Find dy/dx by implicit differentiation. xy + x = 2 Select one: Оа. 1+ y V х O b. 1 + x y O C. 1 + V X O d. 1+x V

The calculated value of the side length in the triangle is 144

From the question, we have the following parameters that can be used in our computation:

The simiar triangles

Using the theorem of corresponding sides, we hav

GH = 2JK

So, we have

10x - 36 = 2 * 4x

Multiply

So, we have

10x - 36 = 8x

Evaluate

2x = 36

So, we have

x = 18

This means that

GK = 4 * 18

GK = 144

Hence, the indicated side length in the triangle is 144

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Answer: 43 g

Step-by-step explanation: For 215 to be divided equally between five people the equation should be set up as 215/5, which equals 43 g for each person.

Answer:

Step-by-step explanation: (a) To expand (1 + e^x) + (e^3x) in ascending powers of x to the term x^2, we can use the Taylor series expansion.

The Taylor series expansion for e^x is given by:

e^x = 1 + x + x^2/2! + x^3/3! + ...

So,

e^x = 1 + x + x^2/2! + x^3/3! + ...

and

e^3x = 1 + 3x + 9x^2/2! + 27x^3/3! + ...

Now, we can substitute these expansions into the original equation to get:

(1 + e^x) + (e^3x) = 1 + (1 + x + x^2/2! + x^3/3! + ...) + (1 + 3x + 9x^2/2! + 27x^3/3! + ...)

Expanding, we get:

(1 + e^x) + (e^3x) = 2 + x + 4x + x^2/2! + 9x^2/2! + ...

So, to the term x^2, the expansion becomes:

(1 + e^x) + (e^3x) = 2 + x + 4x + (x^2/2! + 9x^2/2!) + ...

which simplifies to:

(1 + e^x) + (e^3x) = 2 + x + 4x + 11x^2/2! + ...

(b) The coefficient of x^2 in the expansion is 11/2!. So, n = 11/2! = 11/2.

Answer:

The correct answer is table A on edg 2021

Hope this helps! :D

Answer:

A on edg 2021

Answer:

14.3 sq units

Step-by-step explanation:

this shape is a trapezoid so we need to find height and each parallel base

to find height we can take the midpoint of RS and the midpoint of QP and then find the distance between each midpoint

midpoint of RS = (-3/2,2)

midpoint of QP = (2,-5/2)

distance between the two is 16/2 or 8

d(RS) = √2²+3² = \(\sqrt{13}\)

d(QP) = √3²+6² = √45 = \(\sqrt{9}\)\(\sqrt{5}\) or 3\(\sqrt{5}\)

put values into the formula for area:

A = 1/2(8) + (\(\sqrt{13}\) + 3\(\sqrt{5}\))

A = 4 + (\(\sqrt{13}\) + 3\(\sqrt{5}\))

A ≈ 14.3

The least possible value of "b" is 3. Hence, when "a = 2" and "b = 3," we satisfy all the given conditions. Thus, the least possible value of "b" is 3.

Let's analyze the given information:

The integer "a" has 3 factors: 1, "a," and one other factor.

The integer "b" has "a" factors.

"b" is divisible by "a."

From these conditions, we can deduce that "a" must be a prime number. This is because a prime number only has two factors: 1 and itself.

Therefore, "a" must be the smallest prime number, which is 2. So, "a = 2."

Now, we need to find the least possible value of "b" given that "b" has 2 factors.

Since "b" has 2 factors, it can only be a prime number. The smallest prime number greater than 2 is 3.

Therefore, the least possible value of "b" is 3.

Hence, when "a = 2" and "b = 3," we satisfy all the given conditions. Thus, the least possible value of "b" is 3.

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Answer:

There is no slope because the line has a constant y-value

Step-by-step explanation:

The equation represents the total cost of turkey and amount is y= 3.25x.

We have,

The turkey costs $3. 25 per pound.

let x be the amount in pounds and y be the total cost in dollar.

Then, the relation between x and y

Total cost = 3.25 (amount in  poind)

y = 3.25 x

Thus, the required equation is y= 3.25x.

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Answer:

A = $1034

Step-by-step explanation:

The relevant Amount function is A = P(1 + r/n)^(n*t), where r is the annual interest rate as a decimal fraction, n is the number of compounding periods per year, and t is the number of years.

There are 52 weeks in a year.  Hence, n = 52, and 25 weeks = 25/52 year, or 0.481 year.  

The accumulation (value of the savings) would be

A = ($1000)(1 + 0.07/52)^(52*[25/52]), or approximately

A = ($1000)(1.0013)^25, or approximately A = $1034

Answer: 17.82

Step-by-step explanation:

1.15 x 15.50 = 17.825

17.825 rounded to the nearest hundreth is 17.82

To maximize profits, the firm should produce a quantity of goods x = 5 and y = 10, based on the cost function and price constraints.

To maximize profits, the firm needs to find the quantities of goods x and y that will yield the highest profit. The profit function can be defined as the revenue minus the cost. Revenue is calculated by multiplying the quantity of each good produced with their respective prices, while the cost function is given as C(x, y) = 10x + xy + 10y.

The firm is committed to delivering a total of 15 units, which can be expressed as x + y = 15. To determine the optimal production quantities, we need to maximize the profit function subject to this constraint.

By substituting the price expressions Ps = 50 - x + y and Py = 50 - x + y into the profit function, we obtain the profit equation. To find the maximum profit, we can take the partial derivatives of the profit equation with respect to x and y, set them equal to zero, and solve the resulting system of equations.

Solving the equations, we find that the optimal production quantities are x = 5 and y = 10, which maximize the firm's profits.

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Step-by-step explanation:

\(2p + 2p + 2p + 60 = 360 \\ 6p = 360 - 60 \\ 6p = 300 \\ p = \frac{300}{6} \\ p = 50\)

If she follows the path shown by the dotted line in the graph, the distance from her house to the store would be = 128m. That is option B.

To calculate the distance between her house and the store the Pythagorean formula should be used which is given as follows;

C² = a² + b²

where;

a= 80

b= 100

c= ?

That is;

c²= 80²+100²

= 6400+10000

= 16,400

c = √16400

= 128.1m

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Answer:

>

Step-by-step explanation:

The bars around the numbers symbolize absolute value. The absolute value of a number is its distance from 0. Since distance is always positive the absolute value is that number but positive. In this case, 7 is greater than 2. So, the answer is 7>2.

Look up "Everything You Need To Know About (Your Subject) In One Big Fat Notebook pdf." It's the best thing I've ever been given, I have it with me in my class all the time and I've aced every test. I have it with me right now and it has everything I've ever been taught in it so it might help you.

The simplified expression without absolute value signs is x - 2.

To simplify the expression |x - 2| when x > 2, we can use the fact that if x is greater than 2, then x - 2 will be positive. In this case, |x - 2| simplifies to just x - 2.

This simplification is based on the understanding that the absolute value function, denoted by | |, returns the positive value of a number. When x > 2, x - 2 will be positive, and the absolute value function is not needed to determine its value. In this case, the expression simplifies to x - 2.

However, it's important to note that when x ≤ 2, the expression |x - 2| would simplify differently. When x is less than or equal to 2, x - 2 would be negative or zero, and |x - 2| would simplify to -(x - 2) or 2 - x, respectively.

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The invertible elements in Z10 are {1, 3, 7, 9} and the zero divisors in Z10 are {2, 4, 5, 6, 8, 9}.

1. For the invertible elements and zero divisors in Zn (the integers modulo n), we need to analyze each element and determine if it satisfies the given conditions.

For n = 10, Z10 consists of the elements {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}.

Invertible elements in Z10:

An element a is invertible in Z10 if there exists an element b in Z10 such that (a * b) ≡ 1 (mod 10). In other words, a has a multiplicative inverse.

By checking the multiplication tables for Z10:

1 * 1 ≡ 1 (mod 10) --> Invertible

3 * 7 ≡ 1 (mod 10) --> Invertible

7 * 3 ≡ 1 (mod 10) --> Invertible

9 * 9 ≡ 1 (mod 10) --> Invertible

Therefore, the invertible elements in Z10 are {1, 3, 7, 9}.

Zero divisors in Z10:

An element a is a zero divisor in Z10 if there exists an element b ≠ 0 in Z10 such that (a * b) ≡ 0 (mod 10). In other words, a multiplied by b gives a multiple of 10.

By checking the multiplication tables for Z10, we can identify the zero divisors:

2 * 5 ≡ 0 (mod 10) --> Zero divisor

4 * 5 ≡ 0 (mod 10) --> Zero divisor

5 * 2 ≡ 0 (mod 10) --> Zero divisor

5 * 4 ≡ 0 (mod 10) --> Zero divisor

6 * 5 ≡ 0 (mod 10) --> Zero divisor

8 * 5 ≡ 0 (mod 10) --> Zero divisor

9 * 5 ≡ 0 (mod 10) --> Zero divisor

Therefore, the zero divisors in Z10 are {2, 4, 5, 6, 8, 9}.

2. In Z10, not every nonzero element is either invertible or a zero divisor. For example, the element 7 is nonzero but neither invertible nor a zero divisor.

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The equation will be written as \(A = 325[1.004]^{12t}\). The time taken to reach $200 will be 10 years.

Compound interest is defined as the interest levied upon the interest. The formula to calculate the compound interest will be written as:-

\(A = P[1+\dfrac{r}{m}]^{rt}\)

Given that Hassan places $325 into a savings account that offers a monthly compound interest rate of 4.7%.

The equation for the compounding on monthly basis,

\(A = 325[1+\dfrac{0.047}{12}]^{12t}\)

\(A = 325[1.004]^{12t}\)

The time will be calculated as:-

\(A = 325[1.004]^{12t}\)

\(200 = 325[ 1.004]^{12t}\)

log(0.615) = 12 x t x log(1.004)

12t = 121.77

t = 10 years

Therefore, the equation will appear as  \(A = 325[1.004]^{12t}\). It will take 10 years for the price to reach $200.

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Answer:

Hypotenuse is the longest slanting side

Step-by-step explanation:

Without an angle to consider, the other two could fit in any position

Refer to the attachment

Answer: \(184,724.153\)

Step-by-step explanation:

Given

In 1990, there were 1200 cell phone subscriber in small town of stephenville

It is increasing by 75% per year after 1990

In year 1991 it is

\(\Rightarrow 1200+1200\times 0.75\\\Rightarrow 122(1.75)\)

In year 1992 it is

\(\Rightarrow 1200(1.75)+1200(1.75)\times 0.75\\\Rightarrow 1200(1.75)(1+0.75)\\\Rightarrow 1200(1.75)^2\)

So, it is increasing as \(1200(1.75)^x\)

where \(x=\)no of years spent

After 9 years, it is

\(\Rightarrow 1200(1.75)^9=184,724.153\)

Answer:

5. A.

6. F

Step-by-step explanation:

5. Perpendicular lines have slopes that are negative reciprocals of one another, so slope is 3

y = 3x + b

using coordinates (-6,3)

3 = 3(-6) + b

b = 21

y = 3x + 21

6. I think F is the right answer

The surface area of that part of the plane 10x+7y+z=4 that lies inside the elliptic cylinder \(\frac{x^2}{25} +\frac{y^2}{9}\) is 15π√150 and this can be determined by using the given data.

We are given the two equations are:

10x + 7y + z = 4---------(1)

\(\frac{x^2}{25} +\frac{y^2}{9} =1-------------(2)\)

equation(1) is written as

z = 4 - 10x - 7y-----------(3)

The surface area is given by the equation:

A(S) = ∫∫√[(∂f/∂x)² + (∂f/∂y)² + 1]dA------------(4)

compare equation(4) with equation(3) we get the values of ∂f/∂x and

∂f/∂y

∂f/∂x = -10

∂f/∂y = -7

substitute these values in equation(4)

A(S) = ∫∫√[(-10)² + (-7)² + 1]dA

A(S) = ∫∫√[100 + 49 + 1]dA

A(S) = ∫∫√[150]dA

A(S) = √150 ∫∫dA

Where ∫∫dA is the elliptical cylinder

From the general form of an area enclosed by an ellipse with the formula;

comparing x²/a² + y²/b² = 1  with x²/25 + y²/9 = 1, from that we get the values of a and b

a = 5 and b = 3

So, the area of the elliptical cylinder = πab

Thus;

A(S) = √150 × π(5 × 3)

A(S) = 15π√150

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The value of x with points A ( 4, 3 ) and B ( x ,5 ) on the circle and O(2,3) as centre is equal to 2.

As given in the question,

Points A(4,3 ) and B ( x, 5 ) are on the circle.

Centre of the circle is represented by O( 2,3)

OA and OB represents the radius of the circle.

This implies

OA = OB

Using distance formula we get,

√ ( 2 - 4 )² + ( 3 - 3 )² = √ ( 2 - x )² + ( 3 - 5 )²

⇒ √ 4 + 0 = √ 4 - 4x + x² + 4

⇒4 =  4 - 4x + x² + 4

⇒4 - 4x + x² = 0

⇒ ( x - 2 )² = 0

⇒ x - 2 = 0

⇒ x = 2

Therefore, the value of x for the given point of the circle is equal to 2.

The above question is incomplete , the complete question is :

What is the value of x , if the points A(4, 3) & B(x, 5) are on the circles with Centre O(2, 3), find the value of x.

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a. X and Y are jointly uniform, So, the joint PDF is constant. K =1

b. Marginal PDF of Y is given by

fY(y) = ∫f(x,y)dx

c.  X and Y are not independent.

Given, X and Y are two RVs with joint PDF f(x,y)= K for 0 ≤ y ≤x≤ 1, where X any Y are jointly uniform.

a. Find K:

To find K, we have to integrate the joint PDF f(x,y) over the range of 0 to 1 for x and y in terms of x.

That is,

K = ∫∫f(x,y)dydx

over the range of

0 ≤ y ≤ x ≤ 1

Given, X and Y are jointly uniform, So, the joint PDF is constant.

Therefore,

K = ∫∫f(x,y)dydx

= ∫∫Kdydx

= K ∫∫dydx

= K × 1

= 1

So, K = 1

b. Find the marginal PDFs:

Marginal PDF of X is given by

fX(x) = ∫f(x,y)dy integrating over all possible y

fX(x) = ∫0x1dy

fX(x) = x, where 0 ≤ x ≤ 1

Similarly, Marginal PDF of Y is given by

fY(y) = ∫f(x,y)dx

integrating over all possible x

fY(y) = ∫y11dx

fY(y) = 1-y,

where 0 ≤ y ≤ 1

c. Justify your answer:

X and Y are said to be independent if and only if their joint PDF is the product of their marginal PDFs.

So, let's check for the given case.

f(x,y) = 1 for 0 ≤ y ≤x≤ 1.

Also, marginal PDF of X,

fX(x) = x, and

marginal PDF of Y,

fY(y) = 1 - y.

Now, fX(x) × fY(y) = x(1 - y) ≠ f(x,y)

So, X and Y are not independent.

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Answer:

It depends on how many counters you have in the first place. But if there is 1 red counter and 3 blue counters then you would need 11 more red counters

he required solution is \(y=c_1e^{2x}+c_2e^{-2x}+c_3\sqrt2\cos(\sqrt2x)+c_4\sqrt2\sin(\sqrt2x)\)

where \(c_1,c_2,c_3\) and \(c_4\) are constants.

Let’s assume the general solution of the given differential equation is,

y=e^{mx}

By taking the derivative of this equation, we get

\(\frac{dy}{dx} = me^{mx}\\\frac{d^2y}{dx^2} = m^2e^{mx}\\\frac{d^3y}{dx^3} = m^3e^{mx}\\\frac{d^4y}{dx^4} = m^4e^{mx}\\\)

Now substitute these values in the given differential equation.

\(\frac{d^4y}{dx^4}-2\frac{d^2y}{dx^2}-8y\\=0m^4e^{mx}-2m^2e^{mx}-8e^{mx}\\=0e^{mx}(m^4-2m^2-8)=0\)

Therefore, \(m^4-2m^2-8=0\)

\((m^2-4)(m^2+2)=0\)

Therefore, the roots are, \(m = ±\sqrt{2} and m=±2\)

By applying the formula for the general solution of a differential equation, we get

General solution is, \(y=c_1e^{2x}+c_2e^{-2x}+c_3\sqrt2\cos(\sqrt2x)+c_4\sqrt2\sin(\sqrt2x)\)

Hence, the required solution is \(y=c_1e^{2x}+c_2e^{-2x}+c_3\sqrt2\cos(\sqrt2x)+c_4\sqrt2\sin(\sqrt2x)\)

where \(c_1,c_2,c_3\) and \(c_4\) are constants.

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