The point (-sqrt2/2, sqrt2/2) is the point at which the terminal ray of angle theta intersects the unit circle. What are the values for cosine and cotangent functions for angle theta

Answer:1004.8

Step-by-step explanation:

divide 8 by 2 since we need the radius which gives us 4. Then square it by the second power which will give you 16 since 4x4 equals 16. Then multiply 16 by pie/3.14 and you should get 50.24. then multiply it by the height which is 20in and you should get the answer which is 1004.8

The expression that describe the area of the shaded part is 1/3 × 1/2 (optionD)

The space enclosed by the boundary of a plane figure is called its area. The area of a figure is the number of unit squares that cover the surface of a closed figure. Area is measured in square units like cm² and m². Area of a shape is a two dimensional quantity.

therefore the area of the shaded part is l× w

On the vertical row 3 boxes are shaded out of 6

and on the horizontal 3 are shaded out of 9 boxes

A = 3/6 × 3/9

A = 1/2 × 1/3

therefore the area of the shaded part = 1/3 × 1/2

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a. The equation of the tangent plane is z = 1 + x.

b. The point (4/3, 8/3, 5) lies on both the plane T(0,1) and the line l.

c. The other points on the graph of f(x) whose tangent plane contains the line l are (-9/8, -1/2, -21/8) and (-25/32, -3/4, -47/32)

The function is defined as a mathematical expression that defines a relationship between one variable and another variable.

(a) The partial derivatives of f(x) at this point:

∂f/∂x = 2x + y²

∂f/∂y = x² + 2xy

Evaluating these at (0,1), we get:

∂f/∂x(0,1) = 1

∂f/∂y(0,1) = 0

So the equation of the tangent plane is:

z = f(0,1) + ∂f/∂x(0,1)(x-0) + ∂f/∂y(0,1)(y-1)

z = 1 + x

(b)

The plane T(0,1) contains the line l:

2x = y = (z+3)/2

Substituting y = 2x and z = 2y-3, we get:

z = 2(2x) - 3 = 4x - 3

So any point on the line l can be written as (x, 2x, 4x-3).

Substituting these values into the equation of the plane, we get:

4x-3 = 1 + x

3x = 4

So x = 4/3, y = 8/3, and z = 5.

Therefore, the point (4/3, 8/3, 5) lies on both the plane T(0,1) and the line l.

(c) To find all other points on the graph of f whose tangent plane contains the line l, we need to find the intersection of the graph of f with the plane T(0,1) + λ(2,0,1), where λ is a scalar. This gives us the system of equations:

x² + y²xy = 1 + x + 2λ

2x + y² = 0

y - 1 = λ

Solving for x and y in terms of λ, we get:

y = λ + 1

x = -(y²)/2 = -(λ+1)²/2

Substituting these values into the first equation, we get:

(λ+1)² + (λ+1)²(-(λ+1)²/2) = 1 - (λ+1)²/2 + 2λ

Simplifying and solving for λ, we get:

λ = -1/2, -1/4

Therefore, the other points on the graph of f(x) whose tangent plane contains the line l are:

(-9/8, -1/2, -21/8) and (-25/32, -3/4, -47/32)

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The present value of the annuity is $189,468.24 if the initial payment is $1,000 and the monthly interest rate is 0.3333%.

What is Algebraic expression ?

Algebraic expression can be defined as combination of variables and constants.

To solve this problem, we need to first find the monthly interest rate since the payments are made monthly. The monthly interest rate can be found by dividing the annual interest rate by 12:

i = 4% / 12 = 0.3333% per month

Next, we need to find the present value of the annuity. We can use the formula for the present value of an annuity-immediate:

[tex]PV = P * (1 - (1 + i)^{-n}) / i[/tex]

where PV is the present value, P is the monthly payment, i is the monthly interest rate, and n is the number of payments.

The first year, the payments are level, so we can use the formula with n = 12 to find the present value of the payments for the first year:

[tex]PV1 = 1000 * (1 - (1 + 0.003333)^{-12}) / 0.003333 = \$11,887.87[/tex]

For the second year, the payments increase by 2%, so the monthly payment for the second year will be:

P2 = 1000 * 1.02 = $1,020

We can then use the formula again with n = 12 to find the present value of the payments for the second year:

[tex]PV2 = 1020 * (1 - (1 + 0.003333)^{-12}) / 0.003333 = \$12,061.92[/tex]

We can continue this process for the remaining 18 years, increasing the payment by 2% each year. The total present value of the annuity is the sum of the present values of each year's payments:

PV = PV1 + PV2 + ... + PV20 = $189,468.24

Therefore, the present value of the annuity is $189,468.24 if the initial payment is $1,000 and the monthly interest rate is 0.3333%.

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The answer is m = 0.

Step-by-step explanation:

To find the inverse of the exponential function y = (3/2)^x, we need to interchange the roles of x and y, and then solve for y.

So, starting with y = (3/2)^x, we can write:

x = (3/2)^y

To solve for y, we can take the logarithm of both sides with base 3/2:

log(3/2) x = y

Therefore, the inverse of the exponential function y = (3/2)^x is:

y = log(3/2) x

or in exponential form:

y = (log base 3/2) x

This function is the logarithmic function with base 3/2.

Based on the information, it can be inferred that the probability that a person has four or more cell phones in their home is 0.0494

To find the probability that a person has four or more cell phones in their home, we must carry out the following mathematical procedure.

We must find the total number of people surveyed and the percentage that each group represents:

Now we must establish the probability. For this we must carry out the following mathematical procedure:

According to the above, the probability that someone answers that four or more cell phones are used in her house is 0.0494.

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The unit rate for the problems are;

a. 50pages/hour

b. 4points / game

c. 8 car washed /hour

d. 8 ounces of peanut/ dollar

A unit rate means a rate for one of something. We write this as a ratio with a denominator of one. For example, if you ran 100 yards in 10 seconds, you ran on average 10 yards in 1 second.

a. The unit rate = number of pages/ time

= 100/2 = 50pages/hour

b. The unit rate = number of points /number of games

= 20/5 = 4 points per game

c. The unit rate = number of car washed/ time

= 40/5 = 8car washed per hour

d. unit rate = number of ounces of peanut/ number of dollars

= 20/2.5 = 8 ounces of peanut per dollar

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The surface area of the cone is 48π square centimeters (or approximately 150.8 square centimeters if we use a decimal approximation for π).

Calculating a cone's surface area is as follows:

[tex]\mathrm{SA = \pi r\² + \pi r \boldsumbol l }[/tex]

where l is the cone's slant height and r is the base's radius.

The radius and slant height in this instance are 4 cm and 8 cm, respectively. Therefore:

[tex]SA = \pi (4\²) + \pi (4)(8) \s= 16 \pi + 32 \pi \s= 48 \pi[/tex]

Hence, the cone's surface area is 48 square centimetres (or around 150.8 square centimetres if we round to the nearest decimal).

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Answer:

To compare the times of Paul and Jeff, we need to convert Paul's time to seconds.

Paul's time = 2 minutes 2 seconds = (2 x 60) + 2 = 122 seconds

Now we can compare their times:

Paul's time: 122 seconds

Jeff's time: 121 seconds

Jeff finished first since he has the lowest time.

Answer: To compare the times of Paul and Jeff, we need to convert Paul's time to seconds:

2 minutes and 2 seconds = 2 × 60 seconds + 2 seconds = 122 seconds

Now we can compare their times:

Paul finished in 122 seconds

Jeff finished in 121 seconds

Since Jeff's time is lower than Paul's time, Jeff finished first.

Step-by-step explanation:

Answer:

46

Step-by-step explanation:

your add odd number 1,3,5,7,9,11,13...

The values of the piecewise function {h(x)} for different values of {x} is given above.

An algebraic expression is a made up of terms both constants and variables. For example, we can write -

2x + 3y + z

5x + y

x + 8y

Given is the relation as -

y = {- x² - 6x - 9          for   x < - 2}

y = {x/3 - 4              for x > - 2}

The given function is a piecewise function. We can write the values for different values of {x} as -

{x} = - 4

y{4} = - (-4)² - 6(-4) - 9 = - 1

{x} = - 3

y{-3} = - (-3)² - 6(-3) - 9 = - 0

{x} = - 1

y{-1} = -1/3 - 4= -4.3

{x} = 0

y{-1} = 0/3 - 4 = - 4

Therefore, the values of the piecewise function {h(x)} for different values of {x} is given above.

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The solution of the equation is x = -0.21 and x = -1.79 and the steps used are from the quadratic formula.

The quadratic formula in elementary algebra is a formula that gives the solution(s) to a quadratic problem. In addition to the quadratic formula, there are various methods for solving quadratic equations, including factoring (direct factoring, grouping, and the AC technique), completing the square, graphing, and others.

Given that, the equation is:

8x² + 16x + 3

The steps that could be used to solve the following equation are:

The quadratic formula is given as:

-b ± √b² - 4ac / 2a

Substitute the values:

x = -16 ± √(16)² - 4(8)(3) / 2(8)

x = -16 ± √256 - 96 / 16

x = - 16 ± 12.64 / 16

x = - 16 + 12.64/16 and x = - 16 - 12.64 / 16

x = -0.21 and x = -1.79

Hence, the solution of the equation is x = -0.21 and x = -1.79 and the steps used are from the quadratic formula.

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This is the same result as if we had just taken the product of 5 by itself, which is also equal to 0.

Product is an item or service that is created by a business or organization to meet the needs of their customers. It is anything that is offered to a market for sale or trade. Products can be tangible, such as physical goods or intangible, such as services, ideas, or experiences. Companies need to create products that offer value to their customers. This includes making sure that the product meets the customer's needs, is of good quality, and is priced appropriately.

An empty product is a mathematical term that is used to describe a product of two or more numbers, where the result is equal to the product of just one of the numbers. This is because when you multiply any number by zero, the result is zero. Therefore, if a product contains a zero, then the result will be the same as if you only multiplied one of the numbers in the product. For example, if we take the product of 5 and 0, then the result is 0. This is the same result as if we had just taken the product of 5 by itself, which is also equal to 0.

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The closest option to the cone area is 923.2 m². 

A cone is a shape formed from a series of line segments or lines that connect a common point, called a vertex or vertex, to all points on the base of a circle that do not contain vertices. The distance from the apex of the cone to the base is called the height of the cone.

To solve this problem, we need to find the surface of the cone. Formula for the surface area of cone:

A = [tex]\pi[/tex]r² + [tex]\pi[/tex]rℓ

where r is the radius of the base, ℓ is the height of the depression, and π is a constant of approximately 3.14159.

First, we find the radius of the base. Since the bottom line of the cone is listed as 18 feet and we know the radius is 14 feet, we can use the Pythagorean theorem to find the height of the cone.

h² = ℓ² - r²

h² = 19.3² - 14²

h ≈ 11.48 feet

Now we can compute the surface.

A = [tex]\pi[/tex](14)² + [tex]\pi[/tex](14)(19.3)

A ≈ 923.2 square feet

So the closest option to the cone area is 923.2 m². 

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Mark needs a score of 2 on the 5th test to pass the course

Let X be the score Mark needs to get on the fifth test to pass the course.

To find X, we can use the formula for the mean of five numbers:

(mean of 5 numbers) = (sum of the 5 numbers) / 5

We know that Mark needs a mean score of 10 to pass, so:

10 = (total score on all 5 tests) / 5

Multiplying both sides by 5, we get:

50 = total score on all 5 tests

We also know that Mark's mean score on the first four tests is 12, so:

(mean score on the first four tests) = (total score on the first four tests) / 4

12 = (total score on the first four tests) / 4

total score on the first four tests = 48

To pass the course with a mean score of 10, Mark needs a total score of 50, and he has already scored 48 on the first four tests. Therefore, he needs to score:

X = 50 - 48

X = 2

Mark needs a score of 2 on the fifth test to pass the course with a mean score of 10.

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The worker worked 38 + 5 = 43 hours that week.

What is Algebraic expression ?

Algebraic expression can be defined as combination of variables and constants.

Let's break this problem down into two parts.

Part 1: Calculating the base pay for the 38 hours worked

The worker earned #80 per hour for a 38-hour week, so the base pay for those 38 hours would be:

Base pay = #80/hour x 38 hours = #3040

Part 2: Calculating the overtime pay for the additional hours worked

To find out how many hours were worked beyond the 38-hour week, we can use the fact that the total pay for the week was #3640. We know that the base pay for 38 hours was #3040, so the remaining #600 must be the overtime pay.

Since the company pays overtime at a time and a half, we can use this to find out how many hours were worked beyond the 38-hour week:

Overtime pay = (#80/hour x 1.5) x (number of overtime hours)

We can rearrange this equation to solve for the number of overtime hours:

Number of overtime hours = Overtime pay / (#80/hour x 1.5)

Number of overtime hours = #600 / (#80/hour x 1.5) = 5

Therefore, the worker worked 38 + 5 = 43 hours that week.

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The area of the triangle ABC is, 9 sq units.

A triangle is a three-sided closed-plane figure formed by joining three noncolinear points.

Based on the side property triangles are of three types they are Equilateral triangle, Scalene triangle, and Isosceles triangle.

We know, The area of a triangle is (1/2)×base×height.

Given, x equals 3 less than 6 which is,

x = (6 - 3).

x = 3.

Now, The base of the triangle is x units and the height is 2x units.

Therefore, The area of the triangle is,

= (1/2)×(3)×2(3).

= 9 sq units.

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Answer:

She read 4/5 of a book per month

Step-by-step explanation:

4/5= 4/5per month

Step-by-step explanation:

To find out how many books Tanisha read each month, we can use the formula:

books read per month = total number of books ÷ total number of months

Using the information given in the problem, we know that Tanisha read 4 books in 5 months. So we can plug those values into the formula:

books read per month = 4 ÷ 5

Simplifying the fraction by dividing the numerator and denominator by their greatest common factor, which is 1, we get:

books read per month = 4/5

Therefore, Tanisha read 4/5 of a book per month, or equivalently, 0.8 books per month.

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The food will last the other scouts for 8 days

At a scout's camp, the food will last 72 scouts for 6 days

The first step is to multiply both values(the number of scouts and the number of days spent in the camp)

= 72 × 6

= 432

The number of scouts at the camp can be calculated by subtracting the number of scouts present from the number of days the scouts spent at the camp

= 72-18

= 54

The amount of food left can be calculated as follows

= 432/54

= 8

Hence the food will last for 8 days

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Answer:144

Step-by-step explanation:

Answer:144

Step-by-step explanation:

The algebraic expression for Thabo is, Thabo's age in 6 years' time is x + 6.

There are three primary categories of algebraic expressions, including:

Numeral Expression. Binary Expression. Expression of a Polynomial

Monomial Expression: A monomial is an algebraic expression that only has one term.

Monomial expressions include 3x4, 3xy, 3x, 8y, etc. as examples.

A binomial expression is an algebraic expression with two terms that are opposite each other.

Binomial examples are 5xy + 8; xyz + x3; etc.

Polynomial Expression: In general, a polynomial expression is one that has several terms with non-negative integral exponents of a variable.

Given that, Thabo is x years old and Lizzie is y years old.

In 6 years, Thabo's age will be:

x + 6

Hence, Thabo's age in 6 years' time is x + 6.

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Answer: To find out how much commission Yamilet will receive for selling an $8,125 ring, we need to multiply the price of the ring by her commission rate, which is 12% or 0.12 in decimal form.

Commission = Price of ring x Commission rate

Commission = $8,125 x 0.12

Commission = $975

Therefore, Yamilet will receive a commission of $975 for selling an $8,125 ring.

Step-by-step explanation:

The relative maximum from the given graph is (2, 0). Therefore, options B, C, D and E are the correct answers

Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.

From the given graph,

The zeros of function are x=-3, x=2 and x=5.

So, the number of zeros are 3 and the degree of the polynomial is 3.

The relative maximum from the given graph is (2, 0).

The leading coefficient test tells us that the graph rises or falls depending on whether the leading terms are positive or negative.

Here, the leading coefficient is negative.

The edge multiplicity of a given end vertex in a multigraph is the number of multiple edges sharing that end vertex. The maximum edge multiplicity in such a graph is known as the graph multiplicity.

Here, the multiplicity is 2.

Therefore, options B, C, D and E are the correct answers

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Answer:

number is 8

Step-by-step explanation:

let the number be n then trebling it ( multiplying it by 3 ) is 3n, then subtracting 6 from this is 3n - 6 , so

3n - 6 = 18 ( add 6 to both sides )

3n = 24 ( divide both sides by 3 )

n = 8

that is the number thought of is 8

Answer:

[tex] y = \dfrac{2}{3}x - 1 [/tex]

Step-by-step explanation:

[tex] 2x - 3y = 3 [/tex]

Subtract 2x from both sides.

[tex] -3y = -2x + 3 [/tex]

Divide both sides by -3.

[tex] y = \dfrac{-2}{-3}x + \dfrac{3}{-3} [/tex]

[tex] y = \dfrac{2}{3}x - 1 [/tex]