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3 years ago

Sam is an engineer . Every week he spends 37 hours writing code and going to meetings

Mathematics

1 answer:

Lesechka [4]3 years ago

3 0

Answer:

Step-by-step explanation:

37-4=c

c=33

plz mark brainliest

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Hello! Verify the identity. Please show your work! Use trigonometric identities to verify each expression is equal.

RSB [31]

Answer:

See Below.

Step-by-step explanation:

We want to verify the identity:

$\displaystyle \csc^2 x -2\csc x \cot x +\cot ^2 x = \tan^2\left(\frac{x}{2}\right)$

Note that the left-hand side is a perfect square trinomial pattern. Namely:

$a^2-2ab+b^2=(a-b)^2$

If we let a = csc(x) and b = cot(x), we can factor it as such:

$\displaystyle (\csc x - \cot x)^2 = \tan^2\left(\frac{x}{2}\right)$

Let csc(x) = 1 / sin(x) and cot(x) = cos(x) / sin(x):

$\displaystyle \left(\frac{1}{\sin x}-\frac{\cos x }{\sin x}\right)^2=\tan^2\left(\frac{x}{2}\right)$

Combine fractions:

$\displaystyle \left(\frac{1-\cos x}{\sin x}\right)^2=\tan^2\left(\frac{x}{2}\right)$

Square (but do not simplify yet):

$\displaystyle \frac{(1-\cos x)^2}{\sin ^2x}=\tan^2\left(\frac{x}{2}\right)$

Now, we can make a substitution. Let u = x / 2. So, x = 2u. Substitute:

$\displaystyle \frac{(1-\cos 2u)^2}{\sin ^22u}=\tan^2u$

Recall that cos(2u) = 1 - sin²(u). Hence:

$\displaystyle \frac{(1-(1-2\sin^2u))^2}{\sin ^2 2u}=\tan^2u$

Simplify:

$\displaystyle \frac{4\sin^4 u}{\sin ^2 2u}=\tan^2 u$

Recall that sin(2u) = 2sin(u)cos(u). Hence:

$\displaystyle \frac{4\sin^4 u}{(2\sin u\cos u)^2}=\tan^2 u$

Square:

$\displaystyle \frac{4\sin^4 u}{4\sin^2 u\cos ^2u}=\tan^2 u$

Cancel:

$\displaystyle \frac{\sin ^2 u}{\cos ^2 u}=\tan ^2 u$

Since sin(u) / cos(u) = tan(u):

$\displaystyle \left(\frac{\sin u}{\cos u}\right)^2=\tan^2u=\tan^2u$

We can substitute u back for x / 2:

$\displaystyle \tan^2\left(\frac{x}{2}\right)= \tan^2\left(\frac{x}{2}\right)$

Hence proven.

3 0

3 years ago

82 POINTS! PLEASE READ CAREFULLY!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

fenix001 [56]

Answer:

THE INDEPENDENT IS whether talking to plants would help and the dependent is THE GROWTH OF THE PLQNT

Step-by-step explanation:

4 0

3 years ago

Read 2 more answers

Whole numbers greater than 10 but less than

gayaneshka [121]

Something great than AND less than is equal to.

I thibk 10 itself is the answer. It is greater yet less.

7 0

3 years ago

4^2+4^6 solve this please

Georgia [21]

Answer:

$4,112$

Step-by-step explanation:

$4^2 =16$

$4^6=4096$

$4096+16=4112$

Hope this helps! Please let me know if you need more help, or if you think my answer is incorrect. Brainliest would be MUCH appreciated. Have a great day!

Stay Brainy!

− $xXheyoXx$

8 0

2 years ago

1.The population of the world is approximately 6200 million people. It is increasing by approximately 93 million people each yea

STALIN [3.7K]

The fraction can simplify down to $\frac{93}{6200}$ convert it to a fraction and the yearly increase is 1.5%

2. Well on average there are 365 days in a year. Dividing 93 million by 365 will get your increase per day.
There are 24 hours in a day, so that figure is further divided by 24.
There are also 60 minutes in an hour therefore furthermore divided by 60.
= 176 therefore true

8 0

3 years ago