Separate the variables.
[tex](x^2+1) \dfrac{dy}{dx} = xy \implies \dfrac{dy}y = \dfrac x{x^2+11} \, dx[/tex]
Integrate both sides. On the right, substitute [tex]u=x^2+11[/tex] and [tex]du=2x\,dx[/tex].
[tex]\displaystyle \int \frac{dy}y = \int \frac x{x^2+11}\,dx = \frac12 \int \frac{du}u[/tex]
[tex]\ln|y| = \frac12 \ln|u| + C[/tex]
[tex]\ln|y| = \ln\left(\sqrt{x^2+11}\right) + C[/tex]
[tex]e^{\ln|y|} = e^{\ln\left(\sqrt{x^2+11}\right)+C}[/tex]
[tex]\boxed{y = C\sqrt{x^2+11}}[/tex]
Using separation of variables, the solution to the differential equation is:
y = ksqrt(x² + 11)
What is separation of variables?In separation of variables, we place all the factors of y on one side of the equation with dy, all the factors of x on the other side with dx, and integrate both sides.
In this problem, the differential equation is:
(x² + 11)y' = xy
Applying separation of variables, we have that:
y'/y = x/(x² + 11)
[tex]\int \frac{y^{\prime}}{y} = \int \frac{x}{x^2 + 11}[/tex]
[tex]\ln{y} = \frac{\ln{x^2 + 11}}{2} + K[/tex]
[tex]\ln{y} = \ln{(x^2 + 11}^{\frac{1}{2}}) + K[/tex]
[tex]\ln{y} = \ln{\sqrt{x^2 + 11}} + K[/tex]
Hence the solution is:
y = ksqrt(x² + 11)
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Find the exact value of x.
X =
11
X
00
8
prove 1-cot23 = 2/ ( 1- cot22)
From all the steps below, we have been able to prove that; 1 - cot23° = 2/(1 - cot22°).
How to prove trigonometric functions?We want to prove that 1 - cot23° = 2/(1 - cot22°).
We will prove it using the trigonometric expression
cot(22° + 23°) = cot45°
Using trigonometric identities, we can rewrite as;
(cot22° cot23° - 1)/(cot22° + cot23°) = 1
Cross multiply to get;
cot22° cot23° - 1 = cot22° + cot23°
Rearrange to get;
cot22° cot23° - 1 - cot22° - cot23° =0
⇒ cot22° cot23° - 1 - cot22° - cot23° + 2 =2
⇒ cot22° cot23° + 1 - cot22° - cot23° =2
⇒ cot22° cot23° - cot22° - cot23° + 1 = 2
⇒ cot22° (cot23° - 1) - 1 (cot23° - 1) = 2
⇒ (cot22° - 1) (cot23° - 1) = 2
Divide both sides by (cot23° - 1) to get;
cot23° - 1 = 2/(cot22° - 1)
⇒ 1 - cot23° = 2/(1 - cot22°).
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In order to finance furniture for an office in a new retail store, Tools for Schools signs a 80-day simple discount note with a maturity value of $7700. Find the proceeds if the discount rate is 6%.
Based on the number of periods for the simple discount note to reach maturity and the discount rate, the proceeds are $7,598.74.
What are the proceeds?You can solve for the discounted price as:
= Maturity value x discount rate x number of periods
Solving gives:
= 7,700 x (6% / 365) x 80
= $101.26
The proceeds can then be found by subtracting the discounted price from the maturity price.
Solving for the proceeds gives:
= 7,700 - 101.26
= $7,598.74
Based on the simple discount note period, the maturity value, and the discount rate, the proceeds can be found to be $7,598.74.
In conclusion, the proceeds are $7,598.74.
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Underwood Company is preparing its annual profit plan. As part of its analysis of the profitability of individual products, the controller estimates the amount of manufacturing overhead that should be assigned to each of the two product lines from the information given below. Wall Mirrors Specialty Windows Total units produced 30 30 Total number of material moves 7 18 Direct labor hours per unit 145 145 Budgeted material-handling costs are $30,000. The material-handling cost per wall mirror under activity-based costing is:
The material-handling cost per wall mirror under activity-based costing is $280
What is activity-based costing?
Activity-based costing involves absorbing overheads based on cost drivers which directly impact the incurrence of the overhead, in this case, material moves determine the amount of material-handling costs to be incurred, hence, material-handing overheads would be absorbed into the two products based on material moves, which is the appropriate cost driver.
There 25 materials move in both divisions (i.e. 7+18=25)
Material-handling cost per material move=Budgeted material-handling costs /total material moves
Budgeted material-handling costs =$30,000
Material-handling cost per material move=$30,000/25
Material-handling cost per material move=$1,200
Total material-handing costs for wall mirror=number of material moves for wall mirror*Material-handling cost per material move
Total material-handing costs for wall mirror=7*$120
Total material-handing costs for wall mirror=$8,400
material-handling cost per wall mirror=Total material-handing costs for wall mirror/number of wall mirrors
material-handling cost per wall mirror=$8,400/30
material-handling cost per wall mirror=$280
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A company's sales equal $60,000 and cost of goods sold equals $20,000. Its beginning inventory was $1,600 and its ending inventory is $2,400. The company's inventory turnover ratio equals:
The company's inventory turnover ratio, based on the financial data, equals 10 times.
What is the inventory turnover ratio?The inventory turnover ratio measures the number of times the company sells and replaces its inventory over a given period.
The formula for calculating the Inventory Turnover Ratio is the Cost of Goods Sold divided by the Average Inventory.
The Average Inventory is the mean of the beginning and ending inventories.
Data and Calculations:Sales revenue = $60,000
Cost of goods sold = $20,000
Beginning inventory = $1,600
Ending inventory = $2,400
Average inventory = $2,000 ($1,600 + $2,400)/2
Inventory turnover ratio = 10x ($20,000/$2,000)
Thus, the company sells and replaces its inventory over a period of 10 times.
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Write expressions for the length and width of a rectangle that has an area equal to 3x2-5x+2.
Answer:
x - 2, x - 3
Step-by-step explanation:
3x² - 5x + 2
x² - 5x + 6
(x - 3)(x - 2)
length = x - 2
width = x - 3
find the square roots by division method of
210,681
Answer: square of 459 is 210681
Describe all x-values within a distance of 9 from the number 9
The value |x−9|≤9 is equivalent to [18,0] in interval notation.
According to the statement
We have given that the distance of 9 from the number 9. and we have to find the all value of x between it.
So, For find all x value we use absolute value inequalities.
distance of 9 from number 9.
So, when we draw the number line
we see that the number will become
The distance from x to 9 can be represented using an absolute value symbol, |x−9|.
Write the values of x that satisfy the condition as an absolute value inequality.
So, it become
|x−9|≤9
Now write two inequalities then it become
x−9≤9 and x−9≥−9
x≤18 and x≥0
So, The solution set is x≤18 and x≥0,
then the solution set is an interval including all real numbers between and including 18 and 0.
So |x−9|≤9 is equivalent to [18,0] in interval notation.
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Complete the statement below with the appropriate term. According to John Locke, is how we acquire basic knowledge. Choose the best answer.
Which of the following explains why, in many of the problems, historical data is used?
Information changes rapidly.
It is an opportunity to study history at the same time.
Better math problems can be made from historical data.
Up-to-date information is difficult to find.
According to John Locke, Experience is how we acquire basic knowledge.
What explains why, in many of the problems, historical data is used is; Information changes rapidly.
What is the theory of John Locke?1) John Locke's theory simply means that all knowledge comes exclusively through experience. He argues that at birth the mind is a tabula rasa, that humans fill with ideas as they experience the world through the five senses.
Thus, the missing word in the question is "Experience".
2) The reason why historical data is used in may problems is because Information changes rapidly. The information being circulated currently may be different from that circulated 100 years ago.
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Find the value of x.
The value of x from the given circle is 4
What is intersecting chord theorem?The intersecting chords theorem is a statement in geometry that describes a relation of the four line segments created by two intersecting chords within a circle.
It states that the products of the lengths of the line segments on each chord are equal.
According to the theorem;
x * 3 = 2 * (4 + 2)
3x = 2(6)
3x = 12
Divide both sides by 3
3x/3 = 12/3
x =4
Hence the value of x from the given circle is 4
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Name a pair of opposite rays on plane L.
Answer:
GC and GD
Step-by-step explanation:
The only points on plane L are: J, C, G, D
GC and GD
Solve by graphing. tan(30x - 90°) = -x³
The solution to the equation is 0.07, 0.17, 0.27, 0.38........
How to determine the solution to the trigonometry equation?The trigonometry equation is given as:
tan(30x - 90°) = -x³
We start by splitting the trigonometry equation as follows, by creating two different equations
y = tan(30x - 90°)
y = -x³
Next, we plot the graph of the trigonometry equations y = tan(30x - 90°) and y = -x³
From the graph of the trigonometry equations y = tan(30x - 90°) and y = -x³, we have the x coordinate of the point of intersection to be:
x = 0.07, 0.17, 0.27, 0.38........
Hence, the solution to the trigonometry equation is 0.07, 0.17, 0.27, 0.38........ .
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Find the magnitude of −1−5i
The magnitude of -1-5i is √26.
What is the magnitude of -1-5i ?
Given the complex expression; -1 - 5i
To find the magnitude, we use the formula;
| a+bi | = √[ a² + b² ]
a = -1b = -5| a+bi | = √[ a² + b² ]
| -1-5i | = √[ (-1)² + (-5)² ]
| -1-5i | = √[ 1 + 25 ]
| -1-5i | = √26
Therefore, the magnitude of -1-5i is √26.
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If BC= 48 cm and sin
Using relations in a right triangle, it is found that the length of AC is of 14 cm.
What are the relations in a right triangle?The relations in a right triangle are given as follows:
The sine of an angle is given by the length of the opposite side to the angle divided by the length of the hypotenuse.The cosine of an angle is given by the length of the adjacent side to the angle divided by the length of the hypotenuse.The tangent of an angle is given by the length of the opposite side to the angle divided by the length of the adjacent side to the angle.Researching this problem on the internet, we have that:
The opposite leg to angle A is of 48 cm.sin(A) = 0.96.Hence the hypotenuse is found as follows:
sin(A) = 48/h
0.96 = 48/h
h = 48/0.96
h = 50 cm.
The length of side AC is the other leg of the triangle, found using the Pythagorean Theorem, hence:
[tex]x^2 + 48^2 = 50^2[/tex]
[tex]x^2 = \sqrt{50^2 - 48^2}[/tex]
x = 14 cm.
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Add: 5/7 + 9/11 + 21/77
Answer:
Step-by-step explanation:
You want to begin by making each fraction have the same common denominator. The LCF (least common factor) is 77. So, knowing this, we can now multiply the fractions that need to have a denominator of 77.
1. 5/7*11/11=55/77
2. 9/11 * 7/7 =63/77
Now we can add
55/77 + 63/77 + 21/77 = 139/77 or 1.805194805
need this answered asap Which function has a minimum and is transformed to the right and down from the parent function, f(x) = x2? g(x) = –9(x + 1)2 – 7 g(x) = 4(x – 3)2 + 1 g(x) = –3(x – 4)2 – 6 g(x) = 8(x – 3)2 – 5
The function that has a minimum and is transformed to the right and down from the parent function is; g(x) = 8(x² - 3²) - 5
How to Interpret Functions?By inspection, only Functions B) and D) have a minimum.
For the first function in option B, we have:
g(x) = 4(x²- 6x + 9) + 1
This can be simplified to;
g(x) = 4( x - 3 )² + 1
Thus, we can say that this first function is transformed to the right and up from the parent function.
For the second function in option D, we have;
g(x) = 8(x² - 6x + 9 ) - 5
The function can be simplified to get;
g(x) = 8( x - 3 )² - 5
Thus, we can say that it is transformed to the right and down.
The function that has a minimum and is transformed to the right and down from the parent function is D
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Answer: option D
Step-by-step explanation:
Find the mean for the scores 3,820, 5,500, 8,560, 4,400, 5,350
Answer:
5,526
Step-by-step explanation:
Mean of scores = Total Value of Scores / Number of Values
= [tex]\frac{3820+5500+8560+4400+5350}{5} \\[/tex]
= 5,526
Answer:5526
Step-by-step explanation: Add everything up and divide by 5 because there are 5 numbers
PLEASE I NEED THIS FAST there are 3 denominations of bills in a wallet: $1, $5, and $10. there are 5 fewer $5-bills than $1-bills there are half as many $10-bills if there is $115 altogether, find the number of each type of bill in the wallet
The count of the denominations of the bills of $1, $5, and $10, are 15, 10, and 5, respectively.
In the question, we are given that there are 3 denominations of bills in a wallet: $1, $5, and $10. There are 5 fewer $5-bills than $1-bills. There are half as many $10-bills as $5-bills.
We are asked to find the count of each denomination, given there was altogether $115 in the bag.
We assume the number of $1-bills in the bag to be x.
Total amount in x bills of $1 = x * $1 = $x.
Given that there are 5 fewer $5-bills than $1-bills in the bag, number of $5-bills in the bag = x - 5.
Total amount in (x - 5) bills of $5 = (x - 5) * $5 = $5(x - 5).
Given that there are half as many $10-bills as $5-bills in the bag, number of $10-bills in the bag = (x - 5)/2.
Total amount in (x - 5)/2 bills of $10 = (x - 5)/2 * $10 = $5(x - 5).
Thus, the total amount in the bag = $x + $5(x - 5) + $5(x - 5).
But, the total amount in the bag = $115.
Thus, we get an equation:
$x + $5(x - 5) + $5(x - 5) = $115,
or, x + 5x - 25 + 5x - 25 = 115,
or, 11x = 115 + 50,
or, 11x = 165,
or, x = 165/11,
or, x = 15.
Thus, number of $1-bills = x = 15.
The number of $5-bills = x - 5 = 15 - 5 = 10.
The number of $10-bills = (x - 5)/2 = (15 - 5)/2 = 10/2 = 5.
Thus, the count of the denominations of the bills of $1, $5, and $10, are 15, 10, and 5, respectively.
The provided question is incomplete. The complete question is:
There are 3 denominations of bills in a wallet: $1, $5, and $10. There are 5 fewer $5-bills than $1-bills. There are half as many $10-bills as $5-bills. If there is $115 altogether, find the number of each type of bill in the wallet."
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Write an absolute value equation to satisfy the given solution set shown on a number line
(infinity -1/2]u [-1/2 -1/2] u [1/2 infinity)
Which statement is true?
1-31 = 3 and -1-4| = -4
1-31 = 3 and 1-4| = -4
-131 = 3 and 14| = 4
1-31 = 3 and -14| = 4
Answer:
|-3| = 3 and -|-4| = -4
Step-by-step explanation:
The absolute value function changes the sign to positive, if it isn't already. The usual rules of arithmetic and logic apply to these statements.
|-3| = 3 (true) and -|-4| = -4 (true) ⇒ this statement is true
|-3| = 3 (true) and |-4| = -4 (false) ⇒ this statement is false
-|3| = 3 (false) and |4| = 4 (true) ⇒ this statement is false
|-3| = 3 (true) and -|4| = 4 (false) ⇒ this statement is false
__
Additional comment
A compound "and" statement is only true if all of the parts of it are true.
What index of m will equal to 1/m^2 ?
Answer:
index of m is -2
Step-by-step explanation:
any number or letter to the negatIve power(index) is the same as 1 divided by that number or letter to the positive index.
for example, 10^-2 = 1/10^2 and X^-4 is the same as 1/X^4.
a tree 20 feet tall with a circumference of 3 ft has a vine wound around 7 times how long is the vine?
The length of the vine wounded to the tree is 21 feet.
How to solve circumference?Circumference is the perimeter of a circular object. Therefore,
circumference = 2πr
where
r = radiusThe circumference of the tree is 3 feet. A vine was wound around 7 times .
The length of the vine can be calculated as follows:
Therefore,
circumference = 3 ft
length of the vine = 7 × 3
length of the vine = 21 feet
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Please Help!!!
Type the correct answer in the box. Use numerals instead of words.
The surface area of a cone is square units. The height of the cone is times greater than the radius.
What is the length of the radius of the cone to the nearest foot?
The radius is about
feet.
Answer:
Step-by-step explanation:
9.05737
The length of the radius of the cone to the nearest foot is 5 feet.
What is a cone?A cone is a three-dimensional geometric shape with a smooth and curving surface and a flat base, with an increase in the height radius of a cone decreasing to a certain point.
The volume of a cone is (1/3)πr²h.
The total surface area of a cone is πr(r + l).
The curved surface area is πrl.
Given, The surface area of a cone is 216π sq units and the height of the cone is (5/3) times of the radius.
∴ h = (5/3)r and we know l = √(h² + r²) ⇒ l = √{(25/9)r² + r²} ⇒ l = √{(34/9)r²}.
∴ πrl = 216π.
√{(34/9)r³ = 216.
1.9r³ = 216.
r³ = 113.7.
r = 4.8 feet Or 5 feet.
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Ivanna knit a scarf for each of her 9 friends. Altogether, the scarves had a total length of 41.4 ft. If each scarf was the same length, how long was each scarf? Write your answer in inches. Use the table of conversion facts as necessary, and do not round your answer. Conversion facts for length 12 inches (in) = 1 foot (ft) 3 feet (ft) = 1 yard (yd) 36 inches (in) = 1 yard (yd) 5280 feet (ft) = 1 mile (mi) 1760 yards (yd) = 1 mile (mi)
Answer: 55.2 in
Step-by-step explanation:
1ft = 12 in
41.4/9 = 4.6 ft
4.6 x 12 = 55.2 in
will give brainliest
The sum of the two rational equations is equal to (3 · n² + 5 · n - 10) / (3 · n³ - 6 · n²).
How to simplify the addition between two rational equations
In this question we must use algebra definitions and theorems to simplify the addition of two rational equations into a single rational equation. Now we proceed to show the procedure of solution in detail:
(n + 5) / (n² + 3 · n - 10) + 5 / (3 · n²) Given(n + 5) / [(n + 5) · (n - 2)] + 5 / (3 · n²) x² - (r₁ + r₂) · x + r₁ · r₂ = (x - r₁) · (x - r₂)1 / (n - 2) + 5 / (3 · n²) Associative and modulative property / Existence of the multiplicative inverse[3 · n² + 5 · (n - 2)] / [3 · n² · (n - 2)] Addition of fractions with different denominator(3 · n² + 5 · n - 10) / (3 · n³ - 6 · n²) Distributive property / Power properties / ResultTo learn more on rational equations: https://brainly.com/question/20850120
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Heyy i just need some help with questions 5,7,9 if anyone could help me and show the work that would be amazing thank you!!
Step-by-step explanation:
5)f(g(8))
from the table g(8)=4
f(4) =4 from the table
7)g(f(5))
from the table f(5)=0
g(0)=9 from the table
9)f(f(4))
from the table f(4)=4
f(4)=4 from the table
If 2 angles have the same angle measure they are said to be what
2 angles that have the same angle measure are congruent.
Given that the two angles have the same angle measure.
Congruence is a term reserved for geometry. Two metrics are congruent when you can perfectly map to each other by mirroring, rotating, and translating without distortion.
We know that two shapes or objects are congruent if they have the same shape and the same size. For two angles to be congruent, they must coincide when they are overlapped. This is only possible if the two angles are equal.
Therefore, if two angles have the same measure, then they are said to be congruent.
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Cual es el valor de x+6=15
Answer: 9
Step-by-step explanation: it is what it is
15-6=9 omg i never knew
NEED HELP QUICKLY! 75 POINTS!!!!
Only 2 questions
1. Given the functions f(x) = log2(5x) and g(x) = [tex]5^{x}[/tex] – 2, which of the following statements is true?
a. Both f(x) and g(x) decrease on the interval of (–∞, 1).
b. Both f(x) and g(x) have the same domain of (0, ∞).
c. Both f(x) and g(x) have a common range on the interval (–2, ∞).
d. Both f(x) and g(x) have the same x-intercept of (1, 0).
2. What is the solution to 3y2 + 5y > –2?
a. x < –1 or x is greater than negative two thirds
b. x is greater than or equal to negative two thirds or x < 1
c. negative two thirds is less than or equal to x is less than or equal to 1
d. negative two thirds is greater than x is greater than negative 1
1. Given the functions f(x) = log₂(5x) and g(x) = 5ˣ - 2 only statement c is true
2. The solution of 3y² + 5y > -2 is a. x < –1 or x is greater than negative two thirds
1. How to find which statements are true.Statement a
Since f(x) = log₂(5x) which is a logarithm function is undefined for (-∞, 0) and defined for (0, +∞) and g(x) = 5ˣ - 2 which is an exponential function is defined for (-∞, +∞).
Also, since f(x) is decreasing on the interval (0, 1/5) while g(x) decreases on the interval (-∞, 0). So, they have do not have a common interval on (0, 1).
So, statement a. Both f(x) and g(x) decrease on the interval of (–∞, 1).
is false
Statement b
Since f(x) = log₂(5x) which is a logarithm function is defined for (0, +∞) and g(x) = 5ˣ - 2 which is an exponential function is defined for (-∞, +∞).
So, the statement b Both f(x) and g(x) have the same domain of (0, ∞) is false
Statement c
Since f(x) = log₂(5x) which is a logarithm function has a range of (0, +∞). and g(x) = 5ˣ - 2 which is an exponential function is has a range of (-2, +∞).
So, they have a common interval of (0, +∞).
So, the statement c. Both f(x) and g(x) have a common range on the interval (–2, ∞) is true
Statement d
To find the x-intercept of f(x), we equate f(x) to zero.
So, f(x) = log₂(5x)
0 = log₂(5x)
2⁰ = 5x
1 = 5x
x = 1/5
To find the x-intercept of g(x), we equate g(x) to zero.
g(x) = 5ˣ - 2
0 = 5ˣ - 2
2 = 5ˣ
x = ㏒₅2
Since the x-intercept of f(x) = 1/5 and the x- intercept of g(x) = ㏒₅2. So, they do not have a common x - intercept.
So, the statement d. Both f(x) and g(x) have the same x-intercept of (1, 0) is false.
So, only statement c is true
2. How to find the solution of 3y² + 5y > -2?3y² + 5y > -2
3y² + 5y + 2 > 0
3y² + 3y + 2y + 2 > 0
3y(y + 1) + 2(y + 1) > 0
(3y + 2)(y + 1) > 0
So, the boundary values are at
(3y + 2)(y + 1) = 0
(3y + 2) = 0 or (y + 1) = 0
y = -2/3 or y = -1
So, we require (3y + 2)(y + 1) > 0
For y < -1 say -2, (3y + 2)(y + 1) = (3(-2) + 2)((-2) + 1)
= (-6 + 2)(-2 + 1)
= -4(-1)
= 4 > 0
For -1 < y < -2/3 say -1/3, (3y + 2)(y + 1) = (3(-1/3) + 2)((-1/3) + 1)
= (-1 + 2)(-1 +3)/2
= 1(-2/2)
= -1 < 0
For y > -2/3 say 0, (3y + 2)(y + 1) = (3(0) + 2)((0) + 1)
= (0 + 2)(0 + 1)
= 2(1)
= 2 > 0
So, for (3y + 2)(y + 1) > 0, y < -1 or y > -2/3
So, the solution of 3y² + 5y > -2 is a. x < –1 or x is greater than negative two thirds
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Answer:
1. D. Both f(x) and g(x) have the same x-intercept of (1, 0).
2. A. x < –1 or x is greater than negative two thirds
Step-by-step explanation:
I took the exam
Item3 4.28 points eBookReferencesCheck my workCheck My Work button is now enabledItem 3 Yarra Fabrication estimates that its manufacturing overhead will be $2,342,400 in year 1. It further estimates that direct material costs will amount to $1,464,000. During July, Yarra worked on four jobs with actual direct materials costs of $76,000 for Job 0701, $104,000 for Job 0702, $135,000 for Job 0703, and $67,000 for Job 0704. Actual manufacturing overhead costs for the year were $2,480,000. Actual direct materials costs were $1,630,000. Manufacturing overhead is applied to jobs based on direct materials cost using predetermined rates. Required: a. How much overhead was applied to each of the four jobs, 0701, 0702, 0703, and 0704? b. What was the over- or underapplied manufacturing overhead for year 1?
First of all, we would calculate the predetermined overhead rate by using this formula:
Predetermined overhead rate = Manufacturing overhead/Direct material costs
Predetermined overhead rate = $2,342,400/$1,464,000
Predetermined overhead rate = 1.6 per DM $.
Next, we would calculate the overhead applied by using this formula:
Overhead applied = Job × DM cost
For job 0701, we have:
Overhead applied = 76,000 × 1.6
Overhead applied = $121,600.
For job 0702, we have:
Overhead applied = 104,000 × 1.6
Overhead applied = $166,400.
For job 0703, we have:
Overhead applied = 135,000 × 1.6
Overhead applied = $216,000.
For job 0704, we have:
Overhead applied = 67,000 × 1.6
Overhead applied = $107,200.
Part B.For the overapplied manufacturing overhead for year 1:
Less applied overhead = $1,630,000 × 1.6
Less applied overhead = $2,608,000.
Overapplied manufacturing overhead = Actual overhead cost - Less applied overhead
Overapplied manufacturing overhead = $2,480,000 - $2,608,000
Overapplied manufacturing overhead = $128,000.
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