Regard y as the independent variable and x as the dependent variable and use implicit differentiation to find dx/dy. x3y2 − x4y + 4xy3 = 0
Through applying the techniques of implicit differentiation to the equation x³y² - x⁴y + 4xy³ = 0, the derivative dx/dy is found to be [x⁴ - 4y³ - 2x³y]/[3x²y² - 4x³y].
Explanation:The subject of your question is implicit differentiation in calculus, a branch of mathematics. You wish to know how to differentiate the equation
x³y² - x⁴y + 4xy³ = 0
with respect to y (y is independent and x is dependent).
The initial step in implicit differentiation is to derive every term of an equation. So, we end up with:
3x²y²(dx/dy) + 2x³y(dy/dx) - 4x³y(dx/dy) - x⁴ + 4y³ + 12x²y² = 0.
After grouping like terms together, the equation become:
dx/dy[3x²y² - 4x³y] = x⁴ - 2x³y - 4y³
Eventually, divide both sides by [3x²y² - 4x³y] to isolate dx/dy and get the final answer:
dx/dy = [x⁴ - 4y³ - 2x³y]/[3x²y² - 4x³y]
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A loan of $12,500 at 9% is to be repaid with n level payments. if in = 128.04, what is the value of n?
present value of annuity = annual payment * [ 1 - (1+i)^-n ]/i
=>
12500 = 128.04 * [1-(1+9%/12^-n]/9%/12
=>n = 42 payments
Present value of annuity formula yields approximately 42 payments for $12,500, with $128.04 monthly payments at 9% interest.
Let's break it down:
[tex]\[PV = Pmt \times \left[1 - \frac{{(1 + i)^{-n}}}{i}\right]\][/tex]
Where:
[tex]- \(PV\) is the present value of the annuity.\\- \(Pmt\) is the amount of each payment in the annuity.\\- \(i\) is the interest rate per period, expressed as a decimal.\\- \(n\) is the total number of payments.[/tex]
Given your values:
- [tex]\(PV\)[/tex] is $12,500.
- [tex]\(Pmt\)[/tex] is $128.04.
- [tex]\(i\)[/tex] is the monthly interest rate, which is [tex]\(9\% / 12 = 0.09 / 12\)[/tex] since the annual rate is divided by 12 for monthly payments.
- [tex]\(n\)[/tex] is what we're solving for.
Substituting these values into the formula, we have:
[tex]\[12,500 = 128.04 \times \left[1 - \frac{{(1 + 0.09/12)^{-n}}}{0.09/12}\right]\][/tex]
Now let's solve for [tex]\(n\):[/tex]
[tex]\[12,500 = 128.04 \times \left[1 - \frac{{(1 + 0.0075)^{-n}}}{0.0075}\right]\]\[1 - \frac{{(1 + 0.0075)^{-n}}}{0.0075} = \frac{{12,500}}{{128.04}}\]\[\frac{{(1 + 0.0075)^{-n}}}{0.0075} = 1 - \frac{{12,500}}{{128.04}}\]\[ (1 + 0.0075)^{-n} = 0.0075 \times \left(1 - \frac{{12,500}}{{128.04}}\right)\]\[ (1 + 0.0075)^{-n} = 0.0075 \times \left(1 - \frac{{12,500}}{{128.04}}\right)\]\[ (1 + 0.0075)^{-n} = 0.9920\]Taking the natural logarithm of both sides:\[ -n \ln(1 + 0.0075) = \ln(0.9920)\][/tex]
Using a calculator:
n ≈ [tex]\frac{{-0.008025}}{{-0.007472}}\][/tex]
n ≈ [tex]41.961\][/tex]
So, rounding up, we get , n ≈ 42
Therefore, it would take approximately 42 payments to reach a present value of $12,500 given the annuity with an annual interest rate of 9% compounded monthly and a payment of $128.04 per month.
Alyssa is building a brick mailbox. She is going to stack bricks that are each \dfrac23 \text{ft}
3
2
ftstart fraction, 2, divided by, 3, end fraction, f, t tall, and the finished stack of bricks needs to be 4\dfrac23 \text{ft}4
3
2
ft4, start fraction, 2, divided by, 3, end fraction, f, t tall.
How many bricks will go in the stack?
An observer (O) spots a plane flying at a 35° angle to his horizontal line of sight. If the plane is flying at an altitude of 17,000 ft., what is the distance (x) from the plane (P) to the observer (O)?
20,757 feet
24,251 feet
29,639 feet
31,262 feet
Answer:
here are numerous information's already given in the question. Based on those information's, the answer to the question can be easily deduced.
Angle at which the plane is flying in respect to the observer = 35 degree
Altitude at which the plane is flying = 17000 feet
The distance at which the plane is flying from the observer = x
Then
x = 17000/sin 35
= 17000/0.57357
= 29638.93 feet
= 29639 feet
From the above deduction, we can conclude that the correct option among all the options given in the question is the third option.
GIVE BRainliest plz
The distance between the plane and the observer is 29,638 feet.
Data;
Angle = 35 degreesheight of the plane = 17,000ftdistance from the plane to the observer = xTrigonometric RatioThis is the use of SOHCAHTOA which is the relationship between sides of a right angle triangle and it's angle.
In this case, we have the value of opposite and angle and we need to find the hypothenuse.
Using sine of the angle,
[tex]sin\theta = \frac{opposite}{hypothenuse} \\sin 35 = \frac{17000}{x}\\ x = \frac{17000}{sin35}\\ x = 29,638 feet[/tex]
The distance between the plane and the observer is 29,638 feet.
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Of five letters (a, b, c, d, and e), two letters are to be selected at random without replacement. how many possible selections are there
Item 2
Find −1 1/5+(−3/5). Write your answer as a fraction in simplest form.
A carpenter worked 34 hours a week for half a year. If her hourly wage was $20, how much did she earn during this time period?
The square root of 150 is between
A.10 and 11
B.11 and 12
C.12 and 13
D.13 and 14
if the raidus of mars(3,397 km) is about 13.7% of of neptunes radius, what is the radius of neptune?
indicate the number of significant figures in 3x 10^6
What will be the result of this formula =if(a1<100000,a1*5%,a1*7.5%) , if the cell a1 has a value of 90000?
At what projection angle will the range of a projectile equal to 6 times its maximum height?
When a number decreased by 10% the result in 63. What is the number?
Final answer:
To find the number when decreased by 10%, set up an equation and solve for the number.
Explanation:
When a number decreased by 10% the result in 63. What is the number?
Let the number be x.
Equation: x - 0.10x = 63
Solve for x: 0.90x = 63 => x = 63 / 0.90 = 70
Sara drives 117 miles on 5.2 gallons of gas. She uses this information to calculate how many miles per gallon she can drive. Using this result, how many miles can Sara drive on 12 gallons of gas?
a. 187.5
b. 1.875 c. 270 d. 27Final answer:
To find the number of miles Sara can drive on 12 gallons of gas, divide the total miles she drove by the total gallons of gas she used. Multiply this fuel efficiency by the number of gallons to get the result. (Option C)
Explanation:
To calculate the number of miles Sara can drive on 12 gallons of gas, we need to first find her fuel efficiency in terms of miles per gallon. To do this, we divide the total miles she drove (117 miles) by the total gallons of gas she used (5.2 gallons).
117 miles / 5.2 gallons = 22.5 miles per gallon
Next, we can use this fuel efficiency to calculate the number of miles Sara can drive on 12 gallons of gas. We multiply her fuel efficiency (22.5 miles per gallon) by the number of gallons (12 gallons).
22.5 miles per gallon * 12 gallons = 270 miles
Therefore, Sara can drive 270 miles on 12 gallons of gas.
25°C is what in Fahrenheit?
multiply Celsius by 9/5 then add 32 to get Fahrenheit
25 * 9/5 = 45
45 +32 = 77 degrees Fahrenheit
There are three highways in the county. the number of daily accidents that occur on these highways are poisson random variables with respective parameters .3, .5, and .7. find the expected number of accidents that will happen on any of these highways today.
Final answer:
To find the expected number of accidents on three highways with Poisson distributions, sum the individual expectations: 0.3, 0.5, and 0.7, resulting in an expected 1.5 accidents per day.
Explanation:
The student asked how to find the expected number of accidents that will happen on any of the three highways in a day, given that the number of daily accidents on these highways are Poisson random variables with parameters 0.3, 0.5, and 0.7 respectively. To solve this, we shall sum the parameters of the Poisson distributions because the expectation of the sum of independent random variables is the sum of their expectations.
Therefore, we calculate the expected number of accidents as follows:
For the first highway with parameter 0.3, the expected number of accidents is 0.3.
For the second highway with parameter 0.5, the expected number of accidents is 0.5.
For the third highway with parameter 0.7, the expected number of accidents is 0.7.
Adding these together, we get:
Expected number = 0.3 + 0.5 + 0.7 = 1.5 accidents per day.
The table shows the mass and density of some substances. Density of Substances Mass (g) Density of Iron (g/cm3) Density of Silver (g/cm3) 100 7.8 Q 200 P 19.3 Part 1: Is the value of Q less than, greater than, or equal to the value of P? Part 2: Explain your answer for Part 1.
Answer:
Step-by-step explanation:
greder
Part 1: Q is less than P.
Part 2: The density of silver (Q) is higher than that of iron (P), indicating that silver has a greater mass per unit volume, making P greater than Q.
Part 1: The value of Q is less than the value of P.
Part 2: This conclusion can be drawn by comparing the densities of the two substances, iron, and silver. Density is calculated by dividing mass by volume (D = m/V), and since the mass of iron (100g) is equal to the mass of silver (100g), we can simplify the comparison by focusing on their densities.
The density of iron (7.8 g/cm^3) is significantly less than the density of silver (19.3 g/cm^3). Density is a measure of how much mass is packed into a given volume, so the higher the density, the more mass is concentrated in a smaller space. In this case, silver is much denser than iron, which means that for an equal mass, silver occupies a smaller volume compared to iron.
Since Q represents the density of silver and P represents the density of iron, and the density of silver (Q) is greater than the density of iron (P), we can conclude that Q is indeed less than P. The higher density of silver implies that it has a greater mass concentrated in the same volume. The value of Q is less than the value of p.
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Explain why the hypotenuses of the triangles below have the same slope.
A pooled proportion is calculated by giving each sample proportion an equal weight.
a. True
b. False
Which multiplication property is shown in the equation 3.1x(2x9)=(3.1x2)x9
The given equation, 3.1x(2x9)=(3.1x2)x9, demonstrates the Associative Property of Multiplication. The property means that the way numbers are grouped in multiplication does not change the result.
Explanation:The multiplication property shown in the equation 3.1x(2x9)=(3.1x2)x9 is referred to as the Associative Property of Multiplication. This property states that when three or more numbers are multiplied, the product does not depend on how the numbers are grouped. Therefore, (a x b) x c equals a x (b x c).
In the given equation, we can see this property applied. 3.1x(2x9) can be rearranged as (3.1x2)x9 and the results of both expressions will be the same. This demonstrates that the grouping does not affect the result of the multiplication.
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What is the effect of decreasing the alpha level (for example, from a = .05 to a = .01)? it decreases the probability of a type i error. it decreases the size of the critical region. it decreases the probability that the sample will fall into the critical region. all of the other options are results of decreasing alpha?
If an original conditional statement is represented by p → q, which represents the contrapositive?
~q → ~p that's the answer
Three years ago, Ava lent her sister $400 to buy some clothes. Today Ava’s sister paid her loan in full with $454. What simple annual interest rate did she pay?
The 2015 senior class from puma high school raised funds for an end of the year party at club sizzle. It costs $4,000 to rent out club sizzle plus $20 per student for food and drinks. If the senior class raised 11,000, how many students can attend the end of year party ? Write an equation for the situation and solve.
Which of the articles represent a proper fraction? A. 15/22 B. 8/8 C. 3/2 D. 12/9
Find the mean median mode and range of this date 49,49,54,55,52,49,55, if necessary round to the nearest tenth
Geometry Help!!
For triangle TRI the following facts are given:
Segment AN || Segment RI
AT = 8cm
AR = 2cm
TN = 12cm
(a) use a two-column or paragraph format to prove triangle TAN ~ triangle TRI
(b) use the side splitting theorem to find NI.
At 1 P.M., ship A is 150 km west of ship B. Ship A is sailing east at 35 km/h and ship B is sailing north at 25 km/h. How fast is the distance between the ships changing at 5 P.M.?
The reason that ship A is moving -35km/h is because ship B acts as an "origin" and as things move closer to the "origin" they become negative and as things move away from the "origin" they become positive.
We know that the rate of Ship A is expressed as dAdt=−35 and the rate of Ship B is expressed as dBdt=25
Step 2: We want to figure out how many km Ship A and Ship B traveled in 4 hours
ShipA:−35kmh⋅4hr=−140km
Now if we take this −140km and add it to the 150km we can see that Ship A is now only 10km away from where Ship B began
ShipB:25kmh⋅4hr=100km
This means that Ship B is now 100km from where it originally started
We can now redraw our information
Step 3: We must use the Pythagorean Theorem to find the third side of the triangle
x2+y2=z2→102+1002=z2
z=√102+1002
Step 4: Now that we know z, we must differentiate the original equation in order to find the rate at which z in changing
x2+y2=z2→2xdxdt+2ydydt=2zdzdt
We can simplify by canceling out the 2's
xdxdt+ydydt=zdzdt
Step 5: Write down all the information and then plug into equation
x=10anddxdt=−35
y=100anddydt=25
z=√102+1002anddzdt=?
Now plug in the information
xdxdt+ydydt=zdzdt
10(−35)+100(25)=√102+1002dzdt
−350+2500=√102+1002dzdt
2150=√102+1002dzdt
21.393=dzdt
The distance between the ships are increasing at a rate of 21.393 km/h
A customer has six (6) $1 bills, three (3) $5 bills, four (4) $10 bills, seven (7) quarters, ten (10) dimes, seven (7) nickels, and nine (9) pennies. The customer buys a pair of shoes for $49.86. Based on the combination of bills and coins the customer has, what are the least number of bills and coins the customer can give the cashier in order to buy the shoes for the exact amount and not require any change back?
Using the quadratic formula to solve 2x2 = 4x – 7, what are the values of x
Answer:
C. 2+_ square root 10i / 2
Step-by-step explanation: