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2 years ago

Which equation should be used to calculate the 43rd partial sum for the arithmetic sequence.

Mathematics

1 answer:

MariettaO [177]2 years ago

6 0

Answer: First Option : Sₙ= n/2(a₁ + aₙ)

Step-by-step explanation:

The nth partial sum of an arithmetic sequence or the sum of the first n terms of the arithmetic series can be defined as the sum of a finite number of term in an arithmetic sequence.

It is calculated using the formula:

Sₙ= n/2(a₁ + aₙ)

Where :

a₁ = First term

aₙ = last term

n = number of terms

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Derive the equation of the parabola with a focus at (-5,5) and a directix of y = -1

Paladinen [302]

Answer:

Step-by-step explanation:

From any point (x, y) on the parabola the focus and directrix are equidistant

Using the distance formula

$\sqrt{(x+5)^2+(y-5)^2}$ = | y + 1 |

Squaring both sides

(x + 5)² + (y - 5)² = (y + 1)^2 , that is

(y + 1)² = (x + 5)² + (y - 5)² ← subtract (y - 5)² from both sides

(y + 1)² - (y - 5)² = (x + 5)² ← expand left side and simplify

y² + 2y + 1 - y² + 10y - 25 = (x + 5)²

12y - 24 = (x + 5)² ← factor left side

12(y - 2) = (x + 5)² ← divide both sides by 12

y - 2 = $\frac{1}{12}$ (x + 5)² ← add 2 to both sides

y = $\frac{1}{12}$ (x + 5)² + 2

f(x) = $\frac{1}{12}$ (x + 5)² + 2 → D

7 0

3 years ago

What is an equation of the line that passes through the point (-2,7) and is perpendicular to the line x-6y=42 ?

Natali5045456 [20]

Answer:

The equation of the line that passes through the point (-2,7) and is perpendicular to the line x-6y=42 is

$6x+y=-5$

Step-by-step explanation:

Given:

Let,

point A( x₁ , y₁) ≡ ( -2 , 7)

To Find:

Equation of Line that passes through the point (-2,7) and is perpendicular to the line x-6y=42=?

Solution:

$x-6y=42$ ..................Given

which can be written as

$y=mx+c$

Where m is the slope of the line

∴ $y=\dfrac{x}{6}-7$

On Comparing we get

$Slope = m = \dfrac{1}{6}$

The Required line is Perpendicular to the above line.

So,

Product of slopes = - 1

$m\times m_{1}=-1\\Substituting\ m\\ \dfrac{1}{6} m_{1}=-1\\\\m_{1}=-6$

Slope of the required line is -6

Equation of a line passing through a points A( x₁ , y₁) and having slope m is given by the formula,

i.e equation in point - slope form

$(y-y_{1})=m(x-x_{1})$

Now on substituting the slope and point A( x₁ , y₁) ≡ ( -2, 7) and slope = -6 we get

$(y-7)=-6(x--2)=-6(x+2)=-6x-12\\\\\therefore 6x+y=-5.......is\ the required\ equation\ of\ the\ line$

The equation of the line that passes through the point (-2,7) and is perpendicular to the line x-6y=42 is

$6x+y=-5$

3 0

3 years ago

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butalik [34]

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7 0

3 years ago

What is the ratio 24/16 written in lowest terms

Sonbull [250]

24/16 are both multiples of 8

24/8 = 3 16/8 = 2

3/2

5 0

3 years ago

At work, Brett must check and record the internal temperature of the freezer on an hourly basis. When working properly, the temp

kiruha [24]

Answer:

Zero

Step-by-step explanation:

The temperature will remain constant over time. This means the slope of the graph will be constant from one point of the graph to the other, which cancels out to zero.

8 0

3 years ago