1, 2), (2, 3), (3, 1), (3, 4), (4, 2)} on the set {1, 2, 3, 4}, the composition of r with itself, denoted as r^2, and the composition of r with itself three times, denoted as r^3, are calculated.

The composition of relations involves combining the ordered pairs from two relations based on a specific rule. In this case, we are considering the relation r = {(1, 1), (1, 2), (2, 3), (3, 1), (3, 4), (4, 2)} on the set {1, 2, 3, 4}.

To find r^2, we need to calculate the composition of r with itself. We multiply the ordered pairs from r in such a way that the second element of each pair matches the first element of another pair. Applying this rule, we have r^2 = {(1, 2), (2, 1), (2, 2), (3, 2), (3, 3), (4, 1)}.

To find r^3, we calculate the composition of r with itself three times. By applying the same rule as before, we have r^3 = {(1, 1), (1, 3), (2, 2), (2, 4), (3, 1), (3, 2), (3, 3), (4, 1), (4, 3)}.

Therefore, the compositions −r^2 and r^3 of the given relation r can be expressed as −r^2 = {(1, 3), (2, 1), (2, 3), (3, 1), (3, 3), (4, 1)} and r^3 = {(1, 1), (1, 3), (2, 2), (2, 4), (3, 1), (3, 2), (3, 3), (4, 1), (4, 3)}.

Learn more about composition here:

https://brainly.com/question/13808296

#SPJ11

Answer:

i believe the answer is f(x)=6

Step-by-step explanation:

The highest power of 2 that is less than or equal to 1000 is 2^9, which gives us the required representation of 1000.

In mathematics, a base is the number of digits or distinct symbols used to represent numbers in a positional numeral system. For example, in the decimal system (which we commonly use), the base is 10 because we use 10 distinct digits from 0 to 9.

Now, let's consider the number 1000. In order to find the lowest base in which this could be a valid number, we need to break down 1000 into its constituent digits. Since 1000 has 4 digits, we can represent it as:

1000 = 1 x base^3 + 0 x base^2 + 0 x base^1 + 0 x base^0

where base is the number system we are using. Now, we need to find the lowest value of base that makes this equation valid.

We can see that if we set base = 2, then the equation becomes:

1000 = 1 x 2^9 + 0 x 2^8 + 0 x 2^7 + 0 x 2^6 + 0 x 2^5 + 0 x 2^4 + 0 x 2^3 + 0 x 2^2 + 0 x 2^1 + 0 x 2^0

Here, we have used the binary system, which has a base of 2. As we can see, the highest power of 2 that is less than or equal to 1000 is 2^9, which gives us the required representation of 1000.

To know more about Number visit:

https://brainly.com/question/3589540

#SPJ11

We are given the curve r = 1 + sin(θ), 0 ≤ θ ≤ 2π. We are to find the length of the curve over the given interval.

The length of the curve over the given interval can be calculated using the formula given below:L = ∫a^b sqrt[ r^2 + (dr/dθ)^2 ] dθ

Here, a = 0, b = 2π, r = 1 + sin(θ), dr/dθ = cos(θ).

Substituting the values in the formula,

we get:L = ∫0^2π sqrt[ (1 + sin(θ))^2 + cos^2(θ) ] dθ= ∫0^2π sqrt[ 1 + 2sin(θ) + sin^2(θ) + cos^2(θ) ] dθ= ∫0^2π sqrt[ 2 + 2sin(θ) ] dθ= ∫0^2π sqrt(2) sqrt[ 1 + sin(θ) ] dθ= sqrt(2) ∫0^2π sqrt[ 1 + sin(θ) ] dθ

We can evaluate the integral using substitution. Let u = 1 + sin(θ). Then, du/dθ = cos(θ) and dθ = du/cos(θ).When θ = 0, u = 1 + sin(0) = 1 + 0 = 1.When θ = 2π, u = 1 + sin(2π) = 1 + 0 = 1.

Therefore, the limits of integration change to u = 1 at θ = 0 and u = 1 at θ = 2π.

Substituting the limits of integration and the value of dθ, we get:L = sqrt(2) ∫1^1/cos(θ) sqrt(u) du= sqrt(2) ∫1^1/cos(θ) u^(1/2) du= 0The length of the curve over the given interval is zero.

Therefore, the answer is "0".

We have given the length of the curve over the given interval is 0. The given curve is r = 1 + sin(θ), 0 ≤ θ ≤ 2π.

To know more about integration, click here

https://brainly.com/question/31744185

#SPJ11

Answer: To subtract mixed fractions with different denominators, you need to convert the mixed fractions to equivalent fractions with a common denominator. Once the fractions have a common denominator, you can simply subtract the numerators and keep the denominator the same.

Example:

the difference of 2 1/3 and 1 3/4 is 5/12.

Step-by-step explanation:

First, convert 2 1/3 to an improper fraction: 2 1/3 = 7/3

Next, convert 1 3/4 to an improper fraction: 1 3/4 = 7/4

Now, both fractions have the same denominator, 3. So, you can subtract the numerators:

7/3 - 7/4 = (7 * 4 - 7 * 3) / (3 * 4) = 28/12 - 21/12 = 7/12

Finally, convert the answer back to a mixed fraction: 7/12 = 7 ÷ 12 =  5/12.

Answer:

race run = 27.60 km

Step-by-step explanation:

given data

run = 5 %

race = 1.38 km

to find out

how long is the race

solution

we get here how long he race that is here

1.38 ÷ 5 %  ×  100  

= 20

so

race run = 1.38 ×  20

race run = 27.60 km

The value of g is g = w² - 14w + 49, according to the question.

What do you mean by formula?

A truth or a rule expressed using mathematical symbols is the formula. An equal sign is typically used to connect two or more values. When you are aware of the value of one quantity, you can use the formula to determine the value of the other. It facilitates speedy question resolution. Formulas are used in algebra, geometry, and other subjects to speed up and simplify the process of arriving at the result.

According to the given question,

We have :

w = 7 - √g

Firstly isolate the g,

w = 7 - √g

Do the opposite of PEMDAS, first subtract 7 from both sides,,

w (-7) = -√g + 7 (-7)

w - 7 = -√g

Now, multiply -1 (as -√g is the same as -1√g) to both sides

-1(w - 7) = √g

-1w + 7 = √g

To get rid of the square root, you must square both sides,

Note: -1w is the same as -w.

Note: you are squaring all the terms on the other side, not just one.

(-w + 7)² = (√g)²

g = (-w + 7)²

g = (-w + 7)(-w + 7) (note, this can be the answer your teacher wants, or                                            g = (-w + 7)²    )

Use the FOIL method (First, Outside, Inside, Last)

(-w)(-w) = w²

(-w)(7) = -7w

(7)(-w) = -7w

(7)(7) = 49

g = w² - 7w - 7w + 49

Then, simplify (combine all like terms):

g =w² - 7w - 7w + 49

g = w² - 14w + 49

Therefore, the value of g = w² - 14w + 49 .

To learn more about formula, visit:

https://brainly.com/question/1293486?referrer=searchResults

#SPJ4

The diameter of the circle pen for the sheep of the farmer is 68 yards.

The total length of the fencing used for the preparation of the fencing for sheep is 213.52 yards.

Thus,

circumference = 213.52 yards

The formula for the calculation of the circumference of circle is,

circumference = 2πr,

In which,

π = 3.14  and radius r.

Thus,

213.52 = 2πr

r = 213.52 / 2π

r = 34

Diameter = 2 x radius

Diameter = 2 x 34

Diameter = 68 yards.

Thus, the diameter of the circle pen for the sheep of the farmer is 68 yards.

To know more about the circumference of the circle, here

https://brainly.com/question/18571680

#SPJ4

Answer:

4,600,000,000

Step-by-step explanation:

Don't forget the order of operations

3.243 × 10⁸/7.05

= 46,000,000 × 10²

= 4,600,000,000

or 4.6 × 10⁹

Answer:

4.6x10 to the power of 5

Step-by-step explanation:

7.05×10

2

3.243×10

8

​

Divide them.

\frac{3.243}{7.05}\times \frac{10^8}{10^2}

7.05

3.243

​

×

10

2

10

8

​

Divide numbers and 10's separeately.

0.46\times 10^6

0.46×10

6

Subtract exponents.

(4.6\times 10^{-1})\times 10^6

(4.6×10

−1

)×10

6

Rewrite as a number bigger than 1

4.6\times (10^{-1}\times 10^6)

4.6×(10 −1 ×10 6 )

Associate

4.6\times 10^5

4.6×10 5

Add exponents

Answer:

the answer is x = 4.

1. use the quadratic formula.

2. use a coordinate plane to check your answer.

hope this helps.

Answer:

x = 4

Step-by-step explanation:

(x - 3)(x² + 3x + 9) = 37 ← distribute left side

x³ + 3x² + 9x - 3x² - 9x - 27 = 37 , simplify left side by collecting like terms

x³ - 27 = 37 ( add 27 to both sides )

x³ = 64 ( take cube root of both sides )

x = \(\sqrt[3]{64}\) = 4

Answer:

4. t ≥0

5. x>0

6. k ≤ 3

7. r ≥ 2

8. v ≥ 7

Step-by-step explanation:

I hope this helps

The median weight of the players on the football team is approximately 160 lbs.

The box plot provides a visual summary of the data which shows the distribution of the weights of the players on the football team. The box plot consists of a box and two "whiskers" which represent the upper and lower quartiles of the data. The box is bounded by the upper quartile and lower quartile and the two whiskers represent the highest and lowest values in the data set, excluding any outliers. The median weight of the players is represented by the line in the middle of the box, which is approximately 160 lbs. The box plot is a useful tool for summarizing the data and provides a quick and easy way to visualize the distribution of the players' weights. The median weight of 160 lbs gives us an idea of the average weight of the players, which can be used to determine the overall strength of the team.

Learn more about median here

https://brainly.com/question/28060453

#SPJ4

The complete question is

a high school has 40 players on the football team. the summary of the players' weights is given in the box plot. what is the median weight of the players and find lbs.

Question 1: The item not included in the cost of merchandise inventory is "Purchase discounts."

2: The total cost of the merchandise is $3,332.00.

5: The company's gross margin and operating expenses, are $211,000 and $191,720.

Merchandise inventory expenses normally consist of the price paid for the inventory, deductions from the purchase price resulting from purchase returns and allowances, and freight expenses paid by the purchaser.

Although purchase discounts reduce the cost of merchandise inventory, they are not considered part of it. Instead, they are treated as a distinct discount in the accounting records.

Learn more about merchandise inventory from

https://brainly.com/question/27046371

#SPJ1

The procedure that can be used to show the converse of the Pythagorean theorem using side lengths chosen from 2 cm, 3 cm, 4 cm, and 5 cm is option C.

Knowing that 3^2 +4^2 = 5^2, draw the 3 cm side and the 4 cm side with a right angle between them. The 5 cm side will fit to form a right triangle.

The Pythagorean Theorem is a relationship that exists between the sides of a right triangle, which is a triangle with one interior angle of 90 degrees. According to the Pythagorean Theorem, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

The Converse of the Pythagorean Theorem is an inverse statement that implies that if a triangle's sides satisfy the relationship described in the Pythagorean Theorem, then the triangle is a right triangle.

To know more about Pythagorean visit:

https://brainly.com/question/28032950

#SPJ11

ANSWER

N = 11

EXPLANATION

Given:

3N + 5 = 38

Desired Outcome:

Value of N

Solve for N

Hence, the value of N is 11.

Answer:

14/15÷3/5 =1 5/9

Step-by-step explanation:

14/15÷3/5=?

Dividing two fractions is the same as multiplying the first fraction by the reciprocal (inverse) of the second fraction.

Take the reciprocal of the second fraction by flipping the numerator and denominator and changing the operation to multiplication. Then the equation becomes

14/15×5/3=?

For fraction multiplication, multiply the numerators and then multiply the denominators to get

14×5 15×3=7045

This fraction can be reduced by dividing both the numerator and denominator by the Greatest Common Factor of 70 and 45 using

GCF(70,45) = 5

70÷5 45÷5=14/9

The fraction

14/9

is the same as

14÷9

Convert to a mixed number using

long division for 14 ÷ 9 = 1R5, so

14/9=1 5/9

Therefore:

14/15÷3/5=1 5/9

Please mark brainliest

Answer:

Since the ratio of powdered mix to water is 3:2, we know that for every 3 parts of powdered mix, there are 2 parts of water. Therefore, the total weight of the fruit drink will be 3 + 2 = 5 parts.

To find out how much powdered mix is needed for a certain amount of fruit drink, we can set up a proportion:

3 parts powdered mix : 2 parts water = 120g powdered mix : x (unknown amount of water)

Cross-multiplying, we get:

3x = 240

Dividing both sides by 3, we get:

x = 80

Therefore, 80g of water is needed for the fruit drink. To find the total weight of the fruit drink, we add the weight of the powdered mix to the weight of the water:

Total weight = 120g powdered mix + 80g water = 200g

So, 200g of fruit drink is needed for 120g of powdered mix.

Answer:

Total weight = 120g powdered mix + 80g water = 200g

Step-by-step explanation:

The standard matrices for the given transformations are:

\(A = \left[\begin{array}{ccc}1&-4\\3&5\end{array}\right]\)

\(A' = \left[\begin{array}{ccc}-4\\5\end{array}\right]\)

We have,

To find the standard matrices A and A' for the composite linear transformations T = T_2 o T_1 and T' = T_1 o T_2, we can follow these steps:

- Find the standard matrix for each individual transformation.

Compute the standard matrix for the composite transformation by multiplying the standard matrices of the individual transformations in the correct order.

Let's start by finding the standard matrices for \(T_1\) and \(T_2\):

For \(T_1\): R² → R², \(T_1\)(x, y) = (x - 4y, 3x + 5y)

To find the standard matrix for \(T_1\), we need to determine where the standard basis vectors i = (1, 0) and j = (0, 1) are mapped under \(T_1\).

\(T_1\) (i) = (1 - 40, 31 + 50) = (1, 3)

\(T_2\) (j) = (0 - 41, 30 + 51) = (-4, 5)

Now, the standard matrix A for \(T_1\) is formed by putting the transformed standard basis vectors as its columns:

A = [\(T_1\)(i) | \(T_1\)(j)]

\(A = \left[\begin{array}{ccc}1&-4\\3&5\end{array}\right]\)

Next, let's find the standard matrix for

\(T_2\): R² → R, \(T_2\) (x, y) = (0, x)

To find the standard matrix for \(T_2\), we need to determine where the standard basis vectors i = (1, 0) and j = (0, 1) are mapped under \(T_2\).

\(T_2\)(i) = (0, 1)

\(T_2\)(j) = (0, 0)

The standard matrix for \(T_2\) is a 1 x 2 matrix since the target space is

R (1-dimensional):

A' = [\(T_2\)(i) | \(T_2\)(j)] = [0 0]

Now, let's find the standard matrix for the composite transformation T

= \(T_2\) o \(T_2\):

T = \(T_2\) o \(T_1\)(x, y)

To find the standard matrix for T, we first apply \(T_1\) to the standard basis vectors, and then apply \(T_2\) to the result.

\(T_1\)(i) = (1, 3)

\(T_1\)(j) = (-4, 5)

Now, apply \(T_2\) to the above results:

\(T_2(T_1(i)) = T_2(1, 3) = 3\)

(because the output of T_2 is only the x-coordinate)

\(T_2(T_1(j)) = T_2(-4, 5) = 5\)

The standard matrix A for T is a 1 x 2 matrix:

\(A = [T(T_1(i)) | T(T_1(j))] = [3, 5]\)

Finally, let's find the standard matrix for the composite transformation T' = \(T_1 ~o ~T_2:\)

\(T' = T_1 ~o ~T_2(x, y)\)

To find the standard matrix for T', we first apply \(T_2\) to the standard basis vector (x, y) and then apply \(T_1\) to the result.

\(T_2(x, y) = (0, x)\)

Now, apply \(T_1\) to the above result:

\(T_1(T_2(x, y)) = T_1(0, x) = (0 - 4x, ~3*0 + 5x) = (-4x, ~5x)\)

The standard matrix A' for T' is a 2 x 1 matrix:

A' = [T'(x, y)]

\(A' =\left[\begin{array}{ccc}-4\\5\end{array}\right]\)

Thus,

The standard matrices for the given transformations are:

\(A = \left[\begin{array}{ccc}1&-4\\3&5\end{array}\right]\)

\(A' = \left[\begin{array}{ccc}-4\\5\end{array}\right]\)

Learn more about matrix here:

https://brainly.com/question/28180105

#SPJ12

The complete question:

Find the standard matrices A and A' for T = T_2 о T_1 and T' = T_1 о T_2.

T_1: R² → R², T_1 (x, y) = (x − 4y, 3x + 5y)

T2: R² → R, T_2 (x, y) = (0, x)

A =

A' =

Answer:

⟨-5, -1⟩

This is the right answer Edge 2020

Step-by-step explanation:

U + v in the component form will be -5 \(\hat{i}\) - \(\hat{j}\) hence, ⟨-5, -1⟩ will be the correct answer.

An item with both magnitude and direction is referred to be a vector.

A vector can be visualized geometrically as a straight spline, with a pointing in the orientation and a length equal to the value of the vector.

Geometrical objects with magnitude and direction are called vectors.

A line with an arrow in its direction can also be used to represent a vector, and the length of the line relates to the vector's amplitude.

Given that a vector initial point at (3, 9) and terminal point at (–7, 5). Vector v has initial point at (1, –4) and a terminal point at (6, –1).

So vector A = -10\(\hat{i}\\\) - 4\(\hat{j}\) and B = 5\(\hat{i}\\\) +3\(\hat{j}\) now vector joning by this two will be AB =  -5 \(\hat{i}\) - \(\hat{j}\) .

For more information about vector

https://brainly.com/question/13322477

#SPJ5

we find that the numerical approximation using Euler's method gives y(2) ≈ 1.865, while the analytical solution gives y(2) = 2.5.

Using the formula y(n+1) = y(n) + Δx * f(x(n), y(n)), where f(x, y) = x² √y, we can calculate the values of y at each step. Here's the step-by-step calculation:

Step 1: For x = 0, y = 1 (initial condition).

Step 2: For x = 0.2, y = 1 + 0.2 * (0.2)² * √1 = 1.008.

Step 3: For x = 0.4, y = 1.008 + 0.2 * (0.4)² * √1.008 = 1.024.

Step 4: For x = 0.6, y = 1.024 + 0.2 * (0.6)² * √1.024 = 1.052.

Step 5: For x = 0.8, y = 1.052 + 0.2 * (0.8)² * √1.052 = 1.094.

Step 6: For x = 1.0, y = 1.094 + 0.2 * (1.0)² * √1.094 = 1.155.

Step 7: For x = 1.2, y = 1.155 + 0.2 * (1.2)² * √1.155 = 1.238.

Step 8: For x = 1.4, y = 1.238 + 0.2 * (1.4)² * √1.238 = 1.346.

Step 9: For x = 1.6, y = 1.346 + 0.2 * (1.6)² * √1.346 = 1.483.

Step 10: For x = 1.8, y = 1.483 + 0.2 * (1.8)² * √1.483 = 1.654.

Step 11: For x = 2.0, y = 1.654 + 0.2 * (2.0)² * √1.654 = 1.865.

Therefore, using Euler's method with a step size of Δx = 0.2, we approximate y(2) to be 1.865.

To obtain the analytical solution to the ODE, we can separate variables and integrate both sides:

∫(1/√y) dy = ∫x² dx

Integrating both sides gives:

2√y = (1/3)x³ + C

Solving for y:

y = (1/4)(x³ + C)²

Using the initial condition y(0) = 1, we can substitute x = 0 and y = 1 to find the value of C:

1 = (1/4)(0³ + C)²

1 = (1/4)C²

4 = C²

C = ±2

Since C can be either 2 or -2, the general solution to the ODE is:

y = (1/4)(x³ + 2)² or y = (1/4)(x³ - 2)²

Now, let's evaluate y(2) using the analytical solution:

y(2) = (1/4)(2³ + 2)² = (1/4)(8 + 2)² = (1/4)(10)² = 2.5

Learn more about Integrate here : brainly.com/question/31744185

#SPJ11

Answer:

510 ft²

Step-by-step explanation:

in the triangle

base (b) = 5 ft

height of the triangle (h1) = 12 ft

height of the prism = 15 ft

Now

Lateral surface area (LSA)

= perimeter of triangular base * height

= ( 13 + 5 + 12) * 15

= 450 ft²

Total surface area

= LSA + 2 * area of triangular base

= 450 + 2 * 1 / 2 * b * h1

= 450 + 5 * 12

= 450 + 60

= 510 ft²

Hope it will help :)❤

Answer:

A. 1 cm will represent 300 metres in real life.

B. 2.5 inches will represent 15 miles on the road

Step-by-step explanation:

Part A.

The scale on the map is 1: 30000. This means that for every 1 unit drawn on the paper, it actually represents 30,000 units in real life.

To get the actual distance represented by 1 centimetre, we will first have to convert 1 cm to metre. this is because our answer is required in metres.

This will be 1 cm = 0.01 metres

We can no set up the relation.

if 1 unit represents 30,0000 units in real life

0.01 metres will represent x metres in real life.

This will be got by cross multiplying\(x= \frac{0.01 \times 30,000}{1}=300 metres\)

it will represent 300 metres in real life.

Part B

following the same principle above, we can also set up a relation.

If 1 inch represents 6 miles

2.5 inches will represent x miles on the road.

cross multiplying, we will have

\(x= \frac{2.5 \times6}{1}= 15 miles\)

2.5 inches will represent 15 miles on the road

Answer:

8

Step-by-step explanation:

4 miles= 30= half hour x 2 equals 60= hour so its basic math 4 x 2

Answer:

7000 im pretty sure if not im sorry

Answer:

D) all real number greater than or equal to 0

Step-by-step explanation:

pls mark brainliest

Step-by-step explanation:

i tried to give the answer good luck you all

Answer:

American Revolution!!!

Step-by-step explanation:

Key words- COLONISTS- INDEPENDANCE BRITAN

Answer:

american revolution

Step-by-step explanation:

its the first time that the britian fought the americans