Answer: y = -x
Step-by-step explanation:
The equation of the hyperbola is x² - y² = 16.
Taking the derivative of the equation with respect to x, we get:
2x - 2yy' = 0
y' = x / y
At the point (2,-2), we have x = 2 and y = -2. Thus, the slope of the tangent is:
y' = 2 / (-2) = -1
So, the equation of the tangent through the point (2,-2) is:
y + 2 = -1(x - 2)
y + 2 = -x + 2
y = -x
Solve for x, using a
tangent and a secant line.
64°
X
145°
x = [?]° Remember: a = b
c-b
2
Enter
Considering the secant-tangent theorem, the value of x is given as follows: x = 17º.
What is the secant-tangent theorem?The secant-tangent theorem states that when a tangent and a secant line intersect at a point outside a circle, the measure of the angle of intersection is given by half the difference between the arc length of the far arc by the arc length of the near arc.
Hence the equation is given as follows:
y = (far arc - near arc)/2.
The parameters for this problem are given as follows:
far arc = 145º.near arc = x.Angle = 64º.Hence the value of x is obtained as follows:
64 = (145 - x)/2
145 - x = 128
x = 17º.
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what is the square root of 8
2√2
The square root of 8 in radical form is represented as √8 which is also equal to 2√2 and as a fraction, it is equal to 2.828 approximately.
sams rectangular swimming pool has a volume of 600 cubic feet, the neighbors pools the same length and height but the width is three times larger. what is the volume of the neighbors pool?
Answer: Let's denote the length, width, and height of Sam's pool as l, w, and h, respectively. Then, we have:
lwh = 600
For the neighbor's pool, we know that it has the same length and height as Sam's pool, but the width is three times larger. Let's denote the width of the neighbor's pool as 3w. Then, the volume of the neighbor's pool is:
l(3w)h = 3lwh = 3(600) = 1800 cubic feet
Therefore, the volume of the neighbor's pool is 1800 cubic feet.
Step-by-step explanation:
In a budget, what type of expense is an flu shot?
In a budget, an expense for a flu shot would typically fall under the category of "Healthcare" or "Medical Expenses".
What is Flu Shot?
A flu shot is a vaccine that helps protect against the influenza virus, which can cause the flu. The vaccine works by stimulating the body's immune system to produce antibodies that can recognize and fight off the flu virus. The flu shot is usually given as an injection in the upper arm, and it typically contains small amounts of inactivated flu viruses, which cannot cause the flu.
The Centers for Disease Control and Prevention (CDC) recommends that everyone over the age of six months get a flu shot every year, as the flu can be a serious and sometimes deadly illness. The flu virus can mutate and change each year, so getting a flu shot annually helps protect against the most prevalent strains of the virus that are circulating. While the flu shot does not guarantee that a person won't get the flu, it can greatly reduce the severity and duration of the illness if contracted.
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Bria is a customer who would like to display her collection of soap carvings on top of her bookcase. The collection needs an area of 300 square inches. What should b equal for the top of the bookcase to have the correct area? Round your answer to the nearest tenth of an inch.
help me pls D;
please D:
The breadth, B which the soap carvings should be equal for the top of the bookcase to have the correct area is 5 inches.
How to calculate the area of a rectangle?In Mathematics, the area of a rectangle can be calculated by using the following mathematical equation:
A = LB
Where:
A represent the area of a rectangle.B represent the width or breadth of a rectangle.L represent the length or height of a rectangle.Substituting the given parameters into the area of rectangle formula, we have the following;
Area of soap carvings = length × width
300 = 60B
Width, B = 300/60
Width, B = 5 inches.
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The bells bought a $386,000 house. They made a down payment of $49,000 and took out a mortgage for the rest. Over the course of 15 years they made monthly payments of $2843.81 on their mortgage until it was paid off.
What was the total amount they ended up paying for the house (including the down payment and monthly payments)?
How much interest did they pay on the mortgage?
Answer:
Step-by-step explanation:
The total amount paid for the house is the sum of the down payment and the total amount paid for the mortgage.
The total amount paid for the mortgage can be calculated as follows:
Number of monthly payments = 15 years x 12 months/year = 180 months
Total amount paid for the mortgage = 180 x $2843.81 = $511,086.80
Therefore, the total amount paid for the house is:
$386,000 + $511,086.80 = $897,086.80
To calculate the amount of interest paid, we need to subtract the principal amount (the original amount borrowed) from the total amount paid for the mortgage.
Principal amount = Total amount borrowed - Down payment = $386,000 - $49,000 = $337,000
Total interest paid = Total amount paid for the mortgage - Principal amount = $511,086.80 - $337,000 = $174,086.80
Therefore, they paid a total of $897,086.80 for the house, and they paid $174,086.80 in interest on their mortgage.
Help please need to pass this
Answer:
45%
Step-by-step explanation:
86 people play an instrument out of 192 students.
86/192 = .4479
.4479 x 100% = 44.79% = 45%
Answer: 45 percent
Step-by-step explanation:
Answer this imagine please
The expression that is not equivalent to the model shown is given as follows:
-4(3 + 2). -> Option C.
What are equivalent expressions?Equivalent expressions are mathematical expressions that have the same value, even though they may look different. In other words, two expressions are equivalent if they produce the same output for any input value.
The expression for this problem is given by three times the subtraction of four, plus three times the addition of 2, hence:
3(-4) + 3(2) = -12 + 6 = 3(-4 + 2) = 3(-2) = -6.
Hence the expression that is not equivalent is the expression given in option C, for which the result is given as follows:
-4(3 + 2) = -4 x 5 = -20.
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Consider parallelogram ABCD below.
Use the information given in the figure to find m/BAC, m/B, and x.
Answer:
Since opposite angles in a parallelogram are congruent, we know that:
m∠DAB = m∠BCD = 67°
Since ∠BAC and ∠BCD are adjacent angles, we know that:
m∠BAC + m∠BCD = 180°
So we can solve for m∠BAC:
m∠BAC + 67° = 180°
m∠BAC = 113°
Since opposite angles in a parallelogram are congruent, we know that:
m∠BAD = m∠BC
So we can solve for m∠BC:
m∠BAD = 16
m∠BC = 16°
Finally, we can solve for x by using the fact that the interior angles of a quadrilateral sum to 360 degrees:
m∠DAB + m∠BAC + m∠BCD + m∠CDA = 360°
67° + 113° + m∠BCD + 90° = 360°
m∠BCD = 90°
So we can solve for x:
m∠4B - m∠BCD = 90° - 90° = 0
4x - 59° = 0
4x = 59°
x = 14.75°
Therefore, m/BAC = 113°, m/B = 16°, and x = 14.75°.
Drag each tile to its equivalent measure, rounded to the nearest tenth.
Options: 19.8, 10.2, 22.7, 15.4
Measure Equivalent
4 in. _____ Cm
7 kg _____lb
6 gal _____L
65 ft _____ m
The correct matches are: 4 in. → 10.2 cm , 7 kg → 15.4 lb
6 gal → 22.7 L and 65 ft → 19.8 m.
What are conversions?Conversions refer to the process of changing a measurement from one unit to another unit that measures the same quantity.
For example, converting distance from miles to kilometers, or converting weight from pounds to kilograms.
Here are the conversions:
1 inch = 2.54 cm (approx.)
1 kg = 2.205 lb (approx.)
1 gal = 3.785 L (approx.)
1 ft = 0.3048 m (approx.)
Using these conversions, we can find the equivalent measures:
4 in. → 4 × 2.54 = 10.16 ≈ 10.2 cm
7 kg → 7 × 2.205 = 15.435 ≈ 15.4 lb
6 gal → 6 × 3.785 = 22.71 ≈ 22.7 L
65 ft → 65 × 0.3048 = 19.812 ≈ 19.8 m
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two random vectors follow the same distribution does this mean every marginalized variables have to follow the same distribution
Yes. they can in fact, more than two independent variables can have the same distribution. Two random vectors follow the same distribution, which means that each marginalized variable must follow the same distribution.
In probability theory and statistics, the marginal distribution of a subset of a set of random variables is the probability distribution of the variables contained in that subset. It gives the probability of different values of variables in the subset without reference to the values of other variables. This contrasts with conditional distributions, which give probabilities based on the values of other variables.
The marginal variables are the variables of the subset of variables which are retained. These concepts are "marginal" because they can be found by adding the values of the rows or columns of a table and writing the sum in the blank space of the table.
The distribution of the marginal variable (marginal distribution) is obtained by marginalizing the distribution of the suppressed variable (that is, focusing on the sum in the margin), and the suppressed variable is called marginalized.
Complete Question:
If two random variables have the same PDF/PMF, then does this mean they have the same distribution?
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A spherical balloon is inflated with gas at a rate of 900 cubic centimeters per minute. (a) Find the rates of change of the radius when r-70 centimeters and r 95 centimeters. r 70 X cm/min r = 95 X cm/min
When the radius of spherical balloon r = 70 cm, the rate of change of the radius is approximately 0.002 cm/min and when the radius is 95 cm then the rate of change of the radius is approximately 0.001 cm/min.
The volume of a sphere is given by V = (4/3)πr^3, where r is the radius. Differentiating both sides with respect to time t, we get:
dV/dt = 4πr^2(dr/dt)
where dV/dt is the rate of change of the volume and dr/dt is the rate of change of the radius.
We are given that dV/dt = 900 cm^3/min.
When r = 70 cm, we can solve for dr/dt as follows:
900 = 4π(70)^2(dr/dt)
dr/dt = 900 / (4π(70)^2) ≈ 0.002 cm/min
Therefore, when r = 70 cm, the rate of change of the radius is approximately 0.002 cm/min.
Similarly, when r = 95 cm, we can solve for dr/dt as follows:
900 = 4π(95)^2(dr/dt)
dr/dt = 900 / (4π(95)^2) ≈ 0.001 cm/min
Therefore, when r = 95 cm, the rate of change of the radius is approximately 0.001 cm/min.
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Write a sine function that has a midline of, y=5, an amplitude of 4 and a period of 2.
Answer:
y = 4 sin(π x) + 5
Step-by-step explanation:
A sine function with a midline of y=5, an amplitude of 4, and a period of 2 can be written in the following form:
y = A sin(2π/ x) +
where A is the amplitude, is the period, is the vertical shift (midline), and x is the independent variable (usually time).
Substituting the given values, we get:
y = 4 sin(2π/2 x) + 5
Simplifying this expression, we get:
y = 4 sin(π x) + 5
Therefore, the sine function with the desired characteristics is:
y = 4 sin(π x) + 5
If a data set has an even number of observations, the median a. cannot be determined b. is the average value of the two middle items c. must be equal to the mean d. is the average value of the two middle items when all items are arranged in ascending order
If a data set has an even number of observations, the median is the middle value of the two middle values when all values are placed in ascending order. Thus, option d is correct.
The median is the central value in a set of groups of data. The data should be organized and ordered from smallest value to biggest value. To find the middle value, we should divide the number of observations by two.
To determine the median, we must determine the Mean. Then, we need to calculate out how many observations there are in the data set. If there are an odd number of observations, the median cannot be calculated as a regular calculation.
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what is the integral of e^{\cos\left(e^{\cos\left(e^{\cos\left(e^{\cos\left(x\right)}\right)}\right)}\right)}
The integral of [sin x / cos x] + [cos x / sin x] is (1/2) x ln |tan x| - (1/2) x ln |sec x| + C
The integral you have provided can be rewritten as:
∫ [sin x / cos x] + [cos x / sin x] dx
Using algebraic manipulation, we can simplify this expression to:
∫ (sin² x + cos² x) / (cos x x sin x) dx
Now, we can use the method of partial fractions to break down the integrand into simpler fractions. To do this, we first need to factor the denominator:
cos x x sin x = (1/2) x (sin 2x)
We can then express the integrand as:
(sin² x + cos² x) / [(1/2) x (sin 2x)]
Using the partial fractions technique, we can express the integrand as:
(sin² x + cos² x) / [(1/2) x (sin 2x)] = A / sin 2x + B / cos 2x
where A and B are constants that we need to determine. To solve for A and B, we can multiply both sides by sin 2x x cos 2x, which gives us:
sin² x + cos² x = A x cos 2x + B x sin 2x
We can then use the trigonometric identities sin² x + cos² x = 1 and cos 2x = 2 x cos² x - 1, and sin 2x = 2 x sin x x cos x, to simplify the equation to:
1 = (2A - B) x cos² x + (2B) x sin x x cos x - A
We now have two equations (for x = 0 and x = π/2) and two unknowns (A and B), which we can solve simultaneously to obtain:
A = 1/2 and B = -1/2
Using these values, we can express the integrand as:
(sin² x + cos² x) / [(1/2) x (sin 2x)] = (1/2) x [1 / sin 2x - 1 / cos 2x]
We can now integrate each term separately:
∫ [sin x / cos x] + [cos x / sin x] dx = ∫ [(1/2) x (1 / sin 2x - 1 / cos 2x)] dx = (1/2) x ln |tan x| - (1/2) x ln |sec x| + C
where C is the constant of integration. Therefore, the final answer to the given integral is:
∫ [sin x / cos x] + [cos x / sin x] dx = (1/2) x ln |tan x| - (1/2) x ln |sec x| + C
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Complete Question:
what is the integral of
[sin x / cos x] + [cos x / sin x]
15.with regard to p-charts, the general recommendation for the number of samples to be taken when estimating p is .
With regard to p-charts, the general recommendation for the number of samples to be taken when estimating p is to take at least 20-25 samples.
The number of samples needed when estimating p using p-charts depends on the desired level of accuracy and confidence.
A general recommendation is to take at least 20-25 samples to obtain a reasonably accurate estimate of p. This recommendation is based on the central limit theorem, which states that the distribution of sample proportions approaches a normal distribution as the sample size increases.
With a sample size of 20-25, the estimate of p is likely to be within a reasonable margin of error and have a sufficient level of confidence.
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which of the following correctly relates the measures of the diameter (d) and radius (r) of a circle
The equation which correctly relates the measure of diameter and radius of a circle is (c) r = d/2.
The Diameter (d) of a circle is defined as the distance across the circle through its center. The radius (r) of a circle is defined as the distance from the center of the circle to any point on the circle.
We know that the radius of the circle is half of diameter, because it extends from the center to the edge of the circle, while the diameter extends all the way across the circle.
So, we can express the relationship between d and r as:
⇒ d = 2r
To solve for r, we can divide both sides by 2:
We get,
⇒ r = d/2
Therefore, The correct equation is Option (c) r = d/2.
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The given question is incomplete, the complete question is
Which of the following correctly relates the measures of the diameter (d) and radius (r) of a circle?
(a) d = r/2
(b) r = 2d
(c) r = d/2
(d) d = 2/r
How many yards and feet are equivalent to 10,000 feet
A 3,333 yards , 0 feet
B 3,333 yards , 1 foot
C 277 yards ,28 feet
D 30,000 yards
Answer: B (3,333 yards, 1 foot)
Step-by-step explanation: 10,000 feet / 3yards= 3,333.33 yards
3 feet in every yard so divide 10,000 by 3 and get 3,333.33 yards. since there are 3 feet in every yard the .33 is 1 foot.
Karina is making a quilt and she has determined she needs 420 square inches of green fabric and 688 square
inches of burgundy. How many square yards of each material will she need? Round your answers up to the
nearest quarter yard.
The green fabric:
square yards
The burgundy fabric:
How many total yards of fabric will she have to buy?
square yards
square yards
1. The total yards of each fabric that Karina will buy to make a quilt is as follows:
a) Green Fabric = 12 square yards
b) Burgundy Fabric = 19 square yards
2. The total yards of fabric she will buy is 31 square yards.
How are the total determined?The total yards of fabric can be determined by unit conversion using division operation.
Given that 36 inches = 1 yard, the square inches of fabric are converted to square yards by dividing the total by 36.
The total number of green fabric Karina requires = 420 square inches
= 12 square yards (420/36)
The total number of burgundy fabric Karina requires = 688 square inches
= 19 square yards (688/36)
The total number of fabric (green and burgundy) = 1,108 square inches (420 + 688)
36 inches = 1 yard
1,108 inches = 30.78 square yards (1,108/36)
= 31 square yards or (12 + 19)
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when emotive words are used in a group, which of the following questions should group members ask themselves?
The correct answer is All. (i.e.as a group what do we do?, how would you discuss this issue?, what new rules might this group create to allow for emotive words yet avoid the consequences of their use?)
Group members should ask themselves how their use of emotive words may affect the group dynamic, and should consider how can they use these words to make other group members feel and if it is appropriate to express their opinion in this way and also think about the impact this might have on the group's ability to achieve its goals and objectives.
They should consider what new rules may be created to allow for emotive words yet avoid the consequences of their use. And also they should ask themselves if there are other ways to express their opinion which may be much effective and appropriate. All of these questions should be asked in order to ensure that the group remains respectful and productive.
Full Question:
when emotive words are used in a group, which of the following questions should group members ask themselves?
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At a sale Jenny receives 10% off followed by a further 10% staff discount.
Calculate the first discount on a $300 camera.
93. Electricity Usage The graph shows
the daily megawatts of electricity used
on a record-breaking summer day in
Sacramento, California.
(a) Is this the graph of a function?
(b) What is the domain?
(c) Estimate the number of megawatts
used at 8 A.M.
(d) At what time was the most electric-
ity used? the least electricity?
(e) Call this function f. What is f(12)?
Interpret this answer.
(f) During what time intervals is usage
increasing? decreasing?
Sacramento, California's electricity demand on a scorching summer day is depicted in a function graph. The domain is 24 hours of a day.
The site is available around-the-clock.
One thousand two hundred megawatts are consumed at eight in the morning.
The hours between 4:00 and 6:00 pm saw the highest electricity use, while 4:00 am saw the lowest use.
It would be 1,900 megawatts for f (12).
From 4 am to 5 pm, usage rises, and from 5 pm to 4 am, it falls.
What is displayed by the graph?Because each point on the graph reflects a different megawatt usage, the graph is a function. As this graph of electricity usage illustrates, the domain would be available throughout the entire day.
At 8 a.m., these megawatts are used:
= 1, 300 - ( 200 / 2 )
equal to 1,200 megawatts
As people get ready for work and leave for work, we can observe an increase in power demand from 4 am to 5 pm, but a reduction from 5 pm to 4 am.
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Please answer Full question
(1) 4y-7z is a binomial.
(2) 8-xy² is a binomial.
(3) ab-a-b can be written as ab - (a + b) which is a binomial.
(4) z²-3z+8 is a trinomial.
What are monomials, binomials and trinomials?In algebra, monomials, binomials, and trinomials are expressions that contain one, two, and three terms, respectively.
A monomial is an algebraic expression with only one term. A monomial can be a number, a variable, or a product of numbers and variables.
A binomial is an algebraic expression with two terms that are connected by a plus or minus sign. For example, 2x + 3y and 4a - 5b are both binomials.
A trinomial is an algebraic expression with three terms that are connected by plus or minus signs.
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Classify into monomials, binomials and trinomials.
(1) 4y-7z
(1) 8-xy²
(v) ab-a-b
(ix) z2-3z+8
which of the following statements about the car's motion is true?
Answer: the last one
Step-by-step explanation:
the car went slow at the end
A boat is heading towards a lighthouse, whose beacon-light is 148 feet above the water. The boat’s crew measures the angle of elevation to the beacon, 8 degrees. What is the ships horizontal distance from the lighthouse(and the shore)? Round your answer to the nearest hundredth of a foot if necessary.
We can use trigonometry to solve this problem. Let's call the horizontal distance from the boat to the lighthouse "x". We can use the tangent function to find x:
tangent(8 degrees) = opposite / adjacent
tangent(8 degrees) = 148 / x
To solve for x, we can rearrange the equation:
x = 148 / tangent(8 degrees)
x ≈ 1041.87 feet
So the ship's horizontal distance from the lighthouse (and the shore) is approximately 1041.87 feet or 1041.87 rounded to the nearest hundredth of a foot if necessary.
Answer:
Your answer is 1053.07
Hope I helped!
Step-by-step explanation:
let x be a normal random variable with a mean of 5 and a standard deviation of 10. find p(-20 < x < 15).
The probability of -20 < x < 15, where x be a normal random variable with a mean of 5 and a standard deviation of 10 is approximately 0.8351.
To solve this problem, we need to find the area under the normal distribution curve between -20 and 15, with a mean of 5 and a standard deviation of 10.
We can standardize the normal distribution by subtracting the mean and dividing by the standard deviation, which gives us the standard normal distribution with a mean of 0 and a standard deviation of 1.
So, we can first calculate the z-scores for -20 and 15:
z1 = (-20 - 5) / 10 = -2.5
z2 = (15 - 5) / 10 = 1
Next, we use a standard normal distribution table or calculator to find the probabilities associated with these z-scores:
P(z < -2.5) = 0.0062
P(z < 1) = 0.8413
To find the probability of -20 < x < 15, we subtract the probability associated with the lower z-score from the probability associated with the higher z-score:
P(-20 < x < 15) = P(-2.5 < z < 1) = P(z < 1) - P(z < -2.5)
P(-20 < x < 15) = 0.8413 - 0.0062 = 0.8351
Therefore, the probability of -20 < x < 15 is approximately 0.8351.
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During a manufacturing process, a metal part in a machine is exposed to varying temperature conditions. The manufacturer of the machine recommends that the temperature of the machine part remain below 131°F. The temperature T in degrees Fahrenheit x minutes after the machine is put into operation is modeled by T=-0.005x^2+0.45x+125. Will the temperature of the part ever reach or exceed 131°F? Use the discriminant of a quadratic equation to decide.
answer options
1. No
2. Yes
From the discriminant of the give quadratic equation, the temperature of the machine will part after 50 minutes of operation.
Will the temperature of the part ever reach or exceed 135°F?The given equation that models the temperature of the machine is;
T = -0.005x² + 0.45x + 125
Let check if there's a value that exists for T = 135
Putting T = 135 in the given equation,
135 = -0.005x² + 0.45x + 125
We can simplify this to;
0.005x² - 0.45x + 10 = 0
From the general form of quadratic equation which is ax² + bx + c = 0, where a = 0.005, b = -0.45, and c = 10.
The discriminant of this quadratic equation is given by:
D = b² - 4ac
= (-0.45)² - 4(0.005)(10)
= 0.2025 - 0.2
= 0.0025
The discriminant of the equation is positive which indicates we have two roots. Therefore, the temperature of the machine part will cross 135°F at some point during the operation.
We can also find the roots of the quadratic equation using the formula:
[tex]x = (-b \± \sqrt(D)) / 2a[/tex]
Substituting the values of a, b, and D, we get:
[tex]x = (0.45 \± \sqrt(0.0025)) / 2(0.005)\\= (0.45 \± 0.05) / 0.01[/tex]
Taking the positive value, we get:
x = 50
Therefore, the temperature of the machine part will cross 135°F after 50 minutes of operation.
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FILL IN THE BLANK Random variation in a process indicates __________; whereas non-random variation indicates process __________.
Random variation in a process indicates natural variation ; whereas non-random variation indicates process variation
Random variation in a process refers to the natural variation or randomness that occurs in a process due to various factors that are not controlled or predictable. For example, in a manufacturing process, random variation can be caused by factors such as differences in raw materials, operator error, or environmental conditions that are not controlled.
On the other hand, non-random variation in a process refers to the variation that is not due to chance and is likely caused by specific factors that are affecting the process. Non-random variation is also known as special cause variation. Special cause variation can be caused by factors such as a change in machine settings, a change in process parameters, or a change in the process inputs.
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In Problems 21 through 30, set up the appropriate form of a
particular solution yp, but do not determine the values of the
coefficients.y" – 2y' + 2y = et sin x = . =
The particular solution of Differential equation y" – 2y' + 2y = et sin x is yp = (1/2et - 1/2et cos(x))sin(x).
We assume the particular solution is of the form of given differential equation is
yp = (Aet + Bcos(t))sin(x) + (Cet + Dsin(t))cos(x)
where A, B, C, and D are constants to be determined.
Taking the first and second derivative of yp with respect to t:
yp' = Aet sin(x) - Bsin(t)sin(x) + Cet cos(x) + Dcos(t)cos(x)
yp'' = Aet sin(x) - Bcos(t)sin(x) - Cet sin(x) + Dsin(x)cos(t)
Substituting these into the differential equation and simplifying, we get:
(et sin x) = (A - C)et sin(x) + (B - D)cos(x)sin(t)
Since et sin x is not a solution to the homogeneous equation, the coefficients of et sin x and cos(x)sin(t) on both sides of the equation must be equal. Therefore:
A - C = 1 and B - D = 0
Solving for A, B, C, and D, we get:
A = 1/2, B = 0, C = -1/2, D = 0
So the particular solution is:
yp = (1/2et - 1/2et cos(x))sin(x)
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Find the coordinates of the center and the measure of the radius for a circle whose equation is(x - 8) + (y + 4) = 12
The center coordinates and radius of the given circle (x - 8)^2 + (y + 4)^2 = 12 is given by ( 8 ,-4 ) and 2√3 respectively.
Equation of the circle is equal to ,
(x - 8)^2 + (y + 4)^2 = 12.
Standard form of the equation of the circle is equals to,
( x - a )^2 + ( y - b )^2 = r^2 ___(1)
Where ( a, b ) are the coordinates of the center of the circle.
And r is the radius of the circle.
Convert the equation of the circle (x - 8)^2 + (y + 4)^2 = 12 into standard form we have,
(x - 8)^2 + (y + 4)^2 = ( 2√3 )^2 ___(2)
Compare equation (1) and (2) to get coordinates of the center and radius of the circle.
Here value of a = 8
value of b = -4
Radius of the circle 'r' = 2√3
Therefore, the center of the coordinates and radius of the circle is equal to ( 8 ,-4 ) and 2√3 respectively.
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The above question is incomplete, the complete question is:
Find the coordinates of the center and the measure of the radius for a circle whose equation is(x - 8)^2 + (y + 4)^2 = 12.