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aleksandr82 [10.1K]

3 years ago

5

How many multiples of 9 are there between 100 and 2,000?

1 answer:

Marat540 [252]3 years ago

3 0

First of all, find the first number more than 100 that can divided by 9, and it's 108 (we'll call it as 'a') then, find the number less than 2000 that can divided by 9, it's 1.998 (we'll call it as 'Un')

Un = a + (n-1).b
1998 = 108 + (n-1).9
1998 = 108 + 9n -9
1899 = 9n
211 = n

and the total is
Sn = n/2 (a+un)
s211 = 211/2 (108+1998)
= 222.183

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Find the exact value

Mnenie [13.5K]

By using properties for <em>trigonometric</em> functions and <em>trigonometric</em> expressions, we find that the <em>exact</em> value of the sine of the angle 5π/12 radians is $\frac{\sqrt{2+\sqrt{3}}}{2}$ .

<h3>How to find the exact value of a trigonometric expression</h3>

<em>Trigonometric</em> functions are <em>trascendent</em> functions, these are, that cannot be described algebraically. Herein we must utilize <em>trigonometric</em> formulae to calculate the <em>exact</em> value of a <em>trigonometric</em> function:

$\sin \frac{5\pi}{12} = \sqrt{\frac{1 - \cos \frac{5\pi}{6} }{2} }$

$\sin \frac{5\pi}{12} = \sqrt{\frac{1 + \cos \frac{\pi}{6} }{2} }$

$\sin \frac{5\pi}{12} = \sqrt{\frac{1 + \frac{\sqrt{3}}{2} }{2} }$

$\sin \frac{5\pi}{12} = \sqrt{\frac{2+\sqrt{3}}{4} }$

$\sin \frac{5\pi}{12} = \frac{\sqrt{2+\sqrt{3}}}{2}$

By using properties for <em>trigonometric</em> functions and <em>trigonometric</em> expressions, we find that the <em>exact</em> value of the sine of the angle 5π/12 radians is $\frac{\sqrt{2+\sqrt{3}}}{2}$ .

To learn more on trigonometric functions: brainly.com/question/15706158

#SPJ1

7 0

2 years ago

Jasmine and her brother Nat are saving to buy a digital camera that costs $135. Jasmine earns $15 per week for babysitting and s

zepelin [54]

Answer:

7 weeks

Step-by-step explanation:

Jasmine=$10

Nat=$11

10+11=$22 each week

135/22=6.14

at least 7 weeks

3 0

3 years ago

A simple random sample of size nequals=200200 drivers were asked if they drive a car manufactured in a certain country. of the 2

lord [1]

Answer:

Is there supposed to be a photo

Step-by-step explanation:

8 0

4 years ago

Homework Progress

Ber [7]

Answer:

77

Step-by-step explanation:

2:3:7.

8 0

3 years ago

The width of a rectangle

Luba_88 [7]

Answer:

Hello! The answer to this problem is Length= 27 and Width= 8

Step-by-step explanation:

2(11+2x) +2x = 70

6x + 22 = 70

6x = 48

x = 8

5 0

3 years ago

Read 2 more answers