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3 years ago

What is the lcd of 10/11,29/44

1 answer:

4 0

The LCM of 11 and 44 is 44.

If you wanted to add those it would look like this:
10/11 + 29/44
40/44 + 29/44
69/44 or 1 25/44

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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

If a ball rotates 110 degrees in 8 seconds how many degrees does it rotate in 32 seconds

maks197457 [2]

440 degrees in 32 seconds
8X4=32
110X4=440

3 0

3 years ago

Please Help!

Nezavi [6.7K]

Let the first number = x

The second number would be 5x

The third number would be 100x

Add:

X + 5x + 100+x = 296

Simplify:

7x + 100 = 296

subtract 100 from both sides:

7x = 196

Divide both sides by 7

X = 196 / 7

X = 28

First number is 28

Second number is 28 x 5 = 140

Third number = 128

5 0

3 years ago

What is the value of 9.6 dived by 1.2

elena-14-01-66 [18.8K]

Answer:

Step-by-step explanation:

1.2 * 8 = 9.6

4 0

3 years ago

One pipe can empty a tank in 45 minutes while a second pipe can empty it in 60 minutes. If both pipes are opened at the same tim

Ludmilka [50]

Answer:

It will take 25.7 minutes when they are working together

Step-by-step explanation:

Here, we want to know how long it will take both pipe working together to drain the tank

Let the volume of water to be drained be xL

for the first one, rate is

x/45 L/minutes

for the second x/60 L/minutes

Joint rate will be

x/45 + x/60 = 4x + 3x/180 = 7x/180

Now go get the time involved here, we simply divide the volume by the rate

That would be;

x divided by 7x/180

= x * 180/7x

= 180/7 = 25.7 minutes

8 0

3 years ago