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3 years ago

Sorry for the wait plz help !!!!!!!

Mathematics

2 answers:

harkovskaia [24]3 years ago

8 0

Answer:

it should be 2 units

Step-by-step explanation:

elena55 [62]3 years ago

6 0

18 I believe .........

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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

In the diagram, the length of the external portion of the

aksik [14]

Answer: hi , these are the 3 answers in order : X, 36 & 15.75

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers

Please help!!!!!!!!!!!!!!!!!!!!

Rama09 [41]

Answer:

a)smaller b)equivalent

Step-by-step explanation:

greater because the median height of the indoor plant is 1 cm whereas the full sunlight plant's is 2.5 cm

equivalent because the ratio of growth is limited due to natural circumstance's (standardization)

6 0

3 years ago

How much does he have left in the bank

Eduardwww [97]

First, let's calculate how much money was deposited into his account.
33 × $348 = $11,484

Now, let's add that to his original amount of money in his account.
$11,484 + $1,618 = $13,102

Next, let's calculate how much money was withdrawn from the account.
36 × $16 = $576

Now, you would subtract that from the account balance.
$13,102 - $576 = $12,526

Then, you would add the deposit from his uncle to his account balance.
$12,526 + $261 = $12,787

The last step would be to subtract the money for the bike.
$12,787 - $190 = $12,597

Justin has $12,597 in his bank account.

I hope this helps! (Sorry to post this so late, my computer died before I could finish.)

5 0

3 years ago

Simplify 3 square root of 20/ square root of 5

7nadin3 [17]

-7√5

rewrite 20 as 2^2·5

factor 4 out of 20. negative ∛4(5)-√5

rewrite 4 and 2^2 negative ∛2^2·5-√5

pull terms out from under the radical

-3(2√5)√5

multiply 2 by -3

-6√5-√5

subtract √5 from -6√5

-7√5

the answer is -7√5

8 0

3 years ago