Find the 20th term of the arithmetic sequence 15,9,3,-3

Mathematics

1 answer:

kati45 [8]2 years ago

3 0

Answer:

-99

Step-by-step explanation:

$a = 15 \\ d = - 6 \\ {n}^{th} term = a + (n + 1)d = 15 + (n - 1)( - 6) \\ {20}^{th} term =15 + (20 - 1)( - 6) = 15 - 114 = - 99$

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Find x and round to nearest tenth

Lesechka [4]

Answer:

x=13.5

Step-by-step explanation:

Using the formula:

Sin theta=opposite/hypotenuse

Where theta=57 degrees

opposite =10.8

hypotenuse =x

Sin57=10.8/x

Xsin57=10.8

x=10.8/sin57

x=10.8/0.8

x=13.5

8 0

3 years ago

PLEASE HELP Complete the table with the number of sit-ups you have to do sunday so that the mean number of sit-ups per day is 10

klemol [59]

The complete table will be:

$Monday - 100\\ Tuesday-65\\ Wednesday- 120\\ Thursday-150\\ Friday-90\\ Saturday- 0\\ Sunday-175$

Explanation

Suppose, the number of sit-ups in Sunday is $x$

Mean is the simple average of some numbers. For finding the mean number of sit-ups per day, we need to divide the 'total number of sit-ups' by the 'total number of days'.

Here the total number of days is 7 and the total number of sit-ups for 7 days $= 100+65+120+150+90+0+x= 525+x$

Given that, the mean number of sit-ups per day is 100. So, the equation will be...

$\frac{525+x}{7}=100\\ \\ 525+x=700\\ \\ x= 700-525=175$

So, the number of sit-ups you have to do Sunday is 175.

6 0

3 years ago

Differentiate the function. f(x) = ln(25 sin^2(x))

tigry1 [53]

Use the chain rule.
Let u = 25sin²(x), such that dy/dx = dy/du · du/dx

$\frac{dy}{dx} = \frac{1}{25sin^{2}(x)} \cdot 50cos(x) \cdot sin(x)$
$\frac{dy}{dx} = \frac{2cos(x) sin(x)}{sin^{2}(x)}$

$\frac{dy}{dx} = 2cot(x)$