pweez help!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

To prove the given trigonometric identity: \(cot(x+y) = )\frac{(cot(x)cot(y) - 1) }{(cot(x) + cot(y)}\), we can use the definition of cotangent and some trigonometric identities.

Recall that \(cot(x) = \frac{1}{tanx}\) and \(tan(x) = \frac{sin(x)}{cos(x)}\).
First, let's find the\(tan(x+y)\)using the angle sum formula for tangent:
\(tan(x+y)=\frac{(tan(x) + tan(y))}{ (1 - tan(x)tan(y))}\)
Now, substitute cot(x) and cot(y) using the definition of cotangent:
\(tan(x+y) =\frac{ (1/cot(x) + (1/cot(y)}{(1 - (1/cot(x))(1/cot(y))}\)
To simplify the expression, find the common denominator for the numerators:
\(tan(x+y) = \frac{ (cot(x)cot(y) + cot(x) + cot(y)) }{cot(x)cot(y) - 1}\)
Now, take the reciprocal of both sides to get \(cot(x+y)\)
\(cot(x+y) =\frac{ (cot(x)cot(y) - 1)}{ (cot(x) + cot(y))}\)
So, we have proven that \(cot(x+y) = \frac{ (cot(x)cot(y) - 1)}{ (cot(x)cot(y) - 1)}\)

Learn more about tangent here: https://brainly.com/question/19064965

#SPJ11

To find the general term of an arithmetic sequence, we need to determine the values of the first term (a₁) and the common difference (d). Once we have these values, we can use the formula for the nth term of an arithmetic sequence to find the general term.

Given that the third term of the sequence is 46, we can express it using the formula:

a₃ = a₁ + 2d = 46

Similarly, the eighth term of the sequence is 31, which can be expressed as:

a₈ = a₁ + 7d = 31

Now we have a system of two equations with two unknowns (a₁ and d). We can solve this system of equations to find the values of a₁ and d. Subtracting the first equation from the second equation, we get:

a₈ - a₃ = (a₁ + 7d) - (a₁ + 2d)

31 - 46 = 7d - 2d

-15 = 5d

Dividing both sides of the equation by 5, we find that:

d = -3

Now we substitute the value of d back into one of the original equations, such as the first equation:

46 = a₁ + 2(-3)

46 = a₁ - 6

a₁ = 52

So, we have found that the first term (a₁) is 52 and the common difference (d) is -3. Now we can use the formula for the nth term of an arithmetic sequence to find the general term:

aₙ = a₁ + (n - 1)d

Plugging in the values we found, the general term is:

aₙ = 52 + (n - 1)(-3)

aₙ = 52 - 3n + 3

aₙ = 55 - 3n

Therefore, the general term of the arithmetic sequence is 55 - 3n.

Learn more about arithmetic sequence here:- brainly.com/question/28882428

#SPJ11

Approximately 68% of the cases in a normal distribution are between 0.5 standard deviations above and below the mean.

To find the percentage of cases that are between 0.5 standard deviations above and below the mean, we can add these two probabilities:

34% + 34% = 68%

The normal distribution, also known as the Gaussian distribution or the bell curve, is a probability distribution that is widely used in statistics, science, and engineering. A bell-shaped curve that is symmetrical around the mean value best describes the distribution. The distribution's mean, median, and mode are all equal, and the standard deviation defines the curve's width.

Height, weight, IQ, and measurement mistakes are only a few examples of the numerous random variables and natural phenomena that follow the normal distribution. In addition, the central limit theorem predicts that regardless of the underlying distribution of the variables themselves, the total or average of several independent random variables with similar distributions will converge to a normal distribution. Because of this characteristic, the normal distribution is a key idea in inferential statistics and hypothesis testing.

To learn more about Normal distribution visit here:

brainly.com/question/29509087

#SPJ4

Complete Question:-

What percentage of cases in a normal distribution are between 0.5 standard deviations above and below the mean? Give one percentage.

After performing the calculations The annual lease payment excluding executory costs will be $829,134 (option B).

To calculate the annual lease payment, we need to consider the lessor's desired rate of return and the incremental borrowing rate of the lessee.

In this case, the lessor (Holt Warehouse Company) wants to earn a 9% rate of return, while the lessee (Sandhill, Inc.) has an incremental borrowing rate of 10% per year.

The lease agreement requires equal rental payments at the beginning of each year. Since the lease term is 10 years, we can calculate the annual lease payment by equating the present value of the rental payments to the fair value of the building.

The fair value of the building on January 1, 2018, is $5,800,000. We subtract the book value to Holt ($4,750,000) to find the unearned profit, which is $1,050,000.

Using the implicit rate of the lessor, which is known by Sandhill, Inc., we discount the unearned profit over the 10-year lease term to calculate the annual lease payment.

After performing the calculations, the annual lease payment excluding executory costs is $829,134

learn more about fair value here:

https://brainly.com/question/30027849

#SPJ11

We can conclude that the function f(x) = 3x + 12 is continuous for all real numbers, providing a smooth and uninterrupted mapping from the x-values to the corresponding y-values.

the function f(x) = 3x + 12 is a linear function, which means it is a straight line with a constant slope. linear functions are known to be continuous over their entire domain, which in this case is the set of all real numbers.

to understand why the function f(x) = 3x + 12 is continuous, we can examine the definition of continuity. a function is continuous at a point if the limit of the function as x approaches that point exists and is equal to the value of the function at that point.

for the function f(x) = 3x + 12, the limit as x approaches any real number exists and is equal to 3 times that real number plus 12. since multiplication and addition are continuous operations, the limit of the function exists, and thus the function is continuous for all real numbers.

in simpler terms, as we move along the x-axis, the function f(x) changes smoothly and continuously, without any abrupt jumps or breaks. it forms a straight line with a constant slope, and this line extends infinitely in both directions.

Learn more about linear here:

https://brainly.com/question/31510530

#SPJ11

Option A with a 6-year loan at 8.5% interest compounded quarterly is the better credit option as it results in a lower total amount paid compared to Option B with a 5-year loan at 10% interest compounded annually.

What is the compound interest?

Compound interest can be regarded as the  addition of interest on the loan to the principal sum of the deposit.

Based on the given information, Option A is the better credit option.

Here's why:

Option A:

Option B:

To determine the better option, we can calculate the total amount paid for each option, which includes the principal amount (the initial loan amount) and the interest (the additional amount charged for borrowing the money).

For Option A:

Principal (P) = $12,500

Annual interest rate (r) = 8.5%

Compounding frequency (n) = 4 (quarterly)

Time (t) = 6 years

Using the formula for compound interest:

\(A = P * (1 + r/n)^{(nt)}\)

\(A = $12,500 * (1 + 0.085/4)^{(46)\\A = $12,500 * (1.02125)^{24\)

A = $16,509.63 (rounded to 2 decimal places)

For Option B:

Principal (P) = $12,500

Annual interest rate (r) = 10%

Compounding frequency (n) = 1 (annually)

Time (t) = 5 years

Using the formula for compound interest:

\(A = P * (1 + r/n)^{(nt)}\\A = $12,500 * (1 + 0.10/1)^{(15)}\\A = $12,500 * (1.10)^5\)

A = $19,379.36 (rounded to 2 decimal places)

Hence, Option A with a 6-year loan at 8.5% interest compounded quarterly is the better credit option as it results in a lower total amount paid compared to Option B with a 5-year loan at 10% interest compounded annually.

To learn more about compound interest, Visit

https://brainly.com/question/28020457

#SPJ1

Answer:

Step-by-step explanation:

3x+4y=38

Answer:

x=61; 125; 55

Step-by-step explanation:

2x+3+x-6=180

3x-3=180

3x=183

x=61

Angle 1=2x+3=2*61+3=125

Angle 2=61-6=55

The (1, 4), (1, 5), (1, 6), (3, 4), (3, 5), (3, 6), (4, 4), (4, 5), (4, 6), (5, 4), (5, 5), (5, 6), (6, 4), (6, 5), (6, 6)Out of these possible outcomes, there are only 11 such outcomes where X1 ≠ 2 and X2 ≥ 4: (1, 4), (1, 5), (1, 6), (3, 4), (3, 5), (3, 6), (4, 4), (4, 5), (4, 6), (5, 4), (5, 5)P(X1 ≠ 2 and X2 ≥ 4) = 11/36

Probability that X2 = 4:Since we rolled a fair dice, so the probability of getting a number 4 on the dice would be 1/6.P(X2 = 4) = 1/6b) Probability that X1 + X2 = 7:Now we know that the sum of the outcomes of two fair dices rolled is 7, this can be obtained by the following possibilities:(1, 6), (2, 5), (3, 4), (4, 3), (5, 2), (6, 1)Since each outcome is equally likely, so each of these outcomes has a probability of 1/36.P(X1 + X2 = 7) = 6/36 = 1/6c) Probability that X1 ≠ 2 and X2 ≥ 4:

If we look at the possible outcomes of X1 and X2 then we have the following possibilities:(1, 4), (1, 5), (1, 6), (3, 4), (3, 5), (3, 6), (4, 4), (4, 5), (4, 6), (5, 4), (5, 5), (5, 6), (6, 4), (6, 5), (6, 6)Out of these possible outcomes, there are only 11 such outcomes where X1 ≠ 2 and X2 ≥ 4: (1, 4), (1, 5), (1, 6), (3, 4), (3, 5), (3, 6), (4, 4), (4, 5), (4, 6), (5, 4), (5, 5)P(X1 ≠ 2 and X2 ≥ 4) = 11/36

Learn more about Probability

brainly.com/question/11234923

#SPJ11

The distance from the base of the tree from the swing sets is 15 ft

The situation forms a right angle triangle.

The opposite side of the triangle formed is the distance of Emir from the ground.

Therefore, the distance from the base of the tree from the swing sets is the adjacent side of the triangle.

Hence,

tan 33.69 = opposite / adjacent

tan 33.69 = 10 / x

x = 10 / tan 33.69

x = 10 / 0.66666496431

x = 10 / 0.66666496431

x = 15.0000038265

x = 15 ft

learn more on right triangle here: https://brainly.com/question/26774610?

#SPJ1

Answer:

40 Including membership Price

35 Just for Pizza

Step-by-step explanation:

$5 for Membership for the month (Not sure if the final answer includes this or not)
1.75 x 20 = $35 for Pizza

Answer:

4

Step-by-step explanation:

Answer:

y=5x−4

Step-by-step explanation:

Step 1: Add -5x to both sides.

Step 2: Divide both sides by -1.

The division of (x²+3x-9) by (x-2) using long division is:

Quotient: x

Remainder: 1

To divide the polynomial (x²+3x-9) by (x-2) using long division, follow these steps:

Step 1: Set up the division with the dividend (x²+3x-9) as the numerator and the divisor (x-2) as the denominator.

Write them in the long division format:

      ___________________

x - 2 | x² + 3x - 9

Step 2: Divide the first term of the dividend (x²) by the first term of the divisor (x). Place the result on top:

      ___________________

x - 2 | x² + 3x - 9

      x

Step 3: Multiply the divisor (x-2) by the quotient obtained in Step 2 (x) and write the result below the dividend. Subtract this result from the dividend:

      ___________________

x - 2 | x² + 3x - 9

      x² - 2x

    ____________

          5x - 9

Step 4: Bring down the next term from the dividend (-9):

      ___________________

x - 2 | x² + 3x - 9

      x² - 2x

    ____________

          5x - 9

          - 5x + 10

    _______________

                1

Step 5: Since there are no more terms in the dividend, the remainder is 1.

Therefore, the division of (x²+3x-9) by (x-2) using long division is:

Quotient: x

Remainder: 1

Learn more about long division click;

https://brainly.com/question/28824872

#SPJ1

Using a combination of algorithms and approximations. Most use a combination of Stirling's approximation and the Lanczos approximation.

Calculators use a combination of algorithms and approximations to calculate large factorials. For example, Wolfram Alpha first uses Stirling's approximation to approximate the factorial. This approximation is based on the fact that the factorial can be expressed as an infinite product. Stirling's approximation then gives an approximate value of the factorial as a function of the number. Wolfram Alpha then refines this approximation by using the Lanczos approximation. This approximation takes the Stirling approximation and refines it using a series of coefficients. Finally, Wolfram Alpha uses a combination of the Stirling and Lanczos approximations to compute the final value of the factorial.

Learn more about algorithms here

https://brainly.com/question/29289479

#SPJ4

Answer:

Step-by-step explanation:

You want to know if the given distance calculations are correct (true) or not (false).

The distance between the animals at different coordinates is the absolute value of the difference of the coordinates.

The distance is ...

  |(-38 1/2) -(-84 1/4)| = 45 3/4 . . . . True

The distance is ...

  |-145 -(-84 1/4)| = 60 3/4 ≠ 229 3/4 . . . . False

The distance is ...

  |(18 3/4) -(-38 1/2)| = 57 1/4 . . . . True

The distance is ...

  |(18 3/4) -(-145)| = 163 3/4 ≠ 126 3/4 . . . . False

__

Additional comment

Since we're using the absolute value function, the order in which the subtraction occurs is immaterial. In the first two calculations we subtracted the location of the second animal from the first. In the last two calculations, this order was reversed. The correct distance is found either way.

If you don't use the absolute value function, you want to subtract the smaller coordinate from the larger. This will always give a positive result.

As a rule, distance and length are always positive. Displacement or position can be negative.

<95141404393>

The sixth term of the arithmetic progression is 94.

An arithmetic progression is a sequence of numbers such that the difference between any two successive members of the sequence is a constant.

Let's call the first term of the arithmetic progression "a" and the common difference "d". Then the nth term of the progression can be found using the formula:

an = a + (n-1)d

We know that the sum of the first four terms is 14, so we can set up the following equation:

a + (a+d) + (a+2d) + (a+3d) = 14

We also know that the sum of the first eight terms is 108, so we can set up another equation:

a + (a+d) + (a+2d) + (a+3d) + (a+4d) + (a+5d) + (a+6d) + (a+7d) = 108

Now we can use the first equation to substitute for the first four terms of the second equation:

14 + (a+4d) + (a+5d) + (a+6d) + (a+7d) = 108

This gives us:

a + 4d = 94

So the sixth term can be found by substituting n = 6 into the first formula:

a + (6-1)d = a + 5d = 94

Therefore, the sixth term of the arithmetic progression is 94.

For more information on Arithmetic Progression:

https://brainly.com/question/6561461

https://brainly.com/question/14921993

Answer:

4.734 * 10^-5 miles

Step-by-step explanation:

Given that:

Distance between House to movie theater = 3 inches

Expressing the distance in miles :

Converting inch to miles

1 inch = 1.578 * 10^-5 miles

3 inches = (3 * 1.578*10^-5)

3 inches = 4.734 * 10^-5 miles

Answer:

25p^12q^6πcm²

Step-by-step explanation:

Given the area of the circle expressed as;

A = πr^2

Given

r = 5p^6q^3 cm

Substitute into the formula

A = π(5p^6q^3 )²

A = π(25p^12q^6)

A = 25p^12q^6πcm²

hence the area of this circle in square centimeters is 25p^12q^6πcm²

The area of the circle whose radius be 5p⁶q³ is 25πp¹²q⁶ square centimeters.

It is a locus of a point drawn at an equidistant from the center. The distance from the center to the circumference is called the radius of the circle.

A circle has a radius of \(\rm 5 \ p^6 \ q^3\) cm.

The area of the circle can be found using the formula

\(\rm A = \pi \ r^2\)

Then the area of the circle will be

\(\rm A = \pi (5 \ p^6 \ q^3)^2\\\\A = \pi * 5^2 \ (P^6)^2 (q^3)^2\\\\A = 25 \ \pi \ p^{12} \ q^6\)

Thus, the area of the circle is 25πp¹²q⁶ square cm.

More about the circle link is given below.

https://brainly.com/question/11833983

Answer:

If this is the question then tis is the answer. Thank you. Hope I was of help.

9514 1404 393

Answer:

  11 7/16

Step-by-step explanation:

The integration resolves into finding the area of two triangles. The left has a height of (-3/8(-2/3)+2) = 2 1/4, and a width of (16/3-(-2/3)) = 6. Then its area is ...

  A = (1/2)bh = (1/2)(6)(2 1/4) = 6 3/4

__

The right triangle has a height of |(-3/8)(31/3) +2| = |-31/8+16/8| = 15/8. Its width is (31/3) -(16/3) = 5, so its area is ...

  A = (1/2)(5)(15/8) = 75/16 = 4 11/16

Then the total area, the value of the integral, is ...

  6 3/4 +4 11/16 = 10 23/16 = 11 7/16 . . . the value of the integral

Answer:

x=   \(\frac{9}{2} y\) or  y=  \(\frac{2}{9} x\)

Step-by-step explanation:

Solving for (x)

Step 1: Add -3y to both sides.

2x+3y+−3y=12y+−3y

2x=9y

Step 2: Divide both sides by 2.

\(\frac{2x}{2} = \frac{9y}{2}\)

Solving for (y)

Step 1: Add -12y to both sides.

2x+3y+−12y=12y+−12y

2x−9y=0

Step 2: Add -2x to both sides.

2x−9y+−2x=0+−2x

−9y=−2x

Step 3: Divide both sides by -9.

\(\frac{-9y}{9} = \frac{-2x}{9}\)

Step-by-step explanation:

"which is the measure of angle L?"

the total angle measures of all angles on a triangle should always equal 180

72 + 36 = 108

180 - 108 = 72!

angle L is 72 degrees!

"which angle is the vertex angle?"

from my understanding, the angle opposite the base would be the vertex angle

since j and k are equal, we can only assume 36 is the vertex angle!

hope this helps! if so, pls give brainliest!

Answer:

hi. I'm so sorry I just need to answer some questions. I'm sorry

The difference in the account balances at the end of the loan terms is given as follows:

$1,686.87.

The amount of money earned, in compound interest, after t years, is given by:

\(A(t) = P\left(1 + \frac{r}{n}\right)^{nt}\)

In which:

The parameters for the offer 2 are given as follows:

P = 75000, r = 0.035, n = 12, t = 62/12.

Hence the balance of the offer 2 is given as follows:

B = 75000 x (1 + 0.035/12)^(12 x 62/12)

B = $89,842.51.

The balance of Offer 1 is of $91,529.38, hence the difference in the balances is given as follows:

91529.38 - 89842.51 = $1,686.87.

More can be learned about compound interest at https://brainly.com/question/24274034

#SPJ1

According to the solving the probability  of the spinner and the dice

A.  = 1 / 2.

B.  = 1/6.

Simply put, probability measures how probable something is to occur. We can discuss the probabilities of various outcomes, or how likely they are, whenever we are unsure of how an event will turn out. Statistics is the study of events subject to probability.

Information on possibility of occurrence is provided by probability. For instance, meteorologists can forecast the likelihood of rain by looking at weather patterns. Probability theory is utilized in epidemiology to comprehend how exposures as well as the risk of health impacts are related.

for the spinner

total number of division = 4

the pink colored  sections = 2

Number of Favorable Outcomes / Total Number of Outcomes is the formula for probability.

Probability = 2 / 4.

Probability = 1 / 2.

for the Dice

total number of division = 6

the pink colored  sections = 1

Number of Favorable Outcomes / Total Number of Outcomes is the formula for probability.

Probability = 1/6.

Probability = 1/6.

To know more about Probability visit:

https://brainly.com/question/14210034

#SPJ1

Answer:

Step-by-step explanation:

\(\tan(29.4^o)=\dfrac{?}{56.8}\\\\\tan(29.4^o)\times56.8=?\\\\?\approx0,563471\times56.8\approx32\)

Answer:

y =2

Step-by-step explanation:

Inverse variation is of the form

xy = k

3*6 = k

18 = k

xy = 18

Now when x = 9, find y

9*y = 18

Divide by 9

y = 18/9

y =2

When x =9, y =2

Answer:

y = 2

Step-by-step explanation:

y = 6   ⇔  x= 3

y = ?   ⇔   x = 9

y = 6*3/9

y = 2

(i) The relationship between the OLS estimators of α₂ and ᵝ₂ can be determined by considering the relationship between the consumption function and the savings function. Since X = Y + Z, we can substitute this into the consumption function equation to obtain Y = α₁ + α₂(Y + Z) + e. Simplifying the equation, we get Y = (α₁/(1 - α₂)) + (α₂/(1 - α₂))Z + (e/(1 - α₂)). Comparing this equation with the savings function Z₁ = ᵝ₁ + ᵝ₂X + u₁, we can see that the OLS estimator of ᵝ₂ is related to the OLS estimator of α₂ as follows: ᵝ₂ = α₂/(1 - α₂).

(ii) The residual sum of squares (RSS) will not be the same for the two models of Y₁ = α₁ + α₂X₁ + e and Z₁ = ᵝ₁ + ᵝ₂X₁ + u₁. This is because the error terms e and u₁ are different for the two models. The RSS is calculated as the sum of squared differences between the observed values and the predicted values. Since the error terms e and u₁ are different, the predicted values and the residuals will also be different, resulting in different RSS values for the two models.

(iii) The R² terms of the two models cannot be directly compared. R² is a measure of the proportion of the total variation in the dependent variable that is explained by the independent variables. Since the consumption function and the savings function have different dependent variables (Y and Z, respectively), the R² values calculated for each model represent the goodness of fit for their respective dependent variables. Therefore, the R² terms of the two models cannot be compared directly.

Learn more about function here: brainly.com/question/30660139

#SPJ11

Answer:

He will

have RUB 891,135 present to the same government

Step-by-step explanation:

Here, we want to calculate the amount of money that will be left in the account

To get this, we simply subtract the payments and add up the deposits to the initial

Thus, we have;

850,360 + 119,980 - 79,205 = 891,135