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 sample is selected from a population with m = 50 and s = 12. if the sample mean of m = 56 produces a z-score of z = +1.00, then how many scores are in the sample? 2 4 9 16
Final answer:
The number of scores in the sample is 4.
Explanation:
The question provided asks us to determine the number of scores in the sample based on the z-score of +1.00, given a population with a mean (μ) of 50 and a standard deviation (σ) of 12.
The z-score formula for a sample is
z = (M - μ) / (σ / √n),
where
M is the sample mean, μ is the population mean, and σ is the population standard deviation, n representing the sample size.We are given that M = 56, z = 1, μ = 50, and σ = 12.
To find the sample size (n), we use the formula and rearrange to solve for n:
z = (M - μ) / (σ / √n)1 = (56 - 50) / (12 / √n)1 = 6 / (12 / √n)√n = 12 / 6n = (2)^2n = 4Therefore, the number of scores in the sample is 4.
indicate the number of significant figures in 3x 10^6
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?
[tex] \sqrt{26x+13} = x+7[/tex]
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
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
Explain why the hypotenuses of the triangles below have the same slope.
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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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.
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.
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 are the next three numbers in this pattern? 729, 243, 81, 27, __, __, __
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?
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:
In Jim's class, 5 times as many kids take the bus as thos who walk. A total of 24 kids walk or take the bus. How many more kids take the bus than walk?
Which point does NOT lie on the graph of the line -2x + 5y = 20?
A. (-10, 0)
B. (0, 4)
C. (1, 4)
D. (5, 6)
Your Bank account balance was $235 and 24. After two checks were cashed (each for the same amount) your balance is now -45.58. What was the amount of each of those checks?
235.24 + 45.58 = 280.82
280.82/2 = 140.41
each check was 140.41
A rectangular room is twice as long as it is wide, and its perimeter is 36 meters. Find the width of the room.
The width of the rectangular room is 6 meters.
What is a rectangle?A rectangle is one of the types of quadrilaterals in which all four angles are right angles or equal to 90 degrees. It is four-sided polygon in which the opposite sides are parallel and equal to each other.
For the given situation,
Let the width of the rectangular room, w = x
A rectangular room is twice as long as it is wide,
length of the rectangular room, l = 2x
The perimeter of the rectangle = 36 meters.
The formula of perimeter of rectangle is
[tex]P=2(w+l)[/tex]
⇒ [tex]36=2(x+2x)[/tex]
⇒ [tex]36=2(3x)[/tex]
⇒ [tex]x=\frac{36}{6}[/tex]
⇒ [tex]x=6[/tex]
Hence we can conclude that the width of the rectangular room is 6 meters.
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Which of the articles represent a proper fraction? A. 15/22 B. 8/8 C. 3/2 D. 12/9
The divison of the whole bumber N by 13 gives a quotient of 15 and a remainder of 12. Find N
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?
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.
The standard form of the equation of a circle with center (h, k) and radius r is __________________.
Answer:
The center is at (4, -6), and the length of the radius is 5.
Step-by-step explanation:
(x − 4)2 + (y + 6)2 = 25
(x − 4)2 + (y − (-6))2 = 52
When I compare my equation with the standard form, (x − h)2 + (y − k)2 = r2, I get h = 4, k = -6, and r = 5. The center is at (4, -6), and the length of the radius is 5.
plato answer
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
A regular polygon has possible angles of rotational symmetry of 20°, 40°, and 80°. How many sides does the polygon have? 10 12 18 20
Answer:
18
Step-by-step explanation:
Edge 2021 (^Just to back up the answer above, so nobody feels doubts^.)
We have that the sides of the polygon is mathematically given as
n=20
Option C
From the question we are told
A regular polygon has possible angles of rotational symmetry of 20°, 40°, and 80°.
How many sides does the polygon have? 10 12 18 20
ArithmeticGenerally the equation for the Polygon exterior angle is mathematically given as
[tex]\theta=\frac{360}{n}\\\\18=\frac{390}{18}[/tex]
n=20
OptionC
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Carlos bought a new Mastercraft boat for $17,000. He made a $2,500 down payment on it. The bank's loan was for 60 months, and the finance charges totaled $4,900. What's his monthly payment?
A. $323.33
B. $232.33
C. $313.33
D. $332.33
Answer:
Carlos bought a new Mastercraft boat for $17,000. He made a $2,500 down payment on it. The bank's loan was for 60 months, and the finance charges totaled $4,900. What's his monthly payment?
A. $323.33
B. $232.33
C. $313.33
D. $332.33
Step-by-step explanation:
1.- Carlos paid $ 2,500 of the $ 17,000 that Mastercraft costs and would be equal to: $ 17,000 - $ 2,500 = $ 14,500
2.- We have financial charges amounting to $ 4,900 to be added to the previous amount, and would be equal to: $ 14,500 + $ 4,900 = $ 19,400
3.- The bank loan is for 60 months, which would result in: $ 19,400 / 60 = $ 323.33
The answer is: A. $ 323.33
If an original conditional statement is represented by p → q, which represents the contrapositive?
~q → ~p that's the answer
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