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OverLord2011 [107]
3 years ago
15

Write the first five terms of the sequence defined by the recursive formula an=2*(an-1)+3 with a1=-2

Mathematics
1 answer:
Tasya [4]3 years ago
5 0

Answer:

<u>The first five terms of the sequence are 5, 7, 9, 11 and 13.</u>

Step-by-step explanation:

The first five terms of the sequence are:

a₁ = 2 * (2 - 1) + 3 = 2 * 1 + 3 = 2 + 3 = 5

a₂ = 2 * (3 - 1) + 3 = 2 * 2 + 3 = 4 + 3 = 7

a₃ = 2 * (4 - 1) + 3 = 2 * 3 + 3 = 6 + 3 = 9

a₄ = 2 * (5 - 1) + 3 = 2 * 4 + 3 = 8 + 3 = 11

a₅ = 2 * (6 - 1) + 3 = 2 * 5 + 3 = 10 + 3 = 13

<u>The first five terms of the sequence are 5, 7, 9, 11 and 13.</u>

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Investments historically have doubled every 9 years. if you start with 2,000 investment, how much money would you have after 45
77julia77 [94]

Answer: 64,000

Equation: 2,000*2^(45/9)

4 0
3 years ago
If a monopolist supplies goods at a price; P = 170 - Q, with marginal cost; MC = 52. Find the quantity and price
Arada [10]

Answer:

Quantity = 59 units

Price = $111

Step-by-step explanation:

The Demand function is given by

P = 170 - Q

The Marginal cost is given by

MC = 52

We are asked to find the quantity and price of goods.

Firstly, obtain the Marginal revenue function from the demand function

The Total revenue is given by

TR = P \times Q \\\\TR = (170 - Q) \times Q \\\\TR = 170Q - Q^2

The Marginal revenue is the derivative of the Total revenue,

MR = \frac{d}{dQ} (TR) = 170Q - Q^2 \\\\MR = \frac{d}{dQ} (TR) = 170 - 2Q \\\\

Assuming that the monopolist maximizes profits,

MR = MC \\\\170 - 2Q = 52\\\\2Q = 170 - 52\\\\2Q = 118\\\\Q = 118/2\\\\Q = 59

Therefore, the quantity is 59 units.

The price of each good is

P = 170 - Q \\\\P = 170 - 59 \\\\P = 111

Therefore, the price is $111.

3 0
3 years ago
Find the area of the composite figure
Pavlova-9 [17]

Answer:

45

Step-by-step explanation:

4 0
3 years ago
A piece of cardboard is 13 inches by 26 inches. A square is to be cut from each corner and the sides folded up to make an open-t
Vanyuwa [196]

Answer:

Hence the maximum possible volume will be the 778.53 c.c

Step-by-step explanation:

Given:

A rectangle with 13 x 26 dimensions

And corners are cut to form side squares.

To Find:

Maximum possible volume for box

Solution :

Consider a rectangle of 13 x 26 dimension with and side of square  at corner be x.

(Refer the attachment)

Now,

Formulating the volume equation for the box

So corner square sides we are going to fold up which makes height of the box

and remaining part will be length and breadth

As shown in fig,

Length=26-x

breadth=13-x

And height will be x

V(x)=x*(26-x)*(13-x)

To get maximum volume differentiate the above equation,

V(x)=x*(26*13-26*x-13*x+x^2)

V(x)=x^3-39x^2+338x\\

V'(x)=3x^2-78x+338

V''(x)=6x-78

Now ,Solve the Quadratic Equation to get x values,

3x^2-78x+338=0

x=[-b±(b^2-4ac)^1/2]/2a

x=[78±Sqrt[(78)^2-4*338*3)]/2*3

x=[78±Sqrt(3028)]/6

x=[78±55.027]/6

x=78+55.027/6 or x=78-55.027/6

x=22.17  or x=3.8288

Use these values in 6x-78 to know which value posses the max and min value for the function.

So when x=22.17

6x-78=6*22.17-78

=55.02>0  i.e function will have minimum value .

When x=3.8288

6*3.8288-78

=-55.0272<0 i.e. Function will have maximum value

Now, the function will defines the maximum volume

V(x)=x^3-39x^2+338x

V(x)=3.8288^3-39*(3.82883)^2+338*3.8288

V(x)=56.13-571.73+1294.13

V(x)=778.53 C.C

6 0
3 years ago
Which choice is the slope-intercept equation of the line shown below?
Neporo4naja [7]

Answer:

C is my answer

Step-by-step explanation:

6 0
3 years ago
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