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3 years ago

Prove that sec^2θcosec*2θ-2-cot^2θ=tan2θ

Mathematics

1 answer:

Tema [17]3 years ago

5 0

Answer:

Step-by-step explanation:

I think you mean tan^2θ, not tan2θ.

Use the trigonometric identities

secθ = 1/cosθ

cscθ = 1/sinθ

tanθ = sinθ/cosθ

sin²θ = 1-cos²θ

cos²θ = 1-sin²θ

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You walk through a used car lot and list the price and model year of each car you see determine whether the two variables are re

Blizzard [7]

Answer:

The narrative in the question can not be described as a function

Step-by-step explanation:

For the purpose of clarity, we will rephrase the question. The key point in the question is to determine if the price and the model are related and if they fit into independent and dependent function.

Moving forward, to properly answer this question, it will be good for us to understand what dependent and independent functions are.

DEPENDENT FUNCTIONS: These are functions or can also be refereed to as variable that represents quantities or values whose parameter depends on how the independent variable is manipulated.

Example:

You are doing job to earn your a salary. For each project you do, you earn $10 dollar. In this case, the dependent variable is the amount of money you earn because the amount of money you earn depends on how many job or project you do.

INDEPENDENT FUNCTIONS: These are functions or can also be refereed to as variable that we have control over in the process of an event therefore, we are at liberty to manipulate it as we so wish as indicated in the dependent variable.

Going back to the narrative of the question, the narrative in the question can not be described as a function because the two identifies variables which are the price and the model years are been altered due to the fact that it is a used car lot so they have both lost their true value or worth. However, some might argue that price here is the independent function or variable while model year is the dependent variable.

5 0

3 years ago

A researcher examines 27 water samples for iron concentration. The mean iron concentration for the sample data is 0.802 cc/cubic

Delvig [45]

Answer:

90% confidence interval for the population mean iron concentration is [0.771 , 0.832].

Step-by-step explanation:

We are given that a researcher examines 27 water samples for iron concentration. The mean iron concentration for the sample data is 0.802 cc/cubic meter with a standard deviation of 0.093.

Firstly, the pivotal quantity for 90% confidence interval for the population mean iron concentration is given by;

P.Q. = $\frac{\bar X - \mu}{\frac{s}{\sqrt{n} } }$ ~ $t_n_-_1$

where, $\bar X$ = sample mean iron concentration = 0.802 cc/cubic meter

s = sample standard deviation = 0.093

n = number of water samples = 27

$\mu$ = population mean

<em>Here for constructing 90% confidence interval we have used t statistics because we don't know about population standard deviation.</em>

So, 90% confidence interval for the population mean, $\mu$ is ;

P(-1.706 < $t_2_6$ < 1.706) = 0.90 {As the critical value of t at 26 degree of

freedom are -1.706 & 1.706 with P = 5%}

P(-1.706 < $\frac{\bar X - \mu}{\frac{s}{\sqrt{n} } }$ < 1.706) = 0.90

P( $-1.706 \times {\frac{s}{\sqrt{n} } }$ < ${\bar X - \mu}$ < $1.706 \times {\frac{s}{\sqrt{n} } }$ ) = 0.90

P( $\bar X -1.706 \times {\frac{s}{\sqrt{n} }$ < $\mu$ < $\bar X +1.706 \times {\frac{s}{\sqrt{n} }$ ) = 0.90

<u>90% confidence interval for</u> $\mu$ = [ $\bar X -1.706 \times {\frac{s}{\sqrt{n} }$ , $\bar X +1.706 \times {\frac{s}{\sqrt{n} }$ ]

= [ $0.802 -1.706 \times {\frac{0.093}{\sqrt{27} }$ , $0.802 +1.706 \times {\frac{0.093}{\sqrt{27} }$ ]

= [0.771 , 0.832]

Therefore, 90% confidence interval for the population mean iron concentration is [0.771 , 0.832].

4 0

3 years ago

Kim read 4/5 of her book and Grace read 6/10 of her book. who read more of her book, kim or Grace?

love history [14]

Kim did. Make the fractions into decimals(4 divided by 5, 6 divided by 10) Kim got 0.8, while Grace got 0.6.

3 0

3 years ago

Please help me with this

Cerrena [4.2K]

Answer:

Yes;Each side of triangle PQR is the same length as the corresponding side of triangle STU

Step-by-step explanation:

You can observe the sides of both triangles to see if this property holds

Lets check the length of AB

A(0,3) and B(0,-1)

$AB=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \\\\\\\\AB=\sqrt{(0-0)^2+(-1-3)^2} \\\\\\\\AB=\sqrt{0^2+-4^2} \\\\\\AB=\sqrt{16} =4units$

Now check the length of the corresponding side DE

D(1,2) and E(1,-2)

$DE=\sqrt{(1-1)^2+(-2-2)^2} \\\\\\DE=\sqrt{0^2+-4^2} \\\\\\DE=\sqrt{16} =4units$

The side AB has the same length as side DE.This is also true for the remaining corresponding sides.

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3 years ago

How do the physical and chemical properties of the elements change?

My name is Ann [436]

Answer

Step-by-step explanation: within a group

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3 years ago

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