Answers
BC = a
AC = b= 12√3
AB =c
A= 30°
B=60°
C=90°
Using the sine rule
[tex]\frac{\sin\text{ A}}{a}=\frac{\sin B}{b}[/tex]substitute the values into the above
[tex]\frac{\sin30}{a}=\frac{\sin 60}{12\sqrt[]{3}}[/tex][tex]\frac{\frac{1}{2}}{a}=\frac{\frac{\sqrt[]{3}}{2}}{12\sqrt[]{3}}[/tex][tex]\frac{1}{2\times a}=\frac{\sqrt[]{3}}{2\times12\sqrt[]{3}}[/tex][tex]\frac{1}{2a}=\frac{\sqrt[]{3}}{24\sqrt[]{3}}[/tex][tex]\frac{1}{2a}=\frac{1}{24}[/tex]cross multiply
[tex]2a=\text{ 24}[/tex][tex]a=12[/tex]Therefore BC = 12
Let's proceed to find AB
[tex]\frac{\sin A}{a}=\frac{\sin C}{c}[/tex][tex]\frac{\sin30}{12}=\frac{\sin 90}{c}[/tex][tex]\frac{\frac{1}{2}}{12}=\frac{1}{c}[/tex][tex]\frac{1}{2\times12}=\frac{1}{c}[/tex][tex]\frac{1}{24}=\frac{1}{c}[/tex]cross-multiply
[tex]c=24[/tex]
Related Questions
Question 2 Find the area of the figure below. Ty below. 24 yd 24 yd 24 yd 40 yd
Answers
Answer:
1536 yd²
Explanation:
To find the area of the figure, we need to divide the figure into 2 rectangles as:
So, the area of the first rectangle is equal to:
[tex]\begin{gathered} \text{Area = Base x Height } \\ \text{Area = 24 yd x 24 yd} \\ \text{Area = 576 yd}^2 \end{gathered}[/tex]In the same way, the area of the second rectangle is:
[tex]\begin{gathered} \text{Area = Base x Height } \\ \text{Area = 40 yd }\times24\text{ yd} \\ \text{Area = 960 yd}^2 \end{gathered}[/tex]So, the area of the figure is:
576 yd² + 960 yd² = 1536 yd²
Therefore, the answer is 1536 yd²
Seventh grade M.12 Simple interest E7Y Trisha has $74,430 in a savings account that earns 10% interest per year. The interest is not compounded. How much interest will she earn in 1 year? Use the formula i = prt, where i is the interest earned, p is the principal (starting amount), r is the interest rate expressed as a decimal, and t is the time in years. $ Submit
Answers
Given:
The initial balance = P = $74,430
Interest rate per year = r = 10% = 0.1
The interest is not compounded, so it is a simple interset
Time = t = 1 year
So,
[tex]I=P\cdot r\cdot t=74430\cdot0.1\cdot1=7443[/tex]So, the answer is I = $7,443
Consider the following set of equations:Equation M: 3y = 3x + 6Equation P: y = x + 2Which of the following best describes the solution to the given set of equations? No solutionOne solutionTwo solutionsInfinite solutions
Answers
Solution
Given
Equation M: 3y = 3x + 6
Equation P: y = x + 2
Plot the graph of the two equation
The graph of the two equations are the same. With the same slope and intercept
The graph is shown below
Conclusion:
Because the graph of the equatons are thesame, the system of equations have Infinite solutions
The answer is Infinite solutions
A town's population is 52,525. About 75 people move out of the town each month. Each month, 200 people on average move into town. A nearby town has a population of 56,375. It has no one moving in and an average of 150 people moving away every month. In about how many months will the populations of the towns be equal? Write an equation to model the situation Then solve the equation and answer the question.
Answers
The required equation to model the given situation is 52,525 - 75x +200x = 56,375 - 150x. the value of x = 14; the populations will be equal in 14 months.
Let x represents the number of months, the first town's population rise is 75x and its drop is 200x. The population of the second town has decreased by 150x.
We want to find m such that the increases and decreases equalize the populations of the towns. In each case, we add the increases and subtract the decreases from the base population.
As per the given situation, the required equation would be as:
52,525 - 75x +200x = 56,375 - 150x
Rearrange the terms likewise and apply the arithmetic operation,
150x + 200x - 75x = 56,375 - 52,525
275x = 3850
x = 3850 / 275
x = 14
Thus, the required equation to model the given situation is 52,525 - 75x +200x = 56,375 - 150x. the value of x = 14; the populations will be equal in 14 months.
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Hello, the three problems below is what I need help with.Use the given functions solve:f(x)= 6x+7. g(x)= -2x-4. h(x)= -3x/4Answer:1. f(x-2)2. g(7x+1)3. h(-12)
Answers
Explanation
you have to replace the values in each function
Step 1
[tex]\begin{gathered} f(x)=6x+7 \\ f(x-2)=6(x-2)+7=6x-12+7=6x-5 \\ f(x-2)==6x-5 \\ \end{gathered}[/tex]Step 2
[tex]\begin{gathered} g(x)=-2x-4 \\ g(7x+1)=-2(7x+1)-4 \\ g(7x+1)=-14x-2-4 \\ g(7x+1)=-14x-6 \end{gathered}[/tex]Step 3
[tex]\begin{gathered} h(x)=\frac{-3x}{4} \\ h(-12)=\frac{-3\cdot-12}{4} \\ h(-12)=\frac{36}{4} \\ \\ h(-12)=9 \end{gathered}[/tex]I hope this helps you
To the nearest centimeter, find the surface area of a hemisphere with 15 inch diameter
Answers
Given:
The diameter of the hemisphere is 15 inches.
To find:
The surface area of a hemisphere.
Explanation:
The radius of the hemisphere is
[tex]r=\frac{15}{2}inches[/tex]Using the formula of the surface area of a hemisphere,
[tex]\begin{gathered} S.A=2\pi r^2 \\ =2\times3.14\times(\frac{15}{2})^2 \\ =353.25 \\ \approx353square\text{ }inches \end{gathered}[/tex]Final answer:
The surface area of the hemisphere is 353 square inches.
Would love for an expert to verify my solutions:High school trig.
Answers
The entered responses are correct
Explanation:Write out the points from the given information to see the nature of the ellipse as follows:
[tex]\begin{gathered} x=4\cos\frac{\pi}{2}=0 \\ \\ y=3\sin\frac{\pi}{2}=3 \\ \\ (x,y)=(0,3) \end{gathered}[/tex][tex]\begin{gathered} x=4\cos\pi=-4 \\ \\ y=3\sin\pi=0 \\ \\ (x,y)=(-4,0) \end{gathered}[/tex][tex]\begin{gathered} x=4\cos\frac{3\pi}{2}=0 \\ \\ y=3\sin\frac{3\pi}{2}=-1 \\ \\ (x,y)=(0,-1) \end{gathered}[/tex]1. The average number of students per classroom at Central High School from 2000 to 2010 can be modeled by the equation y = 0.56x + 27.2, where x represents the number of years since 2000, and y represents the average number of students per classroom. Which of the following best describes the meaning of the number 0.56 in the equation? A) The total number of students at the school in 2000.B) The average number of students per classroom in 2000.C) The estimated increase in the average number of students per classroom each year.D) The estimated difference between the average number of students per classroom in 2010 and in 2000.
Answers
Given the equation:
y = 0.56x + 27.2
The equation above represents the average number of students per classroom at a Central High school from 2000 to 2010.
Where,
x represents the number of years since year 2000
y represents the average number of students per classroom
Also, 27.2 represents the number of students at the school in 2000.
Since the equation is in slope intercept form: y = mx + b, where m is the slope.
This means that 0.56 represents the slope and slope can be simply defined as the average rate of change.
Therefore, the statement that best describes the number 0.56 in the equation is the estimated increase in the average number of students per classroom each year.
ANSWER:
C) The estimated increase in the average number of students per classroom each year.
for a function f(x)=x^2, write an equation for that function stretched vertically by a factor of 4, and shifted 2 units to the right
Answers
the initial function is:
[tex]f(x)=x^2[/tex]to stretch the fuction vertically we have to divide by 4 y so:
[tex]\begin{gathered} \frac{f(x)}{4}=x^2 \\ f(x)=4x^2 \end{gathered}[/tex]now to move two units to the right we have to rest 2 in the x so:
[tex]f(x)=4(x-2)^2[/tex]Find the value of x.
Answers
Answer:
this is very simple
Step-by-step explanation:
the answer of this question is x=12 only
The United States Postal Service delivers about 2⁴ * 3 * 5³ pieces of mail each second. There are 2⁸ x 3⁴ x 5² seconds in 6 days. How many pieces of mail does the United States Postal Service deliver in 6 days write your answer as an expression involving three powers.
Answers
To get to the answer, we'll have to multiply the pieces of mail delivered each second by the amount of seconds in 6 days. This is,
[tex]\begin{gathered} (2^4\times3\times5^3)\times(2^8\times3^4\times5^2)^{} \\ \rightarrow2^4\times3\times5^3\times2^8\times3^4\times5^2^{} \end{gathered}[/tex]Using power properties,
[tex]2^4\times3\times5^3\times2^8\times3^4\times5^2\rightarrow2^{12}\times3^5\times5^5[/tex]Therefore,
[tex]2^{12}\times3^5\times5^5[/tex]pieces of mail are delivered by the United States Postal Service in 6 days.
48 feet wide . the sides of the roof meet to form a right angle and both sides of the roof are the same length. find the length of the roof rafters find x
Answers
Given the image in the question, it can be seen that the roof forms a right angled triangle. Therefore, we can get the length of the roof rafters (x) by using the Pythagoras theorem.
Step 1: We define the Pythagoras theorem and state our parameters
[tex]\begin{gathered} \text{hypotenuse}^2=opposite^2+adjacent^2 \\ \text{hypotenuse}=48ft,\text{ adjacent=opposite=}xft \end{gathered}[/tex]Step 2: We substitute the values into the theorem to solve for x
[tex]\begin{gathered} 48^2=x^2+x^2 \\ 2x^2=2304 \\ x^2=\frac{2304}{2} \\ x^2=1152 \\ x=\sqrt[2]{1152} \\ x=33.9411255 \\ x\approx33.94ft \end{gathered}[/tex]Hence, the length of the roof rafters (x) is 33.94ft to the nearest hundredth.
find all real zeros of the function g(x)=-4(x-1)2(x+7)3
Answers
Answer:
1 or -7
Step-by-step explanation:
i hope this is what you were looking for
Can you help me with this assignment
Answers
since the line that is wanted is parallel to the one given means that it has the same slope as this one.
1. write the line given in the slope-intercept form
[tex]\begin{gathered} 6x-5y=15 \\ -5y=15-6x \\ 5y=6x-15 \\ y=\frac{6}{5}x-3 \end{gathered}[/tex]2. after having the slope find the y-intercept using the point given (5,4)
[tex]\begin{gathered} y=\frac{6}{5}x+b \\ 4=\frac{6}{5}\cdot(5)+b \\ 4=6+b \\ 4-6=b \\ -2=b \end{gathered}[/tex]3. rewrite the equation
[tex]y=\frac{6}{5}x-2[/tex]Consider the following compound inequality. 2x+3_<5 or 4x+1>17A)Solve the inequality for x.B) Graph the compound inequality. C) Enter the solution in interval notation.
Answers
step 1
Solve the first inequality
[tex]2x+3\leq5[/tex][tex]\begin{gathered} 2x\leq5-3 \\ 2x\leq2 \\ x\leq1 \end{gathered}[/tex]the solution for the first inequality is the interval (-infinite,1]
step 2
Solve the second inequality
4x+1>17
4x>16
x>4
the solution for the second inequality is the interval (4, infinite)
therefore
the solution of the compound inequality is
(-infinite,1] U (4, infinite)
In a number line, the solution is
At x=1 is a closed circle and at x=4 is an open circle
About what is the average change in distance for each increase of 1 in the iron number? What does this mean in terms of the situation?
Answers
The graph is given with the x-axis iron and y-axis distance in yards.
ExplanationTo determine the average change in distance for each increase of 1 in the iron number
The coordinates from the graph is
[tex](3,155),(4,145)[/tex]The average rate of change is determined as
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Substitute the values.
[tex]\begin{gathered} m=\frac{155-145}{3-4} \\ m=\frac{10}{-1}=-10 \end{gathered}[/tex]AnswerHence the average change in distance for each increase of 1 in the iron number is -10.
The situation represents that the distance decrease by 10 yards for each number of iron.
Please explain why the lowest value is at four why it’s not at six?
Answers
Solution
- The lowest value of the sinusoidal function is usually gotten using the formula:
[tex]\begin{gathered} L=M-A \\ where, \\ M=\text{ The value of the midline} \\ A=\text{ The Amplitude or highest value} \end{gathered}[/tex]- The question says that the sea falls 6ft below sea level and rises 6ft above sea level.
- The midline M represents the sea level and the rise of 6ft represents the amplitude.
- Thus, the above equation can be rewritten as:
[tex]L=M-6[/tex]- The formula for finding the peak of the sinusoidal is:
[tex]\begin{gathered} U=M+A \\ where, \\ U=\text{ The Peak or height of the water} \end{gathered}[/tex]- We can similarly rewrite the equation as:
[tex]U=M+6[/tex]- We have been given the peak height of the water to be 16. Thus, U = 16. Thus, we can find the midline (M) as follows:
[tex]\begin{gathered} U=M+6 \\ put\text{ }U=16 \\ 16=M+6 \\ \text{ Subtract 6 from both sides} \\ M=16-6=10 \end{gathered}[/tex]- Thus, the midline (M) is at 10ft. This also implies that the sea level is at 10 ft.
- Thus, we can find the lowest value or low line as follows:
[tex]\begin{gathered} L=M-6 \\ \text{ We know that }M=10 \\ \\ \therefore L=10-6=4ft \end{gathered}[/tex]Final Answer
The lowest value or Low line is at 4ft
2 + aIf f(a) =5for what value of a does f(a) = fo?
Answers
Answer
Option A is correct.
The value of a for which f(a) is (1/10) is
a = -(3/2)
Step-by-step Explanation
f(a) is given as
[tex]f(a)=\frac{2+a}{5}[/tex]We are then told to find the value of a for which f(a) = (1/10)
Recall that
f(a) = (2 + a)/5
So, we just equate this definition of the function to (1/10)
[tex]\begin{gathered} f(a)=\frac{2+a}{5}=\frac{1}{10} \\ \frac{2+a}{5}=\frac{1}{10} \\ \text{Cross multiply} \\ 10\times(2+a)=1\times5 \end{gathered}[/tex]10(2 + a) = 5
20 + 10a = 5
Subtract 20 from both sides
20 + 10a - 20 = 5 - 20
10a = -15
Divide both sides by 10
(10a/10) = (-15/10)
a = -1.5 = -(3/2)
Option A is correct.
Hope this Helps!!!
Choose the expression that is equivalent to 9w² +3/5(20w² - 15w+10)+2w
Answers
The correct answer or equivalent expression is 21w² - 7w + 6.
What is the equivalent of an expression?X-terms and constants should be combined with any other like and similar terms on either side of the equation. By putting the terms in the same order, with the x-term usually comes before the constants. The two phrases or equation are equal if and only if each of their terms is the same.
It is given in the question that 9w² +[tex]\frac{3}{5}[/tex](20w² - 15w+10)+2w
⇒ 9w² + [tex]\frac{3}{5}[/tex] (20w² - 15w+10)+ 2w
⇒ 9w² + [tex]\frac{3}{5}[/tex] × 5 (4w² - 3w+2) + 2w
⇒ 9w² + 3(4w² - 3w+2) + 2w
⇒ 9w² + 12w² - 9w + 6 + 2w
⇒ 21w² - 7w + 6
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A boat is heading towards a lighthouse, whose beacon-light is 135 feet above the water. The boat's crew measures the angle of elevation to the beacon, 4 deg What is the ship's horizontal distance from the lighthouse (and the shore)? Round your answer to the nearest hundredth of a foot if necessary .
Answers
The ship's horizontal distance from the lighthouse is: 1930.59 feet.
What is tangent or tan in trigonometry?
The ratio of the side opposite the angle we know or want to know over the side next to that angle is known as the tangent, which is sometimes abbreviated as T-A-N. The side touching the angle that is NOT the hypotenuse, or the side opposite the right angle, is the neighboring side.
Given in the question,
Height of lighthouse = 135 feet,
angle of elevation = 4 degree,
We know that, tan Θ = perpendicular/ base
Here, height is perpendicular and distance is base,
Putting the values,
tan4° = 135/B
B = 1930.59 feet
Therefore, distance is 1930.59 feet.
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Answer:The answer is 1930.59
Step-by-step explanation:
Amelia had a total of 1,260 marbles and table tennis balls. She had 40 fewer marbles than table tennis balls.How many table tennis balls did she have?
Answers
Let 'x' represent number of marbles
Let 'y' represent number of table tennis balls
Amelia had a total of 1,260 marbles and table tennis balls,
The mathematical representation is,
[tex]x+y=1260\ldots\ldots\text{.}.1[/tex]She had 40 fewer marbles than table tennis balls.
The mathematical representation is,
[tex]x=y-40\ldots\ldots\ldots2[/tex]Substitute x = y - 40 from equation 2 into equation 1 to solve for y
[tex]\begin{gathered} y-40+y=1260 \\ y+y=1260+40 \\ 2y=1300 \\ \frac{2y}{2}=\frac{1300}{2} \\ y=650\text{ table tennis balls} \end{gathered}[/tex]Hence, she has 650 marbles.
How do you quickly find and graph functions for: f(x)=300-25x
Answers
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data:
f(x) = 300 - 25x
Step 02:
graph function:
You only need 2 points to graph a line:
point 1:
x = 0:
y = 300 - 25x
y = 300 - 25(0)
y = 300
( 0 , 300)
point 2:
y = 0:
y = 300 - 25x
0 = 300 - 25x
25x = 300
x = 300 / 25
x = 12
( 12 , 0)
Graph:
That is the full solution.
Which of the following ordered pairs is a solution to the equation 2x+4y=16? Select all that apply.Select all that apply:(11,−10)(−12,10)(4,2)(6,1)(−8,−6)
Answers
Answer:
[tex]\begin{gathered} (x,y)\Rightarrow(-12,10) \\ (x,y)\Rightarrow(4,2) \\ (x,y)\Rightarrow(6,1) \end{gathered}[/tex]Explanation: The plot of this equation along with ordered pairs is:
Therefore the answer is:
[tex]\begin{gathered} (x,y)\Rightarrow(-12,10) \\ (x,y)\Rightarrow(4,2) \\ (x,y)\Rightarrow(6,1) \end{gathered}[/tex]- 23 = -9+7(v - 3)could I please get some help
Answers
we have
- 23 = -9+7(v - 3)
apply distributive property right side
-23=-9+7v-21
combine like terms
-23=7v-30
Adds 30 both sides
-23+30=7v-30+30
7=7v
Divide by 7 both sides
7/7=7v/7
1=v
v=1Walter went to Japan for a business trip. Walter converted $ 900 US into 80,514 Yen at the local bank. Walter spent 53,944 Yen on this trip and returned with the remaining Yen to the US.Find the remaining amountRound answer to the nearest whole dollar.
Answers
$297
Explanation:Amount taken for the trip = $900 US
Converting to Yen, amount = 80,514 Yen
Amount spent = 53,944 Yen
Amount remaining + Amount spent = Total amount for the trip
Amount remaining + 53944 = 80514
Amount remaining = 80514 - 53944
Amount remaining = 26570 Yen
We need to convert back to US dollars:
if 80,514 Yen = $900 US
let 26570 Yen = y
Cross multiply:
[tex]\begin{gathered} y(80514\text{ Yen) = \$900 (}26570\text{Yen)} \\ y\text{ = }\frac{\text{ \$}900\text{ }\times\text{ }26570}{80514} \end{gathered}[/tex][tex]y\text{ = \$297.00}[/tex]The remaining amount aftert the trip is $297 (nearest whole dollar)
-3x+5y=-8 solve for x and y
Answers
ANSWER
The set of equations has no solution
EXPLANATION
-3x + 5y = -8 ------ equation 1
6x - 10y = 16 -------- equation 2
These two equations can be solve simultaneously either by substitution method or elimination method
To solve for the value of x and y, we will be using the elimination method
-3x + 5y = -8
6x - 10y = 16
Let us eliminate x first.
We need to make the coefficient of x in both equation equal
Hence, multiply equation 1 by 2 and equation 2 by 1
-3x*2 + 5y*2 = -8 x 2
6x * 1 - 10y * 1 = 16 x 1
-6x + 10y = -16 ------------ equation 3
6x - 10y = 16 -------------- equation 4
To eliminate x , add equation 3 and 4 together
-6x + 6x + 10y + (-10y) = -16 + 16
-6x + 6x + 10y - 10y = -16 + 16
0 + 0 = 0
0 = 0
Hence, the set of equations has no solution
A truck is carrying grapefruit juice, tomato juice, and pineapple juice bottles in a ratio of 1:4:3 if there are 76 tomato juice bottles, then how many juice bottles in total are there?
Answers
Answer: Total number of juice bottles is 152
The truck is carrying grapefruit juice, tomato juice, and pineapple juice bottles in a ratio of 1 : 4: 3
There are 76 tomato juice bottle
Let the number of grapefruit bottle = x
Let the number of pineapple juice bottle = y
1: 4 : 3 = x : 76: y
To find the number of juice bottles, we will need to establish a proportion
[tex]\begin{gathered} 1\text{ : 4 = x : 76} \\ \frac{1}{4}\text{ = }\frac{x}{76} \\ \text{Introduce cross multiply} \\ 1\cdot\text{ 76 = 4 }\cdot\text{ x} \\ 76\text{ = 4x} \\ \text{Divide both sides by 4} \\ \frac{76}{4}\text{ = }\frac{4x}{4} \\ x\text{ = }\frac{76}{4} \\ x\text{ = 19} \end{gathered}[/tex]To calculate for y, we will still need to establish a proportion
[tex]\begin{gathered} 4\text{ : 3 = 76 : y} \\ \frac{4}{3}\text{ = }\frac{76}{y} \\ \text{Introduce cross multiply} \\ 4\cdot\text{ y = 76 x 3} \\ 4y\text{ = 228} \\ \text{Divide both sides by 4} \\ \frac{4y}{4}\text{ = }\frac{228}{4} \\ y\text{ = }\frac{228}{4} \\ y\text{ = 57} \end{gathered}[/tex]Since, x is the number of grapefruit bottles, then the number of grapefruit bottles in the truck is 19 bottles
Since, y is the number of pineapple bottles, therefore, the number of pineapple bottle is 57 bottles
Total number of juice bottles in the lorry = 19 + 76 + 57
The total number = 152 juice bottles
The bookstore is selling 4 books for $10 in a clearance sale. If Regina has $28 to spend, how many books can she purchase in the clearance sale?
Answers
The bookstore is selling 4 books for $10 in a clearance sale. If Regina has $28 to spend, how many books can she purchase in the clearance sale?
In this problem
Applying proportion
we have
4/10=x/28
solve for x
x=(4/10)*28
x=11.2
therefore
answer is 11 booksSolve for b.
42 = 42 +9b
Answers
Answer:
b=0
Step-by-step explanation:
42=42+9b
We move all terms to the left:
42-(42+9b)=0
We add all the numbers together, and all the variables
-(9b+42)+42=0
We get rid of parentheses
-9b-42+42=0
We add all the numbers together, and all the variables
-9b=0
b=0/-9
b=0
Answer:
b = 0
Step-by-step explanation:
42 - 42 = 42 + 9b - 42
0 = 9b
9b = 0
9b/9 = 0/9
b = 0
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Sheridan Company purchased a truck for $79,000. The company expected
the truck to last four years or 120,000 miles, with an estimated residual
value of $12,000 at the end of that time. During the second year the truck
was driven 45,000 miles. Compute the depreciation for the second year
under each of the methods below and place your answers in the blanks
provided.
Units-of-activity
Double-declining-balance
Answers
The depreciation in year 2 using the units of activity method is $23,125.
The depreciation in year 2 using the double declining balance is $19,750.
What is the depreciation in year 2?
Depreciation is when the value of an asset declines as a result of wear and tear.
Deprecation in year 2 using the units of activity method = (miles driven in year 2 / total miles) x (cost of the asset - salvage value)
Deprecation = (45,000 / 120,000) x ($79,000 - $12,000)
Deprecation = $23,125
Deprecation using the double declining method = (2/ useful life) x cost of the asset
Depreciation in year 1 = (2/4) x 79,000 = $39,500
Book value in year 2 = 79,000 - $39,500 = $39,500
Depreciation in year 2 = (2/4) x $39,500 = $19,750
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