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3 years ago

13

In the figure, AB¯¯¯¯¯∥CD¯¯¯¯¯ and m∠2=60°. What is m∠6?

1 answer:

PolarNik [594]3 years ago

8 0

<span>mâ 6 = 60Â° Since both AB and CD are parallel to each other, equivalent angles made by the intersection of the third line are equal to each other. â 2 is the upper right hand angle of the intersection between AB and the third line and â 6 is also the upper right hand angle of the intersection between CD and third line.</span>

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Mamont248 [21]

Answer: see proof below

<u>Step-by-step explanation:</u>

Use the Sum & Difference Identity: cos (A + B) = cos A · cos B - sin A · sin B

Recall the following from Unit Circle: cos (π/2) = 0, sin (π/2) = 1

cos (π) = -1, sin (π) = 0

Use the Quotient Identity: $\tan A=\dfrac{\sin A}{\cos A}$

<u>Proof LHS → RHS:</u>

$\text{LHS:}\qquad \qquad \dfrac{\cos \bigg(\dfrac{\pi}{2}+x\bigg)}{\cos \bigg(\pi +x\bigg)}$

$\text{Sum Difference:}\qquad \dfrac{\cos \dfrac{\pi}{2}\cdot \cos x-\sin \dfrac{\pi}{2}\cdot \sin x}{\cos \pi \cdot \cos x-\sin \pi \cdot \sin x}$

$\text{Unit Circle:}\qquad \qquad \dfrac{0\cdot \cos x-1\cdot \sin x}{-1\cdot \cos x-0\cdot \sin x}$

$=\dfrac{-\sin x}{-\cos x}$

Quotient: tan x

LHS = RHS $\checkmark$

7 0

3 years ago

Read 2 more answers

Assume the exponential growth model A(t)equals=Upper A 0 e Superscript ktA0ekt and a world population of 5.95.9 billion in 2006

Whitepunk [10]

Answer:

1.4% is the maximum acceptable annual rate of growth such that the population must stay below 24 billion during the next 100 years.

Step-by-step explanation:

We are given the following in the question:

The exponential growth model is given by:

$A(t) = A_0e^{kt}$

where k is the growth rate, t is time in years and $A_0$ is constant.

The world population is 5.9 billion in 2006.

Thus, t = 0 for 2006

$A_0 = 5.9\text{ billions}$

We have to find the maximum acceptable annual rate of growth such that the population must stay below 24 billion during the next 100 years.

Putting these values in the growth model, we have,

$24 = 5.9e^{100k}\\\\k = \dfrac{1}{100}\ln \bigg(\dfrac{24}{5.9}\bigg)\\\\k = 0.01403\\k = 0.01403\times 100\% = 1.4\%$

1.4% is the maximum acceptable annual rate of growth such that the population must stay below 24 billion during the next 100 years.

8 0

3 years ago

How many people were in the sample?<br><br><br><br> 45<br> 90<br> 5<br> 10

Nina [5.8K]

10

The x’s represent just the people, and because the bottom line only represents time it doesn’t affect the amount of people.

4 0

3 years ago

Read 2 more answers

If an ecosystem can only hold about 12-15 animals what is this called?

V125BC [204]

It is called Ecological Succesion hope that helped:)

5 0

3 years ago

Verify that a+b=b+a by taking a=6 and b=3/6

Klio2033 [76]

Answer:

13

Step-by-step explanation:

substitute all the numbers in

6+3/6+3/6+6=13

4 0

3 years ago