All categories

3 years ago

Find the sum of the arithmetic series 3+8+13+..+438

Mathematics

1 answer:

irina [24]3 years ago

7 0

Answer:

19404

Step-by-step explanation:

sum of arithmetic series is

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

Sn = n/2 (a + an)

a = 1st unit

an = last unit

d = difference

8-3 or 13-8 so d = 5

then first step is to find the value of n

an = a + (n-1)d

438 = 3 + (n-1)5

438 - 3 = 5n - 5

435 = 5n - 5

435 + 5 = 5n

440 = 5n

n = 440/5

n = 88

then we can find the sum

Sn = 88/2 (3 + 438)

S88 = 19404

You might be interested in

What does -8+(-12) / (-4) equal too?

zalisa [80]

Answer:

Step-by-step explanation:

1. Add -8 to -12. This equals -20.

2. Now you have -20/(-4)

3. Solve this by dividing -20 and -4.

4. Two negatives make a positive, so your answer would be 5.

Hope this helps

5 0

2 years ago

Read 2 more answers

Adam went to McDonald's and bought a Big Mac and 2 small fries. Adam spent

Rudiy27

Answer:

the answer is 4.94 because you subtract 10.93-5.99

3 0

2 years ago

If tan theta = startfraction 11 over 60 endfraction, what is the value of cot theta?

Dennis_Churaev [7]

The value of $cot\theta$ when $tan\theta =\frac{11}{60}$ comes to be $\frac{60}{11}$ .

Given that trigonometric ratio:

$tan\theta = \frac{11}{60}$

<h3>What is the tangent of an angle?</h3>

The tangent of an angle is the ratio of the opposite side(to that angle) to the adjacent side(to that angle).

So, for the given problem

Opposite side to $\theta$ = 11

Adjacent side to $\theta$ = 60

So, $cot \theta =\frac{AdjacentSide }{OppositeSide}$

$cot\theta =\frac{60}{11}$

Therefore, the value of $cot\theta$ when $tan\theta =\frac{11}{60}$ comes to be $\frac{60}{11}$ .

To get more about trigonometric ratios visit:

brainly.com/question/24349828

6 0

1 year ago

A The length of a rectangle is 4 m more

Lady bird [3.3K]

Given :

The length of a rectangle is 4m more than the width.
The area of the rectangle is 45m²

⠀

To Find :

The length and width of the rectangle.

⠀

Solution :

We know that,

$\qquad { \pmb{ \bf{Length \times Width = Area_{(rectangle)}}}}\:$

So,

Let's assume the length of the rectangle as x and the width will be (x – 4).

⠀

Now, Substituting the given values in the formula :

$\qquad \sf \: { \dashrightarrow x \times (x - 4) = 45 }$

$\qquad \sf \: { \dashrightarrow {x}^{2} - 4x = 45 }$

$\qquad \sf \: { \dashrightarrow {x}^{2} - 4x - 45 = 0 }$

$\qquad \sf \: { \dashrightarrow {x}^{2} - 9x+ 5 x - 45 = 0 }$

$\qquad \sf \: { \dashrightarrow x(x - 9) + 5(x - 9) = 0 }$

$\qquad \sf \: { \dashrightarrow (x - 9) (x + 5) = 0 }$

$\qquad \sf \: { \dashrightarrow x = 9, \: \: x = - 5}$

⠀

Since, The length can't be negative, so the length will be 9 which is positive.

⠀

$\qquad { \pmb{ \bf{ Length _{(rectangle)} = 9\:m}}}\:$

$\qquad { \pmb{ \bf{ Width _{(rectangle)} = 9 - 4=5\: m}}}\:$

━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

8 0

1 year ago

Graph the equation.<br><br> X squared plus y squared equals 9

BartSMP [9]

Answer:

Step-by-step explanation:

This graph is a circle. The general equation for a circle is x² + y² = r², where r is the radius. In this case, the radius is 3 because √9 = 3. Also, the center is (0,0) because the circle is not translated. Therefore, the graph is a circle with center (0,0) and radius 3. If you still need help, the y-intercepts are (0,±3) and the x-intercepts are (±3,0). Hope this makes sense!

7 0

2 years ago

Read 2 more answers