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3 years ago

The nth term of a sequence is given by 2n+1.Write down the first four terms of the sequence.

Mathematics

1 answer:

ale4655 [162]3 years ago

8 0

Answer:

x, 2x+1, 4x+3, 8x+7

Step-by-step explanation:

If we call the first term x, then the subsequent term is 2x+1. Then, the next term is 2(2x+1)+1=4x+2+1=4x+3. Then, the fourth term is 2(4x+3)+1=8x+6+1=8x+7.

As a matter of fact, the nth term is given by $2^{n-1}x+2^{n-1}-1$ for starting term x.

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Packaging By cutting away identical squares from each corner of a rectangular piece of cardboard and folding up the resulting fl

Vikki [24]

Answer:

Height: 3/2 inches

Length: 12 inches

Width: 4 inches

Step-by-step explanation:

Let x is the side length of the square

The height of the box by cutting squares off :x

The new length of the cardboard = 15 -2x (because we cut from 4 corners)
The new width of the cardboard = 7 -2x (because we cut from 4 corners)

The new volume of it is:

V = (15 -2x) (7 -2x) x

<=> V = $4x^3 -44x^2 +105x$

To maximum volume, we use the first derivative of the volume

$\dfrac{dV}{dx} = 0$

<=> $12x^2-88x+105=0$

<=> $\left(2x-3\right)\left(6x-35\right) = 0$

<=> 2x -3 = 0 or 6x -35 = 0

<=> x = 3/2 or x = 35/6

To determine which value of x gives a maximum, we evaluate

$\dfrac{d^2V}{dx^2}$ = 24x -88

If x = 3/2, we have:

$\dfrac{d^2V}{dx^2}$ = 24(3/2) -88 = -52

If x = 35/6, we have:

$\dfrac{d^2V}{dx^2}$ = 24(35/6) -88 = 52

We choose x = 3/2 to have the maximum volume because the value of x that gives a negative value is maximum.

So the dimensions (in inches) of the box is:

Height: 3/2 inches

Length: 15-2(3/2) = 12 inches

Width: 7 - 2(3/2) = 4 inches

5 0

3 years ago

Helppppppppppppppppppppppppppppppppppppppppppppppppppppppp

SVEN [57.7K]

Answer:

A and E is true. BCD is False

Step-by-step explanation:

Let convert this into slope intercept form

$10y - 200x = 500$

$10y = 200x + 500$

$y = 20x + 50$

So now let answer these questions,

A is TRUE the slope is the number in front of the x value. It is 20 so a is true.

B is False, Using (0, 500) The equation is wrong

$500 = 20(0) + 50 ??$

C is false, we have a positive slope so it shifts upward from left to right.

D is false

the slope isn't 200.

E Is true the y intercept is when the x value is 0, what is the y value so plug it in we get

$y = 20(0) + 50$

It equal 50.

4 0

3 years ago

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Monica [59]

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3 years ago

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Lelu [443]

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3 years ago

Juan rents a car for $29.00 a week. He pays $17.00 per week for the insurance and spends $13.50 weekly on gas. What will his cos

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2 years ago

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The nth term of a sequence is given by 2n+1.Write down the first four terms of the sequence.​

The nth term of a sequence is given by 2n+1.Write down the first four terms of the sequence.