All categories

3 years ago

Write the following series in sigma notation. 8+18+28+38

Mathematics

1 answer:

Mumz [18]3 years ago

5 0

Answer:

$\Sigma\left {n} \atop {1}} \right. (5n^2+3n)$

Step-by-step explanation:

Given the series 8 + 18 + 28 + 38

First, we need to find the sum of the nth term of the sequence as shown

Sn = n/2[2a+(n-1)d]

n is the number of terms

a is the first term = 8

d is the common difference = 18-8 = 28-18 = 10

Substitute

Sn = n/2 [2(8)+(n-1)*10]

Sn = n/2 [16+10n-10]

Sn = n/2[10n+6]

Sn = 2n/2(5n+3)

Sn = n(5n+3)

Sn = 5n²+3n

In Sigma form;

$\Sigma\left {n} \atop {1}} \right. (5n^2+3n)$

You might be interested in

What's an expression that represents the sum of 7 and x?

babunello [35]

Its simple, the expression is 7+x and it does not have an equal sign since it is not an equation

5 0

3 years ago

Read 2 more answers

A 12 foot ladder is leaning against a building. If the bottom of the ladder is sliding along the pavement directly away from the

ira [324]

Using Pythagoras theorem, the top of the ladder moving down when the foot of the ladder is 3 feet from the wall is of -0.518 feet/sec.

Let distance from the wall to the foot of the ladder is 'x' feet and the height of the top of the ladder is 'y' feet.

Pythagoras theorem, $x^{2} + y^{2} = (12)^{2}$ --->(1)

Given, $\frac{dx}{dt}= 2feet/second$ at x=3

Put x=3 in Pythagoras theorem equation (1)

$(3)^{2} + y^{2} = 144$

$y^{2} = 144 - 9$

$y^{2}$ = 135

y = 11.61

Derive equation (1) w.r.t to 't'

$2x\frac{dx}{dt} + 2y\frac{dy}{dt} = 0$ ---->(2)

substitute the value of 'x', 'dx/dt' and 'y' in equation (2), we get the fast of the top of the ladder moving down when the foot of the ladder is 3 feet from the wall

$2(3)(2) + 2 (11.61)\frac{dy}{dt} = 0$

12 + 23.22 $\frac{dy}{dt}$ = 0

$\frac{dy}{dt}= \frac{-12}{23.22}$

$\frac{dy}{dt} = -0.518$

Hence, using Pythagoras theorem the top of the ladder moving down when the foot of the ladder is 3 feet from the wall is of -0.518 feet/sec.

Learn more about Pythagoras theorem here

brainly.com/question/21511305

#SPJ4

5 0

2 years ago

Need help please this question is very confusing i would love some help

Natali [406]

Answer:

Step-by-step explanation:

The equation of a parabola in vertex form is

y = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

here (h, k) = (- 3, - 6), thus

y = a(x + 3)² - 6

To find a substitute (0, 0) into the equation

0 = 9a - 6 ⇒ a = $\frac{6}{9}$ = $\frac{2}{3}$

y = $\frac{2}{3}$ (x + 3)² - 6 ← in vertex form

Expand (x + 3)² and distribute by $\frac{2}{3}$

y = $\frac{2}{3}$ (x² + 6x + 9) - 6

= $\frac{2}{3}$ x² + 4x + 6 - 6

= $\frac{2}{3}$ x² + 4x ← in standard form

7 0

3 years ago

Which points are on the the graph equation -3x+6y+5=-7

algol [13]

-3x + 6y + 5 = -7
 -5 -5
 -3x + 6y = -12
-3x + 3x + 6y = -12 + 3x
 6y = -12 + 3x
 6 6
 y = -2 + 1/2x
-3x + 6(-2 + 1/2x) = -12
 -3x - 12 + 3x = -12
 -3 + 3x - 12 = -12
 0x - 12 = -12
 +12 +12
 0x = 0
 0 0
 x = 0
 -3(0) + 6y = -12
 0 + 6y = -12
 +0 +0
 6y = -12
 6 6
 y = -2
 (x, y) = (0, -2)

6 0

4 years ago

Given the following information about a hypothesis test of the difference between two means based on independent random samples,

HACTEHA [7]

Answer:

$S^2_p =\frac{(13-1)(5)^2 +(10 -1)(3)^2}{13 +10 -2}=18.143$