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3 years ago

Given the arithmetic sequence an = −1 + 7(n − 1), what is the domain for n?

1 answer:

6 0

An arithmetic sequence is that in which the consecutive terms share or have the same difference commonly referred to as the "common difference". The terms in the arithmetic sequence always starts with the term 0 or the initial value. In this item, the value of n should be greater than or equal to. Therefore the answer is the second choice.

If we are to get the first term of the arithmetic sequence, it will become,
first term:
a0 = (-1) + 7(0 - 1) = -8

Therefore, the first term is equal to -8.

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Can you please belp me solve 100÷ 4,031.2

kolezko [41]

This might be wrong but I got .024806509

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3 years ago

Read 2 more answers

Please help it’s due

vampirchik [111]

Answer:

x = 27.8, y = 35

Step-by-step explanation:

Angle D is equal to Angle A

Angle E is equal to Angle B

Angle F is equal to Angle C

So you can set those equal to each other:

2y - 5 = 65

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y = 35

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3 years ago

2x^2 -8x + 1 = 0 solving using quadratic formula round to the nearest 10

Mazyrski [523]

Answer:

x=0.129171

x=3.87083

Step-by-step explanation:

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3 years ago

Write an equation of a line in slope intercept form that is perpendicular to the line 2x -3y = 12 and passes through the point (

Scilla [17]

Answer:

The equation of the line would be y = -3/2x + 9

Step-by-step explanation:

In order to solve this, start by finding the slope of the original line. You can do this by solving for y.

2x - 3y = 12

-3y = -2x + 12

y = 2/3x - 4

Now that we have a slope of 2/3, we know that the perpendicular slope is -3/2 (since perpendicular lines have opposite and reciprocal slopes). We can use this and the new point in point-slope form to find the equation.

y - y1 = m(x - x1)

y - 6 = -3/2(x - 2)

y - 6 = -3/2x + 3

y = -3/2x + 9

4 0

3 years ago

A Norman window is a window with a semi-circle on top of regular rectangular window. (See the picture.) What should be the dimen

Vikki [24]

Answer:

bottom side (a) = 3.36 ft

lateral side (b) = 4.68 ft

Step-by-step explanation:

We have to maximize the area of the window, subject to a constraint in the perimeter of the window.

If we defined a as the bottom side, and b as the lateral side, we have the area defined as:

$A=A_r+A_c/2=a\cdot b+\dfrac{\pi r^2}{2}=ab+\dfrac{\pi}{2}\left (\dfrac{a}{2}\right)^2=ab+\dfrac{\pi a^2}{8}$

The restriction is that the perimeter have to be 12 ft at most:

$P=(a+2b)+\dfrac{\pi a}{2}=2b+a+(\dfrac{\pi}{2}) a=2b+(1+\dfrac{\pi}{2})a=12$

We can express b in function of a as:

$2b+(1+\dfrac{\pi}{2})a=12\\\\\\2b=12-(1+\dfrac{\pi}{2})a\\\\\\b=6-\left(\dfrac{1}{2}+\dfrac{\pi}{4}\right)a$

Then, the area become:

$A=ab+\dfrac{\pi a^2}{8}=a(6-\left(\dfrac{1}{2}+\dfrac{\pi}{4}\right)a)+\dfrac{\pi a^2}{8}\\\\\\A=6a-\left(\dfrac{1}{2}+\dfrac{\pi}{4}\right)a^2+\dfrac{\pi a^2}{8}\\\\\\A=6a-\left(\dfrac{1}{2}+\dfrac{\pi}{4}-\dfrac{\pi}{8}\right)a^2\\\\\\A=6a-\left(\dfrac{1}{2}+\dfrac{\pi}{8}\right)a^2$

To maximize the area, we derive and equal to zero:

$\dfrac{dA}{da}=6-2\left(\dfrac{1}{2}+\dfrac{\pi}{8}\right )a=0\\\\\\6-(1-\pi/4)a=0\\\\a=\dfrac{6}{(1+\pi/4)}\approx6/1.78\approx 3.36$

Then, b is:

$b=6-\left(\dfrac{1}{2}+\dfrac{\pi}{4}\right)a\\\\\\b=6-0.393*3.36=6-1.32\\\\b=4.68$

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3 years ago