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3 years ago

If the nth partial sum of the sequence an is given by

Mathematics

1 answer:

Art [367]3 years ago

6 0

This is an example of a series in arithmetic progression.

The nth term an can be calculated using the formula:

an = a1 + (n – 1) d

where: a1 = is the 1st term of the series

d = common difference

Calculating for the 1st term:

a1 = 2k + 4 = 2 (1) + 4 = 6

Calculating for the common difference by :

d = a2 – a1

d = 2 (2) + 4 – 6

d = 2

Therefore calculating for an:

an = 6 + (n – 1) 2

an = 6 + 2n -2

an = 2n + 4

Therefore the answer is B. 2n+4

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Maria's fish tank has 17 liters of water in it. She plans to add 6 liters per minute until the tank has more than 47 liters. Wha

kondaur [170]

Answer:

t < 5

Step-by-step explanation:

47 > 6t + 17

30 > 6t

5 > t

t < 5

5 0

3 years ago

Solve the equation a=m-n for the variable n

Bogdan [553]

Answer:

m-a = n

Step-by-step explanation:

a=m-n

Subtract m from each side

a-m = m-n-m

a-m = -n

Multiply each side by -1

-a+m = n

m-a = n

7 0

3 years ago

i f N(-7,-1) is a point on the terminal side of ∅ in standard form, find the exact values of the trigonometric functions of ∅.

Natali [406]

Answer:

$sin\ \varnothing = \frac{-1}{10}\sqrt 2$

$cos\ \varnothing = \frac{-7}{10}\sqrt 2$

$tan\ \varnothing = \frac{1}{7}$

$cot\ \varnothing = 7$

$sec\ \varnothing = \frac{-5}{7}\sqrt 2$

$csc\ \varnothing = -5\sqrt 2$

Step-by-step explanation:

Given

$N = (-7,-1)$ --- terminal side of $\varnothing$

Required

Determine the values of trigonometric functions of $\varnothing$ .

For $\varnothing$ , the trigonometry ratios are:

$sin\ \varnothing = \frac{y}{r}$ $cos\ \varnothing = \frac{x}{r}$ $tan\ \varnothing = \frac{y}{x}$

$cot\ \varnothing = \frac{x}{y}$ $sec\ \varnothing = \frac{r}{x}$ $csc\ \varnothing = \frac{r}{y}$

Where:

$r^2 = x^2 + y^2$

$r = \sqrt{x^2 + y^2$

In $N = (-7,-1)$

$x = -7$ and $y = -1$

So:

$r = \sqrt{(-7)^2 + (-1)^2$

$r = \sqrt{50$

$r = \sqrt{25 * 2$

$r = \sqrt{25} * \sqrt 2$

$r = 5 * \sqrt 2$

$r = 5 \sqrt 2$

Solving the trigonometry functions

$sin\ \varnothing = \frac{y}{r}$

$sin\ \varnothing = \frac{-1}{5\sqrt 2}$

Rationalize:

$sin\ \varnothing = \frac{-1}{5\sqrt 2} * \frac{\sqrt 2}{\sqrt 2}$

$sin\ \varnothing = \frac{-\sqrt 2}{5*2}$

$sin\ \varnothing = \frac{-\sqrt 2}{10}$

$sin\ \varnothing = \frac{-1}{10}\sqrt 2$

$cos\ \varnothing = \frac{x}{r}$

$cos\ \varnothing = \frac{-7}{5\sqrt 2}$

Rationalize

$cos\ \varnothing = \frac{-7}{5\sqrt 2} * \frac{\sqrt 2}{\sqrt 2}$

$cos\ \varnothing = \frac{-7*\sqrt 2}{5*2}$

$cos\ \varnothing = \frac{-7\sqrt 2}{10}$

$cos\ \varnothing = \frac{-7}{10}\sqrt 2$

$tan\ \varnothing = \frac{y}{x}$

$tan\ \varnothing = \frac{-1}{-7}$

$tan\ \varnothing = \frac{1}{7}$

$cot\ \varnothing = \frac{x}{y}$

$cot\ \varnothing = \frac{-7}{-1}$

$cot\ \varnothing = 7$

$sec\ \varnothing = \frac{r}{x}$

$sec\ \varnothing = \frac{5\sqrt 2}{-7}$

$sec\ \varnothing = \frac{-5}{7}\sqrt 2$

$csc\ \varnothing = \frac{r}{y}$

$csc\ \varnothing = \frac{5\sqrt 2}{-1}$

$csc\ \varnothing = -5\sqrt 2$

3 0

3 years ago

How many solutions exist for the given equation?

sladkih [1.3K]

Answer:

Infinitely many

Step-by-step explanation:

12x + 1 = 3(4x + 1) - 2

12x + 1 = 12x + 3 - 2

12x + 1 = 12x + 1

Both sides are equal for all x, so infinite solutions

8 0

3 years ago

Read 2 more answers

Grace earns $7 for each car she washes. She always saves $25 of her weekly earnings.This week,she wants to have at least $65 in

Irina-Kira [14]

Answer:

she must wash 8 cars because 7 x 8 = 56 so yeah bye

Step-by-step explanation:

7 0

3 years ago