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Elden [556K]
2 years ago
12

Which is the graph of g(x) = 2x – 1 + 3? On a coordinate plane, an exponential function has a horizontal asymptote at y = 3 and

crosses the y-axis at (0, 4). On a coordinate plane, an exponential function has a horizontal asymptote at y = negative 3 and crosses the y-axis at (0, negative 2) On a coordinate plane, an exponential function has a horizontal asymptote at y = negative 1 and crosses the y-axis at (0, 7). On a coordinate plane, an exponential function has a horizontal asymptote at y = negative 1 and crosses the y-axis at (0, negative 1).
Mathematics
2 answers:
IceJOKER [234]2 years ago
5 0

Answer:

Graph D

Step-by-step explanation:

Anit [1.1K]2 years ago
3 0

Answer:

D i just took the test

Step-by-step explanation:

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Consider the following differential equation. x^2y' + xy = 3 (a) Show that every member of the family of functions y = (3ln(x) +
Veronika [31]

Answer:

Verified

y(x) = \frac{3Ln(x) + 3}{x}

y(x) = \frac{3Ln(x) + 3 - 3Ln(3)}{x}

Step-by-step explanation:

Question:-

- We are given the following non-homogeneous ODE as follows:

                           x^2y' +xy = 3

- A general solution to the above ODE is also given as:

                          y = \frac{3Ln(x) + C  }{x}

- We are to prove that every member of the family of curves defined by the above given function ( y ) is indeed a solution to the given ODE.

Solution:-

- To determine the validity of the solution we will first compute the first derivative of the given function ( y ) as follows. Apply the quotient rule.

                          y' = \frac{\frac{d}{dx}( 3Ln(x) + C ) . x - ( 3Ln(x) + C ) . \frac{d}{dx} (x)  }{x^2} \\\\y' = \frac{\frac{3}{x}.x - ( 3Ln(x) + C ).(1)}{x^2} \\\\y' = - \frac{3Ln(x) + C - 3}{x^2}

- Now we will plug in the evaluated first derivative ( y' ) and function ( y ) into the given ODE and prove that right hand side is equal to the left hand side of the equality as follows:

                          -\frac{3Ln(x) + C - 3}{x^2}.x^2 + \frac{3Ln(x) + C}{x}.x = 3\\\\-3Ln(x) - C + 3 + 3Ln(x) + C= 3\\\\3 = 3

- The equality holds true for all values of " C "; hence, the function ( y ) is the general solution to the given ODE.

- To determine the complete solution subjected to the initial conditions y (1) = 3. We would need the evaluate the value of constant ( C ) such that the solution ( y ) is satisfied as follows:

                         y( 1 ) = \frac{3Ln(1) + C }{1} = 3\\\\0 + C = 3, C = 3

- Therefore, the complete solution to the given ODE can be expressed as:

                        y ( x ) = \frac{3Ln(x) + 3 }{x}

- To determine the complete solution subjected to the initial conditions y (3) = 1. We would need the evaluate the value of constant ( C ) such that the solution ( y ) is satisfied as follows:

                         y(3) = \frac{3Ln(3) + C}{3} = 1\\\\y(3) = 3Ln(3) + C = 3\\\\C = 3 - 3Ln(3)

- Therefore, the complete solution to the given ODE can be expressed as:

                        y(x) = \frac{3Ln(x) + 3 - 3Ln(3)}{y}

                           

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6 0
3 years ago
Wats 80 times 80? please answer
Anastasy [175]

Answer:

6400

Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
Your friend borrows $7500 to buy an all-terrain vehicle (ATV). The simple annual interest rate is 6%. She pays off the loan afte
e-lub [12.9K]

Answer:

$162.50

Explanation:

The total amount to be paid is 7500+5(7500)(0.06)=$9750.

There were a total of (5)(12)=60 payments, so each payment is 9750/60 = $162.50.

6 0
2 years ago
Cody is designing a pattern for a wood floor the length of the pieces of wood are 1 1/2 inches 1 13/16 inches and 2 1/8 inches w
Verdich [7]
The length of the fifth piece is 2 3/4 inches.

Given:
1st piece of wood = 1 1/2 inches
2nd piece of wood = 1 13/16 inches
3rd piece of wood = 2 1/8 inches

f(n) = 1st term + common difference(n-1)

To get the common difference, we need to deduct the fraction from its preceding fraction.

1st piece: 1 1/2 = (2*1 + 1)/2 = 3/2
2nd piece: 1 13/16 = (16*1+13)/16 = 29/16
3rd piece: 2 1/8 = (8*2+1)/8 = 17/8

29/16 - 3/2 = 29/16 - (3/2 * 8/8) = 29/16 - 24/16 = (29-24)/16 = 5/16
17/8 - 29/16 = (17/8 *2/2) - 29/16 = 34/16 - 29/16 = (34-29)/16 = 5/16

Find: 5th piece's measurement
1st term : 1 1/2 or 3/2
common difference : 5/16

f(5) = 3/2 + 5/16 (5-1)
      = 3/2 + 5/16 (4)
      = 3/2 + (5*4)/16
      = 3/2 + 20/16
      = (3/2 * 8/8) + 20/16
      = 24/16 + 20/16
      = (24 + 20)/16
f(5) = 44/16
f(5) = 2 12/16 simplified to 2 3/4 inches.
6 0
3 years ago
3) Jaidee invests $1,966 in a savings account with a fixed annual interest rate of 2.45% compounded continuously. What will the
Mama L [17]

Answer:

87

Step-by-step explanation:

6 0
3 years ago
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