If A is the angle between the vectors u = (5, 0, 48 ) and v = (0, 0, 1). What is the value of cosine of A ?

the area inside the curve R is approximately 42.4115 square units.

To find the area inside the curve R, we can use a double integral. The formula for finding the area of a region using a double integral is:

A = ∬R dA

where A is the area of the region R, and dA is an infinitesimal element of area in the region R.

In polar coordinates, dA can be expressed as:

dA = r dr dθ

where r is the radius and θ is the angle.

Substituting this into the formula for the area, we get:

A = ∫₀^2π ∫₀^(5+sinθ) r dr dθ

We can evaluate this integral by integrating first with respect to r and then with respect to θ:

A = ∫₀^2π [1/2 r²] from 0 to (5+sinθ) dθ

A = ∫₀^2π 1/2 (5+sinθ)² dθ

Expanding the square and simplifying, we get:

A = ∫₀^2π 1/2 (25 + 10sinθ + sin²θ) dθ

A = 1/2 ∫₀^2π (25 + 10sinθ + sin²θ) dθ

Using the trigonometric identity sin²θ = (1-cos2θ)/2, we can simplify this to:

A = 1/2 ∫₀^2π (25 + 10sinθ + 1/2 - 1/2cos2θ) dθ

A = 1/2 ∫₀^2π (27/2 + 5sinθ - 1/2cos2θ) dθ

Integrating each term separately, we get:

A = 1/2 [27/2θ - 5cosθ + 1/4sin2θ] from 0 to 2π

A = 1/2 [(27/2)(2π) - 5cos2π + 1/4sin2(2π) - (27/2)(0) - 5cos0 + 1/4sin0]

A = 1/2 (27π)

A = 13.5π

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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.

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Answer:

I can't answer that if there is no picture, I'm sorry

Answer:

49

Step-by-step explanation:

Add up all the numbers and divide by how many numbers there are.

Answer:

49

Step-by-step explanation:

the sum of all the numbers is 294

294÷6=49

Answer:

1. 60 seconds.

2. 9 minutes.

3. 3 minutes, 180 seconds.

4. 300 seconds, 5/60 horas.

Your question has been heard loud and clear/

we know,

4cos³x = 3cosx + cos3x

put here, x = 20°

then, 4cos³20° = 3cos20° + cos3 × 20°

= 3cos20° + cos60°

cos³20° = (3cos20° + cos60°)/4 -------(1)

similarly ,

4sin³x = 3sinx - sin3x

put here, x = 10°

4sin³10° = 3sin10° - sin30°

sin³10° = (3sin10° - sin30°)/4 -----------(2)

now,

LHS = cos³20° + sin³10°

put equations (1) and (2)

= 1/4(3cos20° + cos60°) + 1/4 ( 3sin10° - sin30°)

= 1/4( 3cos20° + cos60° + 3sin10° - sin30°)

we know,

cos60° = sin30° = 1/2

= 1/4 ( 3cos20° + 3sin10°)

= 3/4(cos20° + sin10°) = RHS

hence proved

Thank you

Answer:  see proof below

Step-by-step explanation:

Use the following identities & Unit Circle calculations:

 4cos³x = 3cos x + cos 3x

--> cos³x = (1/4)[3cos x + cos 3x]

 4sin³x = 3sin x - sin 3x

--> sin³x = (1/4)[3sin x - sin 3x]

cos 60° = sin 30° = (1/2)

Proof: LHS → RHS

Given:                          cos³ 20° + sin³ 10°

Triple Angle Identity: (1/4)[3cos 20° + cos 3·20°] + (1/4)[3sin 10° - sin 3·10°]

Simplify:                      (1/4)[3cos 20° + cos 60° + 3sin 10° - sin 30°]

                                   (1/4)[3cos 20° + (1/2) + 3sin 10° - (1/2)]

                                   (1/4)[3cos 20° + 3sin 10°]

Factor:                         (3/4)[cos 20° + sin 10°]        

Proven:  (3/4)[cos 20° + sin 10°]  = (3/4)[cos 20° + sin 10°]    \(\checkmark\)

Answer:

20000(.05)^x-750

Step-by-step explanation:

That's the equation for figuring out the population

Answer:

B

Step-by-step explanation:

sohcahtoa

sin = opp/hyp

sin A = 16/20= 4/5

Rounding to two decimal places, we get the answer to be d) 2.19. Therefore, the F statistic is 2.19.

To find the F statistic, we use the formula:

F = (SSB/dfb) / (SSW/dfw)

where SSB is the sum of squares between groups, dfb is the degrees of freedom between groups, SSW is the sum of squares within groups, and dfw is the degrees of freedom within groups.

Substituting the given values, we get:

F = (13.73/4) / (23.45/15)
F = 3.4325 / 1.5633
F = 2.195

Rounding to two decimal places, we get the answer to be d) 2.19. Therefore, the F statistic is 2.19.

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read this backwards bc it wont let me do it forward

LOL snap my add should you but no

sereenagamble

Step-by-step explanation:

sunaina's alona work=

1/6-1/10

10-6/60

4/60

1/15

therefore sunaina can alone do the work in 15 days

Answer:

Step-by-step explanation:

5y or 5x which ever one you see

Answer:

240 students

Step-by-step explanation:

     To find the minimum number of students, we have to find the LCM of 10, 12, 16

10 = 2 * 5

12 = 2 * 2 * 3

16 = 2 * 2 * 2 * 2

LCM = 2 * 2 *  2 * 2 * 3 * 5

       = 240

Solution of the given algebraic expression (f-g)(x) is equal to 4x³+6x²-7x-1

Algebraic equations are defined as mathematical statements in which two algebraic expressions are set equal to each other. An algebraic expression usually consists of  variables,  coefficients and  constants. Algebraic equations can be of many types, such as monomial algebraic equations, binomial algebraic equations, quadratic algebraic equations, polynomial equations.  

Given in the question that the value of f(x) is equal to 4x³+6x²-3x-4

and the value of g(x) is equal to 4x-3.

Subtracting g(x) from f(x) we get,

(f-g)(x)= 4x³+6x²-3x-4-4x+3

4x³+6x²-7x-1

Therefore, solution of the given algebraic expression (f-g)(x) is equal to 4x³+6x²-7x-1.

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Based on the fact that the problem to be modeled is about finding the number of nurses on duty using ratios, then it can be modeled by A) making a tape diagram.

This is a diagram that is used in mathematical calculations to visually support the calculations that a person is making.

They can be drawn such that they will have 15 cells to represent all the people working on duty. Then the proportion of doctors to nurses can be used to shade in the cells that would represent the number of people who are nurses.

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Hello!

surface area

= 2(6*2) + 2(4*2) + 4*6

= 2*12 + 2*8 + 24

= 24 + 16 + 24

= 64 square inches

Answer:

The last one is correct: 3(x+5)=3 . X + 3 . 5

Answer:

Ratio of student who signed up for art club:

1/5

Ratio who signed other club:

4/5

Step-by-step explanation:

First find out ratio who signed up for art club

you have 16 out of 80

find the common factor: 16

16/16 = 1

80/16 = 5

so 1/5

other clubs is the rest so 5/5 - 1/5 = 4/5

please give thanks :)

Answer:

-33

Step-by-step explanation:

With the brackets in an equations, it just means you are going to be solving within there first before moving on.

For any equations such as this, you'll want to follow PEMDAS.

Parenthesis (x)
Exponents \(x^{2}\)
Multiplication x * y
Division x/y or x÷y or \(\frac{x}{y}\)
Addition x+y
Subtraction x-y

To start, we're just going to take the bracket equations 2+4 x 2 + (10 - 5)

\(2+4*2+5/5\)

Moving down PEMDAS we have no exponents, but multipication and division, whichever comes first in the equation.

4*2 = 8

5/5 = 1

2+8+1 = 11

-3[11] = (You use multiplication here) -33

-39

Step-by-step explanation:

\({ \blue{ \sf{ - 3{[2 + 4 \times 2 + (10 - 5) \div 5]}}}}\)

\({ \blue{ \sf{ - 3{[6 \times 2 + (10 - 5) \div 5]}}}}\)

\({ \blue{ \sf{ - 3{[12 + (10 - 5) \div 5]}}}}\)

\({ \blue{ \sf{ - 3{[12 + (5) \div 5]}}}}\)

\({ \blue{ \sf{ - 3{[12 + 1]}}}}\)

\( { \blue{ \sf{ - 3[13]}}}\)

\({ \red{ \sf{ - 39}}}\)

Answer:

the answer is 133

Step-by-step explanation:

we do substitution

2*3^2=18

3^3=27

5(27-4)=115

27+115=133

The statement which must be true are Options B, C and D

which are the triangles have the same size and shape, the corresponding sides of the triangles are congruent and the corresponding angles of the triangles are congruent.

Congruent triangles are triangles that have corresponding sides, angles which are all equal in measure.

They can be rotated and turned to be look be identical.

Thus, the statement which must be true are Options B, C and D

which are the triangles have the same size and shape, the corresponding sides of the triangles are congruent and the corresponding angles of the triangles are congruent.

The complete question is

If two triangles are congruent which of the following statements must be true? CHECK ALL THAT APPLY

A. The triangles have the same size but not the same shape.

B. The triangles have the same size and shape

C. The corresponding sides of the triangles are congruent.

D. The corresponding angles of the triangles are congruent.

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The probability that two or more companies will announce plans to expand is 0.819.

This problem can be modeled using a binomial distribution, where the probability of success (announcing plans to expand) is p = 0.24, and the number of trials is n = 20.

To find the probability that precisely two companies will announce plans to expand, we can use the binomial probability formula:

P(X = 2) = (20 choose 2) * (0.24)^2 * (1 - 0.24)^(20-2)

where (20 choose 2) = 190 is the number of ways to choose 2 companies out of 20. Using a calculator, we get:

P(X = 2) = 0.242

Therefore, the probability that precisely two companies will announce plans to expand is 0.242.

To find the probability that fewer than two companies will announce plans to expand, we can use the cumulative binomial probability:

P(X < 2) = P(X = 0) + P(X = 1)

To find P(X = 0), we can use the binomial probability formula with k = 0:

P(X = 0) = (20 choose 0) * (0.24)^0 * (1 - 0.24)^(20-0) = 0.032

To find P(X = 1), we can use the binomial probability formula with k = 1:

P(X = 1) = (20 choose 1) * (0.24)^1 * (1 - 0.24)^(20-1) = 0.149

Therefore, the probability that fewer than two companies will announce plans to expand is:

P(X < 2) = 0.032 + 0.149 = 0.181

To find the probability that two or more companies will announce plans to expand, we can use the complementary probability:

P(X >= 2) = 1 - P(X < 2) = 1 - 0.181 = 0.819

Therefore, the probability that two or more companies will announce plans to expand is 0.819.

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Answer:

86.6 feet (3 s.f.)

Step-by-step explanation:

Please see attached picture.

tan60°= height of tower/ 50

Height of tower

= 50tan60°

= 50√3

= 86.6 ft (3 s.f.)

tanѲ= opp/ adj

The values of the sides are;

41. x = 18√3. Option D

42. x = 6√3. Option A

Using the different trigonometric identities, we have;

41. Using the tangent identity, we have;

tan 60 = 9√2/y

cross multiply the values

y =9√2 ×√3

y = 9√6

Using the sine identity;

sin 45 = y/x

1/√2 = 9√6/x

cross multiply the values, we have;

x = 9√2 ×√3 ×√2

x = 18√3

42. Using the cosine identity

cos 60 = 3√3 /x

cross multiply, we have;

x = 6√3

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Answer:

23x + 8

Step-by-step explanation:

Answer:

17.6 weeks

Step-by-step explanation:

The computation of the time taken to reach the target weight is shown below:

35, 34.6, 34.2...............28

As we know that

a_n = a + (n - 1)d

28 = 35 + (n - 1)(-0.4)

28 = 35 -0.4n + 0.4

28 = 35.04 - 0.4n

0.4n = 35.04 - 28

0.4n = 7.04

n = 17.6

The given statement "In one scene in 8 1/2, Guido steps onto an elevator that takes on the characteristics of a confession booth" is True.

What is 8 1/2?8 1/2 is an Italian drama movie which was released in the year 1963. It was directed by Federico Fellini. The movie is widely recognized as a highly influential classic of world cinema. The story is about a renowned filmmaker named Guido Anselmi. He is in the middle of making a film but is struggling to come up with a plot for it. In one scene of the movie, Guido steps onto an elevator that takes on the characteristics of a confession booth.MAIN ANS:True, In one scene in 8 1/2, Guido steps onto an elevator that takes on the characteristics of a confession booth.The elevator in 8 1/2 takes on the characteristics of a confession booth as a result of its setting and characters. The elevator setting in the film emphasizes that Guido is in a confessional box and is confessing his sins. It was a unique way of depicting Guido's guilt. The way the elevator shook and rattled, making him feel like he was in a confessional box, was symbolic of how he felt. It was as if he was being taken to a higher power who was listening to him.

The scene emphasizes the religious imagery in the movie. It allows us to gain insight into Guido's psyche and the struggles he was having. The religious imagery in the movie suggests that Guido is trying to connect with a higher power to overcome his guilt. The scene also shows the extent to which he is willing to go to gain clarity.

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Answer:

19.504

Step-by-step explanation:

divide the mass value by 2.205

Answer: 6.4

Step-by-step explanation:

divide in half