16Acos(x)-Bsin(x)-2Asin(x)+19Bcos(x)=65cos(x) can someone helps me to find the exactly value of A and B ?

Answers

Answer 1

The exact values of A and B that satisfy the equation are A = -65/22 and B = 65/11.

To find the exact values of A and B in the equation 16Acos(x) - Bsin(x) - 2Asin(x) + 19Bcos(x) = 65cos(x), we need to equate the coefficients of the corresponding trigonometric functions on both sides of the equation.

Comparing the coefficients of cos(x) on both sides:

16A + 19B = 65 (Equation 1)

Comparing the coefficients of sin(x) on both sides:

-2A - B = 0 (Equation 2)

We now have a system of two equations with two unknowns (A and B). We can solve this system to find the values of A and B.

Let's solve the system of equations:

From Equation 2, we can express B in terms of A:

B = -2A

Substituting this expression for B in Equation 1:

16A + 19(-2A) = 65

16A - 38A = 65

-22A = 65

A = -65/22

Substituting the value of A back into the expression for B:

B = -2A

B = -2(-65/22)

B = 65/11

Therefore, the exact values of A and B that satisfy the equation are:

A = -65/22

B = 65/11

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Related Questions

given the rectangular coordinates (-8,15), which of the following polar coordinate pairs represents the same point in radians?

a(17,2.65)
b(-17,-1.08)
c(12.7,2.65)
d(-12.7,-0.49)

Answers

Answer:

1. (x,y)=

2. (3, 480°), (3,-240°), (-3, -60°)

3. (-17, -1.08)

4. on the second circle from the center and 153° clockwise from the horizontal axis

Step-by-step explanation:

took quiz...100%

Solve Systems of Equations Algebraically.
y=x-8
y=5x

Answers

Answer:

(- 2, - 10 )

Step-by-step explanation:

Given the 2 equations

y = x - 8 → (1)

y = 5x → (2)

Substitute y = 5x into (1)

5x = x - 8 ( subtract x from both sides )

4x = - 8 ( divide both sides by 4 )

x = - 2

Substitute x = - 2 into either of the 2 equations for y

Substituting into (1)

y = - 2 - 8 = - 10

solution is (- 2, - 10 )

Triangle ABC is an isosceles triangle where angles angle A and B are congruent of angle B measures 35 what is the measurement of angle c

Answers

Answer:

m<C = 110

Step-by-step explanation:

<a = <b

<b = 35 so,

<a = 35

<c = x

<a + <b + <c = 180

35 + 35 + x = 180

70 + x = 180

x = 180 - 70

x = 110

HELP ASAP!!! select all the descriptions that apply to the transformation!

Answers

Answer: A and B

Step-by-step explanation:

The shape is moving from right to left and down

we are conducting many hypothesis tests to test a claim. In every case, assume that the null hypothesis is true. Approximately how many of the tests will incorrectly find significance?
40 tests using a significance level of 10%.

Answers

is there any answer choices or is it a free write

You take out a loan for $478 at an interest rate of 8% compounded annually. What is the
total amount that you will have paid at the end of 4 years?

Answers

Answer:

650.3

Step-by-step explanation:

Answer:

the total payment will be 91.43 and the total interest pay will be 13.43.

Step-by-step explanation:

Tbh I dont get what you mean that much, but I think you mean 48 months of payment times the monthly payment, soooo.

13.43x 48= 644.64

644.64 after four years. I really really hope this helps you. Have a good day

X^2-18x-2=0. Which number would have to be added to “complete the square”?

Answers

Step-by-step explanation:

its83

(a+b)^2=a^2+2ab+b^2

x^2+(-9)2x-2=0

b^2=81

83+(-2)=81

The driveshaft lifespan is measured in operating hours before failure, and the distribution of lifespans is known to follow a Gamma distribution. A sample of 50 driveshafts is carefully tracked until failure and their lifespans are measured to have sample mean of 1274 hours, and a standard deviation of 108 hours.

(a)Assuming a normal distribution with the mean and standard deviation of the sample, estimate the proportion of driveshafts that would fail prior to reaching 1200 operating hours.

(b)Using the central limit theorem and corresponding normality assumption, calculate a 95% confi- dence interval for the true mean lifespan.

Answers

a. The estimated proportion of driveshafts that would fail prior to reaching 1200 operating hours is approximately 0.246, or 24.6%.

b. The 95% confidence interval for the true mean lifespan is approximately (1244.79, 1303.21) hours.

How to calculate the value

(a) First, we need to standardize the value 1200 using the sample mean and standard deviation. We calculate the z-score as follows:

z = (x - μ) / σ,

z = (1200 - 1274) / 108

≈ -0.685

Using a standard normal distribution table or calculator, we find that the proportion is approximately 0.246.

(b) The formula for the confidence interval is:

CI = x ± z * (σ / √n),

CI = 1274 ± 1.96 * (108 / √50)

CI = 1274 ± 1.96 * (108 / √50)

CI ≈ 1274 ± 1.96 * 15.297

The 95% confidence interval for the true mean lifespan is approximately (1244.79, 1303.21) hours.

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what is the area of the rectangular pool below whose dimension are 2 x +1 and units x-1 units​

Answers

Answer:

(2x+1)(x-1) = 2x^2 - x - 1

Step-by-step explanation:

Answer:

2x^2 - x - 1

Step-by-step explanation:

Lets rewrite it to the area formula

(2x+1)(x-1)

Simplify-(distributive property of multiplication)

(2x*x) + (2x*-1) + (1*x) + (1*-1) =

Simplify

2x^2 + (-2x) + x + (-1)

Simplify

2x^2 - x - 1

The answer is 2x^2 - x - 1

If my answer is wrong, pls correct me

If you like my answer and my explanation, mark me as brainliest!

-Chetan K

How much interest is earned on a principal of $316 invested at an interest rate of 9%
compounded annually for four years?

Answers

Answer:

$130.06

Step-by-step explanation:

Interest is calculated as shown;

I = A - P

A is the amount

P is the principal

Given

Principal = $316

Rate R = 9% = 0.09

Time t = 4yrs

Substiutte and get Amount A

A  =P(1+r)^n

A = 316 (1+0.09)^4

A = 316(1.09)^4

A = 316(1.4116)

A = 446.06

Interest = 446.06 - 316

Interest = 130.06

Hence the interest is $130.06

how do I write an equation for a quadratic function represented by a table ?​

Answers

Answer:

Hello There!!

Step-by-step explanation:

Firstly,select three ordered pairs from the table. Secondly,substitute the first pair of values in to the form of the quadratic equation: f(x) = ax^2 + bx + c and then solve for a.

hope this helps,have a great day!!

~Pinky~

Y= -3/2x +3 is the same line as x + y =

Answers

I don’t know this question but you can’t divided by number and multiply

How am I supposed to do this?

Answers

Take it step by step by doing the 2 fractions on top

The weather reporter says that there is a 12% chance that it will be moderately windy tomorrow.


What is the probability that it will not be windy? & Will tomorrow be a good day to fly a kite? Explain.

(______Be specific ya numptys______)

Answers

There is an 88% chance that it will not be windy tomorrow the probability for wind is not very good

The probability that it will not be windy is 88% or 0.88.

No, tomorrow be not a good day to fly a kite.

What is Probability?

Probability refers to potential. A random event's occurrence is the subject of this area of mathematics.

The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.

The degree to which something is likely to happen is basically what probability means

The weather reporter says that there is a 12% chance that it will be moderately windy tomorrow.

Now, the probability that it will not be windy

= 100 - 12

= 88%

= 0.88

No, the lite totally depends on the wind but the next day the probability of no wind is 88%.

This probability is high probability.

So, there is huge probability that the kite will not fly.

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How are youaefljsofjsnjvlsdnbvjklxfclkjmzlv

Answers

GOOD BUT ANYONE WANT TO HELP ME WITH MY HISTORY BEFORE I FAIL

Which of the following variables could theoretically be measured on a continuous scale? (a) Method of contraception used (b) length of time of residence in a state (c) task completion time (d) intelligence (e) authoritarianism (f) alienation (g) county of residence.

Answers

The variable that could theoretically be measured on a continuous scale is task completion time.

Task completion time is the duration between the initiation and completion of a specific task. It is continuous as it can take a large range of values on a continuous scale without any gap. It is frequently calculated in various businesses and researches to determine the efficiency and productivity of a particular task or process.

The other variables, such as method of contraception used, length of time of residence in a state, intelligence, authoritarianism, alienation, and county of residence, are all discrete variables. These variables take non-numerical values and are separate from each other by a gap.

These variables can be classified and counted into different categories, such as the number of individuals using a particular method of contraception, number of years of residence in a particular state, number of individuals belonging to a particular county, or number of individuals showing authoritarianism.

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if h(x) = 3(x + 6), find h(-1).
a.3
b.9
c.15
d.21​

Answers

It will be 15 I Believe

Find the common difference of the arithmetic sequence -3, -9, -15

Answers

Answer:

they are subtracting 6 from each number

You add 11/4 tablespoons of olive oil for every 3/2 tablespoons of balsamic vinegar to make 34 tablespoons of bread dip. How much olive oil and balsamic vinegar do you use?

You use ___ tablespoons of olive oil and

___ tablespoons of balsamic vinegar.

Answers

Answer:

The amount of olive oil and balsamic vinegar to use are;

You use 22 tablespoons of olive oil and 12 tablespoons of balsamic vinegar

Step-by-step explanation:

From the question, we have;

The number of tablespoons of olive oil added for every 3/2 tablespoon of balsamic vinegar = 11/4 tablespoons

Therefore, in the mixture, the ratio of olive oil to balsamic vinegar = 11/4:3/2

Let 'x', and 'y' represent the the number of tablespoons of olive oil and balsamic vinegar, in the mixture 34 tablespoons of bread dip, we can write;

x + y = 34 tablespoons

x/y = (11/4)/(3/2) = 11/6

∴ x = 11/6 × y

∴ x + y = 11/6 × y + y = 34

11/6 × y + y = 17·y/6 = 34

17·y = 34 × 6 = 204

y = 204/17 = 12

The number of tablespoons of balsamic vinegar in the bead dip, y = 12 tablespoons of balsamic vinegar

x = 11/6 × y = 11/6 × 12 = 22

The number of tablespoons of olive oil in the bead dip, x = 22 tablespoons of olive oil.

please help!

if a trail runner zig-zags 15m to the west and then 15m to the east:

what is the runner's total distance?
what is the runner's total displacement?​

Answers

Answer:

Total distance = 30m

Total displacement = 0m

Step-by-step explanation:

a) Distance is a scalar quantity that does not specify direction

Hence if a trail runner zig-zags 15m to the west and then 15m to the east, the total distance will be the sum of the distance travelled both to the west and east.

total distance =  distance through west + distance through east

total distance = 15m + 15m

total distance = 30m

Hence the runner's total distance is 30m

b) Displacement is a vector quantity and it specifies direction. Hence we will take into consideration the direction taken

Since East direction is positive, the displacement through east is +15m

Since West direction is negative, the displacement through west is -15m

Total displacement  = +15 - 15

Total displacement = 0m

Hence the runner's total displacement is 0m

What is the midpoint of EF with endpoints E (−9,7) and F(0,−4)?

Answers

Answer:

midpoint = -4.5, 1.5

Step-by-step explanation:

x1 = -9, y1 = 7, x2=0 , y2=-4

midpoint = (x1 +x2)/2 , (y1 + y2)/2

= (-9 + 0)/2 , (7 + -4)/2

=-9/2 , 3/2

midpoint = -4.5, 1.5

HELP ASAP PLZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZZ

Answers

Answer:

a. The price per ticket is 4 bucks, and b. you get 1/4 of a ticket for a dollar.

1. the penguin walks 75 feet in 45 seconds, and 2. it takes 27 seconds to walk 45 feet.

Step-by-step explanation:

Tickets:

16 dollars divided by 4 tickets is 4 dollars, so 4 dollars = 1 ticket. therefore, 1 dollar gives you 1/4 of a ticket.

Penguins

formula: X = feet, Y = seconds

X*0.6=Y

10 feet*0.6=6 seconds

(?) feet*0.6= 45 seconds

75 feet*0.6=45 seconds

same thing, but backwards this time

45 feet*0.6=(?) seconds

45 feet*0.6= 27 seconds

Hey can I have brainly please I am really close to leveling up

thx

Answer:

Step-by-step explanation:

The measures of the angles of a triangle are shown in the figure below. Solve for x.

Answers

Answer:

26 degrees

Step-by-step explanation:

180 - 48 = 132 - 106 = 26

this one should work

Answer: x = 106°

Step-by-step explanation:

106° + 48° + x° = 180°

154 + x = 180

x = 106°

Can someone please help me with this

Answers

Answer:

Step-by-step explanation:

5- There are 2 right-angled triangles and 1 equilateral triangle or you can just say triangles

6- area for a triangle is a=bh(1/2)

so 4×3=12(1/2)=6

and 4×3=12(1/2)=6

In both triangles, they're a=6

7- 4×6=24(1/2)=12

the top flag is a=12

8-12+6+6=24

9- the rectangular flag has an area of 24 since a=bh and the added areas of the triangles are 24. I conclude that these are two ways of finding the area of this rectangular flag.

hope this helps : )

Find the confidence interval specified. Assume that the population is normally distributed. The principal randomly selected six students to take an aptitude test. Their scores were: 84.1 79.8 79.6 81.3 88.1 81.0 Determine a 90% confidence interval for the mean score for all students.

Answers

The 90% confidence interval for the mean score for all students is [79.35, 86.75].

What is the range within which the mean score for all students lies with 90% confidence?

A 90% confidence interval was calculated to estimate the mean score for all students based on a sample of six students' scores. The sample mean was found to be 82.83, and the standard deviation was 3.67.

Using a t-distribution with five degrees of freedom (n-1), the critical value for a 90% confidence level was determined to be 2.571. By applying the formula for confidence intervals, the lower bound of the interval was calculated as 82.83 - (2.571 * (3.67/√6)) = 79.35, and the upper bound was calculated as 82.83 + (2.571 * (3.67/√6)) = 86.75.

This means that we can be 90% confident that the mean score for all students falls within the range of 79.35 to 86.75.

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Twenty-five wooden beams were ordered for a construction project. The sample mean and the sample standard deviation were measured: xbar = 260 cm, s = 2 cm. Calculated confidence interval for the mean is [259.32;260.68].
Which confidence level was chosen? assume distribution to be normal.

Answers

The answer tο the questiοn "Which cοnfidence level was chοsen?" is that it cannοt be determined based οn the given infοrmatiοn.

What is Statistical Inference?

Statistical inference refers tο the prοcess οf drawing cοnclusiοns οr making predictiοns abοut a pοpulatiοn based οn sample data. It invοlves using statistical methοds and techniques tο analyze the data and make inferences abοut the underlying pοpulatiοn parameters. Statistical inference allοws researchers tο generalize their findings frοm a sample tο the entire pοpulatiοn and make infοrmed decisiοns οr predictiοns.

Twenty-five wοοden beams were οrdered fοr a cοnstructiοn prοject. The sample means and the sample standard deviatiοn was measured:[tex]\bar{x} = 260 \, \text{cm}$, $s = 2 \, \text{cm}$.[/tex] The calculated confidence interval for the mean is [tex][259.32; 260.68]$.[/tex]

To determine the confidence level chosen, we need to consider the properties of a confidence interval. In this case, the confidence interval is given as[tex]$[259.32; 260.68]$[/tex], which represents an interval estimate for the population mean.

A confidence interval is typically written as [tex]\bar{x} \pm E$,[/tex]where [tex]$\bar{x}$[/tex] is the sample mean and E is the margin οf errοr. The margin οf errοr depends οn the sample size, standard deviatiοn, and the desired level οf cοnfidence.

In the given infοrmatiοn, the sample mean [tex]$\bar{x}$[/tex] is 260 cm, and the sample standard deviatiοn s is 2 cm. Hοwever, the level οf cοnfidence is nοt directly prοvided.

Tο determine the cοnfidence level chοsen, we need additiοnal infοrmatiοn abοut the calculatiοn οr the specific cοnfidence level used. Withοut this infοrmatiοn, we cannοt determine the exact cοnfidence level that cοrrespοnds tο the given cοnfidence interval.

Therefοre, the answer tο the questiοn "Which cοnfidence level was chοsen?" is that it cannοt be determined based οn the given infοrmatiοn.

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Please please help I swear I will give you brainlist if it’s right and please explain for part a and part b thank you

Answers

Answer:

A. Reduction

B. 2

Step-by-step explanation:

A: A reduction is when the image is getting smaller. The apostrophes show the new, or second, image. It is called "prime." Because the prime is smaller than the original, it is a reduction.

B: Scale factor is when you divide, which number changes it. In other words, the image moved from 4 to 2, from 2 to 1, etc, which means we are DIVIDING by 2.

Write the system x' = e²tx - 8ty + 7 sin(t), y' = 2 tan(t) y + 7x - 2 cos(t) in the form Use prime notation for derivatives and write x and ï', etc., instead of ï(t), x'(t), or dr. 1-1 dt = P60 [*] + F(0). P(t)

Answers

The system in the requested form, using prime notation for derivatives and ï notation for variables, is ï' = e^2tï - 8tï' + 7sin(t) and ï'' = 2tan(t)ï' + 7ï - 2cos(t).

The system can be written in the form:

x' = e^2tx - 8ty + 7sin(t)

y' = 2tan(t)y + 7x - 2cos(t)

Using prime notation for derivatives, the system becomes:

x' = e^2tx - 8ty + 7sin(t)

y' = 2tan(t)y + 7x - 2cos(t)

Furthermore, we can write x and y using ï' notation as:

x = ï

y = ï'

Substituting these expressions into the system, we have:

ï' = e^2tï - 8tï' + 7sin(t)

ï'' = 2tan(t)ï' + 7ï - 2cos(t)

In summary, the system in the requested form is:

ï' = e^2tï - 8tï' + 7sin(t)

ï'' = 2tan(t)ï' + 7ï - 2cos(t)

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A simple random sample of size n is drawn from a population that is normally distributed. The sample mean, X, is found to be 100, and the sample standard deviation found to be 8.
Construct a 98% confidence interval about µ, if the sample size n, is 20.
Lower bound ______ Upper bound _______
(Round to one decimal place as needed.)

Answers

As per the confidence interval Lower Bound is 94.874 and the Upper Bound is 105.126

Sample Mean = 100

Sample Standard Deviation = 8

Sample Size = 20

Calculating the confidence interval -

Confidence Interval = Sample Mean ± (Critical Value) x (Standard Deviation / √(Sample Size))

Substituting the values

= 100 ± (2.860) x (8 / √20)

= 100 ± 2.860 x (8 / 4.472)

= 100 ± 2.860 x 1.789

= 100 ± 5.126

Calculating the lower bound -

Lower Bound

= 100 - 5.126

= 94.874

Calculating the upper bound -

Upper Bound

= 100 + 5.126

= 105.126

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Find value(s) of k so that the linear system is consistent? (Enter your answers as a comma-separated list.) 8x1-7x2 = 2 12x1 + kx2 =-1

Answers

There are no values of k that make the linear system consistent.

To determine the values of k for which the linear system is consistent, we need to check if the system of equations has a unique solution, infinitely many solutions, or no solution.

The given system of equations is:

8x1 - 7x2 = 2

12x1 + kx2 = -1

We can solve this system using various methods, such as substitution or elimination. Let's use the elimination method to simplify the system.

To eliminate x2, we can multiply equation 1 by k:

8kx1 - 7kx2 = 2k

Now, we can subtract equation 2 from equation 3:

(8k - 12)x1 + (-7k - k)x2 = (2k + 1)

Simplifying equation 4, we have:

(8k - 12)x1 - 8kx2 = 2k + 1

Now, for the system to be consistent, the coefficient of x1 and the coefficient of x2 in the resulting equation should be the same.

Comparing the coefficients, we get:

8k - 12 = 0 (coefficient of x1)

-8k = -1 (coefficient of x2)

Solving the first equation:

8k - 12 = 0

8k = 12

k = 12/8

k = 3/2

Now, substitute the value of k in the second equation to check if it is satisfied:

-8k = -1

-8(3/2) = -1

-12 = -1

The equation -12 = -1 is false. Therefore, there are no values of k for which the linear system is consistent.

In conclusion, there are no values of k that make the given linear system consistent.

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