Answers
Answer:
[tex]\dfrac{dy}{dx}=-y\left(4+\dfrac{1}{x}\right)[/tex]
or written in rational form:
[tex]\dfrac{dy}{dx}=\dfrac{-4xy-y}{x}[/tex]
Step-by-step explanation:
[tex]\ln(xy)+4x=45[/tex]
[tex]\textsf{Apply the product log law}\quad\ln(ab)=\ln(a)+\ln(b):[/tex]
[tex]\implies \ln(x)+\ln(y)+4x=45[/tex]
[tex]\textsf{Add}\:\dfrac{d}{dx}\:\textsf{in front of each term}:[/tex]
[tex]\implies \dfrac{d}{dx}\ln(x)+\dfrac{d}{dx}\ln(y)+\dfrac{d}{dx}4x=\dfrac{d}{dx}45[/tex]
[tex]\textsf{Differentiate the}\: x \: \textsf{terms and constant terms first}:[/tex]
[tex]\implies \dfrac{1}{x}+\dfrac{d}{dx}\ln(y)+4=0[/tex]
[tex]\textsf{When differentiating with respect to}\:y,\: \textsf{differentiate and add}\: \dfrac{dy}{dx}:[/tex]
[tex]\implies \dfrac{1}{x}+\dfrac{1}{y}\dfrac{dy}{dx}+4=0[/tex]
[tex]\textsf{Rearrange to make}\:\dfrac{dy}{dx}\:\textsf{the subject}:[/tex]
[tex]\implies \dfrac{1}{y}\dfrac{dy}{dx}=-4-\dfrac{1}{x}[/tex]
[tex]\implies \dfrac{dy}{dx}=y\left(-4-\dfrac{1}{x}\right)[/tex]
[tex]\implies \dfrac{dy}{dx}=-y\left(4+\dfrac{1}{x}\right)[/tex]
If you want it in rational form, then:
[tex]\implies \dfrac{dy}{dx}=-4y-\dfrac{y}{x}[/tex]
[tex]\implies \dfrac{dy}{dx}=\dfrac{-4xy-y}{x}[/tex]
[tex]~~~~~\ln(xy) +4x = 45\\\\\\\implies \dfrac{d}{dx} \left[\ln(xy) +4x \right] = \dfrac{d}{dx} ( 45)\\\\\\\implies \dfrac{1}{xy} \cdot \dfrac{d}{dx} (xy) + 4 = 0\\\\\\\implies \dfrac 1{xy} \left( x\dfrac{dy}{dx} + y \right) +4 =0\\\\\\\implies x\dfrac{dy}{dx} + y + 4xy=0\\\\\\\implies x \dfrac{dy}{dx} =-y-4xy\\\\\\\implies \dfrac{dy}{dx} = \dfrac{-y-4xy}x[/tex]
Related Questions
Faleye Consulting is deciding which of two computer systems to purchase. It can purchase state-of-the-art equipment (System A) for an after-tax cost of $19,000, which will generate after-tax cash flows of $6,000 at the end of each of the next 6 years. Alternatively, the company can purchase equipment with an after-tax cost of $13,000 that can be used for 3 years and will generate after-tax cash flows of $6,000 at the end of each year (System B). If the company’s WACC is 10% and both “projects” can be repeated indefinitely, which system should be chosen, and what is its EAA? Do not round intermediate calculations. Round your answer to the nearest cent.
Choose Project
-Select-
, whose EAA = $
Answers
If Faleye Consulting’s WACC is 10% and both “projects” can be repeated indefinitely, the system that should be chosen is System A, and its EAA is $2,866.91.
What is the EAA of a project?The EAA of a project is the Equivalent Annual Annuity. The EAA can be determined using the following formula.
EAA = r x NPV1 - (1 + r)-n
Where the EAA = Equivalent Annual Annuity
r = interest rate per period
n = project duration
NPV = Net present value of project
We can also compute the EAA by using an online finance calculator as follows:
Data and Calculations:System A System B
After-tax cost $19,000 $13,000
After-tax cash flows $6,000 $6,000
Equipment duration 6 years 3 years
WACC = 10%
Annuity factor 4.355 2.487
Present value of cash flows $26,130 $14,922 ($6,000 x 2.487)
NPV $7,130 $1,922 ($14,922 - $13,000)
EAA (an online calculator) $2,866.91 $800.966
Thus, using the EAA rule, the computer system that should be chosen is System A because it has a higher EAA than System B.
Learn more about the equivalent annual annuity at https://brainly.com/question/20566589
CAN SOMEONE FIND X pls
Answers
Answer:
Step-by-step explanation:
22x - 13 = 20x + 1
2x - 13 = 1
2x = 14
x = 7
Pls help WILL GIVE BRAINLIST
A person looking out a window, 40 feet above street level can sight the top and
bottom of the building. The angle of elevation to the top of the building is 61 degrees and the angle
f depression to the bottom of the building is 37 degrees. How tall is the building that the person is looking at
Answers
Answer:
135.94 feet
Step-by-step explanation:
Split the problem into two parts :
Distance between viewer and buildingHeight of the top part of the buildingDistance between viewer and building
The lower part of the building is 40 feet, as it is mentioned the viewer is 40 feet above street levelLet the distance be called 'd'Therefore, tan37° = 40/dtan37° = 3/4 = 0.75⇒ 40/d = 0.75⇒ d = 40/(3/4) = 40 x 4/3 = 160/3 = 53.3 feetHeight of the top part of the building
Let the height of the top part be 'h'Therefore, tan61° = h/d = h/53.3tan61° = 1.8⇒ h/53.3 = 1.8⇒ h = 53.3 x 1.8 = 95.94 feetTotal height of building
Lower part + Top part40 + 95.94135.94 feetI NEED HELP PLEASE MATH
MATH MATH
Answers
Answer:
write a number for t and f
Step-by-step explanation:
Answer:
Cant See
Step-by-step explanation:
Please take a clearer version of this image.
What is the equation of the line that is parallel to the graph of y = 2x - 5 and passes through the point (4,2)?
Answers
Answer:
[tex]y=2x-6[/tex]
Step-by-step explanation:
A line parallel to another will have the same gradientSo the equation will be [tex]y=2x+c[/tex]We need to find out what c is, so substitute in the values for x and y[tex]2=2\times 4 + c[/tex][tex]2=8+c[/tex][tex]c=2-8=-6[/tex]So your equation is [tex]y=2x-6[/tex]!Answer:
2x-6
Step-by-step explanation:
Have a good day!
Dan and George share 18
is in the ratio 1:2
How many bananas does Dan get?
Answers
Dan gets 6 bananas and George gets 12 bananas
hope it helps...!!!
Find X exactly. Answer should be in a square root.
Answers
Answer:
7 in <==== no sqrt in the answer
Step-by-step explanation:
x = 7 sqrt 2 * cos 45
= 7 sqrt 2 * sqrt 2 /2
= 7 (2)/2 = 7
5. The ratio of the number of John's stamps to the number of Peter's stamps is 5:8. Peter has 18 more stamps than John. If Peter gives 22 stamps to John, what will be the new ratio of the number of John's stamps to Peter's?
Answers
Answer:
2:1
Step-by-step explanation:
J:P = 5:8
30:48
48-30= 18
48-22= 26
30+22= 52
new ratio
52:26
2:1
How many different ways can someone arrange the all letter in AMERICA to make a world
Answers
Answer:
2520 different ways
$3.00 with the
same number of nickels and dimes
Answers
Answer:
15 each i think
Step-by-step explanation:
Help me with this math question please
Answers
Answer:
60 small and 140 large = 60 + 280 = 340 this is correct!
Step-by-step explanation:
I guess we just use the process of eleimation.
50 small and 150 Large = 50+300 = 350 so that's not right.
130 small and 70 large = 130 + 140 = 270 so, that's not right.
120 small and 80 large = 120 + 160 = 280 so, that's not right.
60 small and 140 large = 60 + 280 = 340 this is correct!
solve this question.....
Answers
Answer:
22.5 km
Step-by-step explanation:
Since 1 cm on the map is 250000 cm in real life :
We can convert 250000 cm to km :
First we convert to m :
250000 ÷ 100 = 2500 m
Now we convert m into km :
2500 ÷ 1000 = 2.5 km
Now we multiply 2.5 km by 9 cm to get :
2.5 × 9 = 22.5 km
Therefore the 2 villages are 22.5 km apart.
Hope this helped and brainliest please.Answer:
2.25 million km
Step-by-step explanation:
Step 1. Write ratio with "x"
Step 2. Create a proportion
Step 3. Cross multiply
Step 4. Solve for "x"
1 : 250,000
9 cm : x km
1/250,000 = 9/x
x = (9)(250,000)
x = 2.25 million km
BRAINLIEST please if this helped!What is the formula for the Pythagorean theorem?
Answers
Answer:
a^2 + b^2 = c^2
Step-by-step explanation:
a^2 + b^2 = c^2
Answer:
[tex]\Longrightarrow: \boxed{\sf{A^2+B^2=C^2}}[/tex]
Step-by-step explanation:
In the Pythagorean theorem, the formula is:
[tex]\underline{\text{PYTHAGOREAN THEOREM FORMULA:}}}[/tex]
[tex]\Longrightarrow: \sf{A^2+B^2=C^2}[/tex]
Thus, the Pythagorean theorem's formula is "a²+b²=c²".
I hope this helps. Let me know if you have any questions.
2. You want to buy some beans. A
7-ounce package costs $2.38. A
15-ounce package costs $5.25. A
26-ounce package costs $8.58. Which
package is the best buy?
Answers
Answer:
Step-by-step explanation:
Remark
If you find out the cost of 1 oz of each of them, that will determine the best buy. The smallest number is the best buy.
Givens
7 oz cost $2.38
15 oz cost $5.25
26 oz cost $8.58
Solution
7 oz7 oz cost $2.38
1 oz cost x This is a proportion. 3 quatities are known. Find x Cross multiply.
7/1 = 2.38/x
7x = 2.38
x = $0.34 dollars
15 oz15 oz cost 5.25
1 oz costs x
15.1/1 = 5,25 x Cross Multiply
15x = 5.25 * 1 Divide by 15
x = 5.25 / 15
x = $0.35
26 oz26 oz cost 8.58
1 oz cost x
26/1 = 8.38/x Cross Multiply
26x = 8.38 Divide by 26
x = 8.38/20
x = 0.32 dollars
Answer
7 oz cost 0.34
15 oz cost 0.35
26 oz cost 0.32
The best buy is 0.32 / oz for 26 ozF is the velocity field of a fluid flowing through a region in space. Find the flow along the given curve in the direction of increasing t. F = (z-x)i + xk r(t) = (sin t)i + (Cost) k, 0 <= t <= 2π
Answers
Answer: 177.65
Step-by-step explanation:
its the only accurate answer.........
Log20x=3 need the answer for algebra 2
Answers
Answer:
x = 50
Step-by-step explanation:
Consider the following y-intercept and slope:
(0,−5)m=5
Step 1 of 2 :
Find the equation of the line for the y-intercept and slope given above.
Answers
Answer:
y = 5x - 5
Step-by-step explanation:
Paul wants to order flowers for Mother’s Day and can choose any number of roses and lilies for his mother’s flower arrangement. He has a maximum of $50 to spend. Each stem of lilies costs $3.00, and roses cost $3.50 each. Which inequality represents the situation? Let the number of lilies = x and the number of roses = y.
A. 3.50x - 3y ≥ 50
B. 3x + 3.50y ≤ 50
C. 3x + 50y < 50
D. 3x - 3.50y > 50
Answers
Answer:
b
Step-by-step explanation:
it has to add the two cost of the flowers and it has to be less than or equal to 50 dollars
Find the missing dimension of the triangle.
1.5 in. base
Area = 2 in. squared
h = ? in.
Answers
Answer:
Fraction form:
h = 4/1.5 in
Decimal form:
2.667 in
Step-by-step explanation:
I've attached my work
The formula use is usually use to find the area of a triangle but allowed us to work backward after inputing given values
Hope it helps, Let me know if yoy have any more questions/concerns !
Have a nice rest of your day :)
The measures of the angles between the resultant and two applied forces are 26° and
20°, and the magnitude of the resultant is 80 pounds. Find the magnitude of the
larger force, to the nearest 10th of a pound.
Answers
Answer:
48.8 lbs
Step-by-step explanation:
The forces can be modeled by a triangle with acute angles 20° and 26°, and obtuse angle 134° opposite a side of length 80. The larger component force will be opposite the angle 26°, and can be found using the Law of Sines:
a/sin(A) = c/sin(C)
x/sin(26°) = 80/sin(134°)
x = 80sin(26°)/sin(134°) ≈ 48.753 . . . . pounds
The larger component force is about 48.8 pounds.
HELPPP
Carmen is going to build some large wooden storage boxes. The boxes are shaped like rectangular prisms, as shown below. She wants to cover all the sides of
each box with special wallpaper. If she has a total of 1498 ft? of wallpaper, how many boxes can she cover?
Answers
Answer:
7 boxes
Step-by-step explanation:
The area of a rectangular prism is given by the formula ...
A = 2(LW +H(L+W))
The amount of wallpaper Carmen needs for one box is found by computing the area of the box.
__
One boxA = 2(5·6 +7(5+6)) = 2(30 +7·11) = 2(107) = 214 . . . square feet
All boxesCarmen will be using a total of 214x square feet of wallpaper to cover x boxes. She has 1498 ft² available, so can cover ...
1498 ft²/(214 ft²/box) = 7 boxes
Carmen has enough wallpaper to cover 7 storage boxes.
I don't know the answer marked stylish random
Answers
Answer:
A
Step-by-step explanation: i am in math 8
lol
Please help!! I will give brainiest
Answers
Answer:
1) 13.9
2) 96. 0
3) 667.2
Step-by-step explanation:
Edge
Hope this helps!!
The height of a projectile that is thrown upward from ground level with an initial velocity of 98 meters per second can be modeled by the equation h = −4.9t2 + 98t, where h is the height in meters and t is the elapsed time in seconds. Find the time it takes for the projectile to hit the ground.
10 seconds
20 seconds
15 seconds
5 seconds
Answers
It is found that the time it takes for the projectile to hit the ground would be after 20 seconds.
When does the projectile hit the ground?The projectile would hit the ground when its height h(t), is equal to zero.
The given function that models its height is given by:
[tex]h(t) = -4.9t^2 + 98t.[/tex]
where h is the height in meters and t is the elapsed time in seconds.
Then,
h(t) = 0
[tex]-4.9t^2 + 98t = 0\\-4.9t(t - 20) = 0\\\\t - 20 = 0[/tex]
t = 20
Thus, The projectile hits the ground after 20 seconds.
Learn more about projectile here;
https://brainly.com/question/11422992
#SPJ1
What will happen to the measures of central tendency if the outlier is removed
Answers
Bill has a farm where he raises pigs and cows. The ratio of cows to total animals on a farm is 5 to 12.
Which number below could be the number of pigs on the farm?
A. 6
B. 20
C. 21
D. 24
Answers
Maya mailed 3 packages. their weights were 4.5 lbs,2.75 lbs,and 3.4 lbs.
what was the total weight of the 3 packages.
question 2 is explain how u found the answer to the first question (only answer if you know the answer)
Answers
Explanation: Since there is only one number in the hundredth place, i didn’t need to add. Instead i put that number as my hundredth place AKA 5. then i added the tenth place which was 5+7+4 which = 16. i carried the one over. then i added the ones place. 4+2+3= 9. the one i carried over got added to the 9. therefore my final answer was 10.65
If (-1, y) lies on the graph of y = 2^2x, then y =
04
1/4
01
Answers
Answer:
y = 1/4
Step-by-step explanation:
substitute the given value of x = -1 into the equation.
y^2^2 (^-1) =2^-2 = 1/2^2 = 1/4
Which shows how to solve the equation 3/4x -6 for x in one step
Answers
Answer:
A
Step-by-step explanation:
You can multiply both sides on an equation by the reciprocal to cancel the fraction on the first side.
7) Find x- intercepts
Answers
Answer:
See below:
Step-by-step explanation:
At x axis intercepts, the value of y = 0
0 = -3/5 ( x+7)^2 + 6
-6(-5/3) = (x+7)^2
10 = (x+7)^2
x = -7 +- sqrt (10)
Answer:
[tex] x = -7 \pm \sqrt{10 [/tex]
Step-by-step explanation:
The x-intercepts occur where y = 0.
-3/5(x + 7)² + 6 = 0
-3(x + 7)² + 30 = 0
-3(x² + 14x + 49) + 30 = 0
-3x² - 42x - 147 + 30 = 0
3x² + 42x + 117 = 0
[tex] x = \dfrac{-42 \pm \sqrt{42^2 - 4(3)(117)}}{2(3)} [/tex]
[tex] x = \dfrac{-42 \pm \sqrt{360}}{6} [/tex]
[tex] x = \dfrac{-42 \pm 6\sqrt{10}}{6} [/tex]
[tex] x = -7 \pm \sqrt{10 [/tex]