Simplify. 8(10m) 18m 810m 80 + m 80m

Please help me thank you

Hoochie [10]

Answer:

$\large\boxed{\sin2\theta=\dfrac{\sqrt3}{2},\ \cos2\theta=\dfrac{1}{2}}$

Step-by-step explanation:

We know:

$\sin2\theta=2\sin\theta\cos\theta\\\\\cos2\theta=\cos^2\theta-\sin^2\thet$

We have

$\sin\theta=\dfrac{1}{2}$

Use $\sin^2\theta+\cos^2\theta=1$

$\left(\dfrac{1}{2}\right)^2+\cos^2\theta=1\\\\\dfrac{1}{4}+\cos^2\theta=1\qquad\text{subtract}\ \dfrac{1}{4}\ \text{from both sides}\\\\\cos^2\theta=\dfrac{4}{4}-\dfrac{1}{4}\\\\\cos^2\theta=\dfrac{3}{4}\to\cos\theta=\pm\sqrt{\dfrac{3}{4}}\to\cos\theta=\pm\dfrac{\sqrt3}{\sqrt4}\to\cos\theta=\pm\dfrac{\sqrt3}{2}\\\\\theta\in[0^o,\ 90^o],\ \text{therefore all functions have positive values or equal 0.}\\\\\cos\theta=\dfrac{\sqrt3}{2}$

$\sin2\theta=2\left(\dfrac{1}{2}\right)\left(\dfrac{\sqrt3}{2}\right)=\dfrac{\sqrt3}{2}\\\\\cos2\theta=\left(\dfrac{\sqrt3}{2}\right)^2-\left(\dfrac{1}{2}\right)^2=\dfrac{3}{4}-\dfrac{1}{4}=\dfrac{3-1}{4}=\dfrac{2}{4}=\dfrac{1}{2}$

3 0

2 years ago

The probability distribution for the number of defects in a shipment of alarm clocks, based on past data, is given below. Find t

Kay [80]

Answer:

0.29

Step-by-step explanation:

Given :

n : ___ 0 _____ 1 ____ 2 ____ 3 ____ 4

P(n) : 0.82___ 0.11 ___0.04 _0.02 ___0.01

The expected number of defect in a shipment can be obtained using the expected value formula :

Expected value, E(X) = Σx*p(x)

Σx*p(x) = (0*0.82) + (1*0.11) + (2*0.04) + (3*0.02) + (4*0.01)

E(X) = 0.29

Hence, the expected number of defect in shipment is 0.29

3 0

2 years ago

What best describes the expression 6 over y?

Simora [160]

6 divided by some number.

4 0

3 years ago

Jaime has 5 over 11 spaceof a project completed while Tim has finished 7 over 13 spaceof the same project.

lina2011 [118]

Tim has completed greater amount of work and overall they have completed 142/143 of the project work

Step-by-step explanation:

Given

Work completed by Jaime = j = 5/11

Work completed by Tim = t = 7/13

a. Who has completed the greater amount of work?

In order to see that we have to convert the fractions in decimal

So,

j = 5/11 = 0.45

t = 7/13 = 0.53

As we can see that the decimal for Tim's work space is large, Tim has completed greater amount of work

b. How much of the project have they completed together? Show your work.

We have to find the total work done by them

$Total\ work = j + t\\= \frac{5}{11} + \frac{7}{13}\\=\frac{65+77}{143}\\=\frac{142}{143}$

Hence,

Tim has completed greater amount of work and overall they have completed 142/143 of the project work

Keywords: Fractions, LCM

Learn more about fractions at:

#LearnwithBrainly

4 0

2 years ago

Help me pleaseeeeeeeeeeee

Leya [2.2K]

Answer:

Step-by-step explanation:

a) 6305/65= 97

b) 94+94= 188

306-188= 118

4 0

1 year ago

Read 2 more answers